Nothing
R/signatures.discovery.lasso.R
In SparseSignatures: SparseSignatures
#' Perform the assessment of different nmfLasso solutions by cross validation for K (unknown) somatic mutational signatures given a set of observations x. The estimation can slow down because of
#' memory usage and intensive computations, when a big number of cross validation repetitions is asked and when the grid search is performed for a lot of configurations. In this case,
#' an advice may be to split the computation into multiple smaller sets.
#'
#' @examples
#' data(background)
#' data(patients)
#' res = nmfLassoCV(x=patients[1:100,],
#' K=3:5,
#' background_signature=background,
#' nmf_runs=1,
#' lambda_values_alpha=c(0.00),
#' lambda_values_beta=c(0.00),
#' cross_validation_repetitions=2,
#' num_processes=NA,
#' seed=12345)
#'
#' @title nmfLassoCV
#' @param x count matrix for a set of n patients and 96 trinucleotides.
#' @param K a range of numeric value (each of them greater than 1) indicating the number of signatures to be discovered.
#' @param starting_beta a list of starting beta value for each configuration of K. If it is NULL, starting betas are estimated by
#' NMF.
#' @param background_signature background signature to be used. If not provided, a warning is thrown and an initial value for it is
#' estimated by NMF. If beta is not NULL, this parameter is ignored.
#' @param normalize_counts if true, the input count matrix x is normalize such that the patients have the same number of mutation.
#' @param nmf_runs number of iteration (minimum 1) of NMF to be performed for a robust estimation of starting beta. If beta is not NULL,
#' this parameter is ignored.
#' @param lambda_values_alpha value of LASSO to be used for alpha between 0 and 1. This value should be greater than 0. 1 is the value of LASSO
#' that would shrink all the signatures to 0 within one step. The higher lambda_rate_alpha is, the sparser are the resulting exposures,
#' but too large values may result in a reduced fit of the observed counts.
#' @param lambda_values_beta value of LASSO to be used for beta between 0 and 1. This value should be greater than 0. 1 is the value of LASSO
#' that would shrink all the signatures to 0 within one step. The higher lambda_rate_beta is, the sparser are the resulting exposures,
#' but too large values may result in a reduced fit of the observed counts.
#' @param cross_validation_entries Percentage of cells in the count matrix to be replaced by 0s during cross validation.
#' @param cross_validation_iterations For each configuration, the first time the signatures are discovered form a matrix with a
#' percentage of values replaced by 0s. This may result in poor fit/results. Then, we perform predictions of these entries and replace them with
#' such predicted values. This parameter is the number of restarts to be performed to improve this estimate and obtain more stable solutions.
#' @param cross_validation_repetitions Number of time cross-validation should be repeated. Higher values result in better estimate, but are computationally more expensive.
#' @param iterations Number of iterations to be performed. Each iteration corresponds to a first step where beta is fitted
#' and a second step where alpha is fitted.
#' @param max_iterations_lasso Number of maximum iterations to be performed during the sparsification via Lasso.
#' @param num_processes Number of processes to be used during parallel execution. To execute in single process mode,
#' this parameter needs to be set to either NA or NULL.
#' @param seed Seed for reproducibility.
#' @param verbose boolean; Shall I print all messages?
#' @param log_file log file where to print outputs when using parallel. If parallel execution is disabled, this parameter is ignored.
#' @return A list of 2 elements: grid_search_mse and and grid_search_loglik. Here, grid_search_mse reports the mean squared error for each configuration of performed
#' cross validation; grid_search_loglik reports for each configuration the number of times the algorithm converged.
#' @export nmfLassoCV
#' @import NMF
#' @import nnlasso
#' @import nnls
#' @import parallel
#'
"nmfLassoCV" <- function( x, K = 3:10, starting_beta = NULL, background_signature = NULL, normalize_counts = TRUE, nmf_runs = 10, lambda_values_alpha = c(0.00, 0.01, 0.05, 0.10), lambda_values_beta = c(0.00, 0.01, 0.05, 0.10), cross_validation_entries = 0.01, cross_validation_iterations = 5, cross_validation_repetitions = 50, iterations = 30, max_iterations_lasso = 10000, num_processes = Inf, seed = NULL, verbose = TRUE, log_file = "" ) {
# set the seed
set.seed(seed)
# check the input parameters
if(min(K)<2) {
if(verbose) {
cat("The minimum value of K is 2...","\n")
}
K <- K[K>=2]
if(length(K)==0) {
K <- 2
warning("No value of K greater than 2 is provided: setting K to 2...")
}
}
if(nmf_runs<1) {
if(verbose) {
cat("The minimum value of nmf_runs is 1...","\n")
}
nmf_runs <- 1
}
x <- as.matrix(x)
if(normalize_counts) {
x <- (x/rowSums(x))*2500
}
lambda_values_alpha <- sort(unique(lambda_values_alpha))
lambda_values_beta <- sort(unique(lambda_values_beta))
# perform a grid search to estimate the best values of K and lambda
if(verbose) {
cat("Performing a grid search to estimate the best values of K and lambda with a total of",cross_validation_repetitions,"cross validation repetitions...","\n")
}
# setting up parallel execution
parallel <- NULL
close_parallel <- FALSE
if(is.null(parallel)&&cross_validation_repetitions>1) {
if(is.na(num_processes) || is.null(num_processes)) {
parallel <- NULL
}
else if(num_processes==Inf) {
cores <- as.integer((detectCores()-1))
if(cores < 2) {
parallel <- NULL
}
else {
num_processes <- min(num_processes,cross_validation_repetitions)
parallel <- makeCluster(num_processes,outfile=log_file)
close_parallel <- TRUE
}
}
else {
num_processes <- min(num_processes,cross_validation_repetitions)
parallel <- makeCluster(num_processes,outfile=log_file)
close_parallel <- TRUE
}
if(verbose && !is.null(parallel)) {
cat("Executing",num_processes,"processes via parallel...","\n")
}
}
# estimate the background signature
if(is.null(background_signature)&&is.null(starting_beta)) {
warning("No background signature has been specified...")
background_signature_beta <- basis(nmf(t(x),rank=1,nrun=nmf_runs))
background_signature_beta <- t(background_signature_beta)
background_signature_beta <- background_signature_beta / rowSums(background_signature_beta)
background_signature <- as.numeric(background_signature_beta[1,])
}
# structure to save the starting values of beta for each K
if(is.null(starting_beta)) {
background_signature <- as.numeric(background_signature)
background_signature <- background_signature / sum(background_signature)
starting_beta <- array(list(),c(length(K),1))
rownames(starting_beta) <- paste0(as.character(K),"_Signatures")
colnames(starting_beta) <- "Value"
# estimate the contribution of the background to the observed counts
background_signature_beta <- t(background_signature)
background_signature_alpha <- matrix(0,nrow=dim(x)[1],ncol=1)
for(i in 1:dim(x)[1]) {
background_signature_alpha[i,] <- nnls(t(background_signature_beta),as.vector(x[i,]))$x
}
curr_x <- x - (background_signature_alpha %*% background_signature_beta)
curr_x[curr_x<0] <- 0
if(length(which(rowSums(t(curr_x))==0))>0) {
invalid_cols <- as.numeric(which(rowSums(t(curr_x))==0))
for(inv_cols in invalid_cols) {
curr_x[sample(1:length(curr_x[,inv_cols]),size=1),inv_cols] <- 1e-05
}
}
# compute starting values for beta
pos_k <- 0
for(k in K) {
# compute the initial values of beta
if(verbose) {
cat(paste0("Computing the initial values of beta by standard NMF for K equals to ",k,"..."),"\n")
}
pos_k <- pos_k + 1
beta <- NULL
beta <- basis(nmf(t(curr_x),rank=(k-1),nrun=nmf_runs))
beta <- t(beta)
beta <- rbind(background_signature,beta)
# normalize and save beta for the current value of K
rownames(beta) <- c("Background",paste0("S",1:(nrow(beta)-1)))
colnames(beta) <- colnames(x)
beta <- beta / rowSums(beta)
starting_beta[[pos_k,1]] <- beta
}
}
if(verbose) {
cat("Starting cross validation with a total of",cross_validation_repetitions,"repetitions...","\n")
}
# structure to save the results of the grid search
grid_search_mse <- array(list(),c(length(lambda_values_alpha),length(lambda_values_beta),length(K)),dimnames=list(paste0(as.character(lambda_values_alpha),"_Lambda_Alpha"),paste0(as.character(lambda_values_beta),"_Lambda_Beta"),paste0(as.character(K),"_Signatures")))
grid_search_loglik <- array(list(),c(length(lambda_values_alpha),length(lambda_values_beta),length(K)),dimnames=list(paste0(as.character(lambda_values_alpha),"_Lambda_Alpha"),paste0(as.character(lambda_values_beta),"_Lambda_Beta"),paste0(as.character(K),"_Signatures")))
# now starting cross validation
if(is.null(parallel)) {
# perform a total of cross_validation_repetitions repetitions of cross validation
set.seed(round(runif(1)*100000))
for(cv_repetitions in 1:cross_validation_repetitions) {
if(verbose) {
cat(paste0("Performing repetition ",cv_repetitions," out of ",cross_validation_repetitions,"..."),"\n")
}
# randomly set the cross validation entries for the current iteration
valid_entries <- which(x>0,arr.ind=TRUE)
cv_entries <- valid_entries[sample(1:nrow(valid_entries),size=round(nrow(valid_entries)*cross_validation_entries),replace=FALSE),]
# consider all the values for K
cont <- 0
pos_k <- 0
for(k in K) {
# consider the first k signatures to be used for the current configuration
pos_k <- pos_k + 1
# consider all the values for lambda
pos_l_alpha <- 0
for(l_alpha in lambda_values_alpha) {
pos_l_alpha <- pos_l_alpha + 1
pos_l_beta <- 0
for(l_beta in lambda_values_beta) {
pos_l_beta <- pos_l_beta + 1
# repeat the estimation for a number of cross_validation_iterations
x_cv <- NULL
cont <- cont + 1
for(cv_iteration in 1:cross_validation_iterations) {
if(verbose) {
cat(paste0("Performing cross validation iteration ",cv_iteration," out of ",cross_validation_iterations,"..."),"\n")
}
# set a percentage of cross_validation_entries entries to 0 in order to perform cross validation
if(cv_iteration==1) {
x_cv <- x
x_cv[cv_entries] <- 0
}
else {
if(!is.na(curr_iter_alpha[1])&&!is.na(curr_iter_beta[1])) {
predicted_counts <- curr_iter_alpha %*% curr_iter_beta
x_cv[cv_entries] <- predicted_counts[cv_entries]
}
}
# perform the inference
curr_results <- nmfLasso(x = x_cv,
K = k,
beta = starting_beta[[pos_k,1]],
background_signature = background_signature,
normalize_counts = normalize_counts,
nmf_runs = 10,
lambda_rate_alpha = l_alpha,
lambda_rate_beta = l_beta,
iterations = iterations,
max_iterations_lasso = max_iterations_lasso,
seed = round(runif(1)*100000),
verbose = FALSE)
curr_iter_alpha <- curr_results[["alpha"]]
curr_iter_beta <- curr_results[["beta"]]
curr_iter_loglik <- curr_results[["loglik_progression"]]
}
# save an estimate of mean squared error and stability of the solution
if(!is.na(curr_iter_alpha[1])&&!is.na(curr_iter_beta[1])) {
curr_predicted_counts <- round(curr_iter_alpha%*%curr_iter_beta)
curr_true_considered_counts <- as.vector(x[cv_entries])
curr_predicted_considered_counts <- as.vector(curr_predicted_counts[cv_entries])
error <- mean((curr_true_considered_counts-curr_predicted_considered_counts)^2)
grid_search_mse[pos_l_alpha,pos_l_beta,pos_k][[1]] <- c(grid_search_mse[pos_l_alpha,pos_l_beta,pos_k][[1]],error)
}
if((!is.na(curr_iter_loglik)[1])&&(curr_iter_loglik[1]<curr_iter_loglik[length(curr_iter_loglik)])) {
grid_search_loglik[pos_l_alpha,pos_l_beta,pos_k][[1]] <- c(grid_search_loglik[pos_l_alpha,pos_l_beta,pos_k][[1]],"increasing")
}
else if((!is.na(curr_iter_loglik)[1])&&(curr_iter_loglik[1]>=curr_iter_loglik[length(curr_iter_loglik)])) {
grid_search_loglik[pos_l_alpha,pos_l_beta,pos_k][[1]] <- c(grid_search_loglik[pos_l_alpha,pos_l_beta,pos_k][[1]],"decreasing")
}
if(verbose) {
cat("Progress",paste0(round((cont/(length(K)*length(lambda_values_alpha)*length(lambda_values_beta)))*100,digits=3),"%..."),"\n")
}
}
}
}
}
# save the results
results <- list(grid_search_mse=grid_search_mse,grid_search_loglik=grid_search_loglik)
}
else {
# perform the inference
res_clusterEvalQ <- clusterEvalQ(parallel,library("nnls"))
res_clusterEvalQ <- clusterEvalQ(parallel,library("nnlasso"))
clusterExport(parallel,varlist=c("x","K","starting_beta","background_signature","normalize_counts","cross_validation_entries"),envir=environment())
clusterExport(parallel,varlist=c("lambda_values_alpha","lambda_values_beta","cross_validation_iterations","iterations","max_iterations_lasso"),envir=environment())
clusterExport(parallel,varlist=c("grid_search_mse","grid_search_loglik","cross_validation_repetitions","verbose"),envir=environment())
clusterExport(parallel,c('nmfLasso','nmfLassoDecomposition','basis','nmf'),envir=environment())
clusterSetRNGStream(parallel,iseed=round(runif(1)*100000))
curr_results <- parLapply(parallel,1:cross_validation_repetitions,function(cv_rep) {
if(verbose) {
cat(paste0("Performing repetition ",cv_rep," out of ",cross_validation_repetitions,"..."),"\n")
}
# randomly set the cross validation entries for the current iteration
valid_entries <- which(x>0,arr.ind=TRUE)
cv_entries <- valid_entries[sample(1:nrow(valid_entries),size=round(nrow(valid_entries)*cross_validation_entries),replace=FALSE),]
# consider all the values for K
cont <- 0
pos_k <- 0
for(k in K) {
# consider the first k signatures to be used for the current configuration
pos_k <- pos_k + 1
# consider all the values for lambda
pos_l_alpha <- 0
for(l_alpha in lambda_values_alpha) {
pos_l_alpha <- pos_l_alpha + 1
pos_l_beta <- 0
for(l_beta in lambda_values_beta) {
pos_l_beta <- pos_l_beta + 1
# repeat the estimation for a number of cross_validation_iterations
x_cv <- NULL
cont <- cont + 1
for(cv_iteration in 1:cross_validation_iterations) {
# set a percentage of cross_validation_entries entries to 0 in order to perform cross validation
if(cv_iteration==1) {
x_cv <- x
x_cv[cv_entries] <- 0
}
else {
if(!is.na(curr_iter_alpha[1])&&!is.na(curr_iter_beta[1])) {
predicted_counts <- curr_iter_alpha %*% curr_iter_beta
x_cv[cv_entries] <- predicted_counts[cv_entries]
}
}
# perform the inference
curr_results <- nmfLasso(x = x_cv,
K = k,
beta = starting_beta[[pos_k,1]],
background_signature = background_signature,
normalize_counts = normalize_counts,
nmf_runs = 10,
lambda_rate_alpha = l_alpha,
lambda_rate_beta = l_beta,
iterations = iterations,
max_iterations_lasso = max_iterations_lasso,
seed = round(runif(1)*100000),
verbose = FALSE)
curr_iter_alpha <- curr_results[["alpha"]]
curr_iter_beta <- curr_results[["beta"]]
curr_iter_loglik <- curr_results[["loglik_progression"]]
}
# save an estimate of mean squared error and stability of the solution
if(!is.na(curr_iter_alpha[1])&&!is.na(curr_iter_beta[1])) {
curr_predicted_counts <- round(curr_iter_alpha%*%curr_iter_beta)
curr_true_considered_counts <- as.vector(x[cv_entries])
curr_predicted_considered_counts <- as.vector(curr_predicted_counts[cv_entries])
error <- mean((curr_true_considered_counts-curr_predicted_considered_counts)^2)
grid_search_mse[pos_l_alpha,pos_l_beta,pos_k][[1]] <- c(grid_search_mse[pos_l_alpha,pos_l_beta,pos_k][[1]],error)
}
if((!is.na(curr_iter_loglik)[1])&&(curr_iter_loglik[1]<curr_iter_loglik[length(curr_iter_loglik)])) {
grid_search_loglik[pos_l_alpha,pos_l_beta,pos_k][[1]] <- c(grid_search_loglik[pos_l_alpha,pos_l_beta,pos_k][[1]],"increasing")
}
else if((!is.na(curr_iter_loglik)[1])&&(curr_iter_loglik[1]>=curr_iter_loglik[length(curr_iter_loglik)])) {
grid_search_loglik[pos_l_alpha,pos_l_beta,pos_k][[1]] <- c(grid_search_loglik[pos_l_alpha,pos_l_beta,pos_k][[1]],"decreasing")
}
}
}
}
# save the results
curr_results <- list(grid_search_mse=grid_search_mse,grid_search_loglik=grid_search_loglik)
return(curr_results)
})
# save the results
results <- list(grid_search_mse=grid_search_mse,grid_search_loglik=grid_search_loglik)
for(par_res in 1:length(curr_results)) {
curr_par_res <- curr_results[[par_res]]
curr_par_res_grid_search_mse <- curr_par_res$grid_search_mse
curr_par_res_grid_search_loglik <- curr_par_res$grid_search_loglik
for(a in 1:dim(curr_par_res_grid_search_mse)[1]) {
for(b in 1:dim(curr_par_res_grid_search_mse)[2]) {
for(c in 1:dim(curr_par_res_grid_search_mse)[3]) {
if(!is.null(unlist(curr_par_res_grid_search_mse[a,b,c]))) {
results$grid_search_mse[[a,b,c]] <- c(unlist(results$grid_search_mse[a,b,c]),unlist(curr_par_res_grid_search_mse[a,b,c]))
results$grid_search_loglik[[a,b,c]] <- c(unlist(results$grid_search_loglik[a,b,c]),unlist(curr_par_res_grid_search_loglik[a,b,c]))
}
}
}
}
}
}
# close parallel
if(close_parallel) {
stopCluster(parallel)
}
return(results)
}
#' Perform the evaluation of different nmfLasso solutions by bootstrap for K (unknown) somatic mutational signatures given a set of observations x. The estimation can slow down because of
#' memory usage and intensive computations, when a big number of bootstrap repetitions is asked and when the analysis is performed for a big range of signatures (K). In this case,
#' an advice may be to split the computation into multiple smaller sets.
#'
#' @examples
#' data(background)
#' data(patients)
#' res = nmfLassoBootstrap(x=patients[1:100,],
#' K=3:5,
#' background_signature=background,
#' nmf_runs=1,
#' bootstrap_repetitions=2,
#' num_processes=NA,
#' seed=12345)
#'
#' @title nmfLassoBootstrap
#' @param x count matrix for a set of n patients and 96 trinucleotides.
#' @param K a range of numeric value (each of them greater than 1) indicating the number of signatures to be discovered.
#' @param starting_beta a list of starting beta value for each configuration of K. If it is NULL, starting betas are estimated by
#' NMF.
#' @param background_signature background signature to be used. If not provided, a warning is thrown and an initial value for it is
#' estimated by NMF. If beta is not NULL, this parameter is ignored.
#' @param normalize_counts if true, the input count matrix x is normalize such that the patients have the same number of mutation.
#' @param nmf_runs number of iteration (minimum 1) of NMF to be performed for a robust estimation of starting beta. If beta is not NULL,
#' this parameter is ignored.
#' @param bootstrap_repetitions Number of time bootstrap should be repeated. Higher values result in better estimate, but are computationally more expensive.
#' @param iterations Number of iterations to be performed. Each iteration corresponds to a first step where beta is fitted
#' and a second step where alpha is fitted.
#' @param max_iterations_lasso Number of maximum iterations to be performed during the sparsification via Lasso.
#' @param num_processes Number of processes to be used during parallel execution. To execute in single process mode,
#' this parameter needs to be set to either NA or NULL.
#' @param seed Seed for reproducibility.
#' @param verbose boolean; Shall I print all messages?
#' @param log_file log file where to print outputs when using parallel. If parallel execution is disabled, this parameter is ignored.
#' @return A list of 3 elements: stability, RSS and evar. Here, stability reports the estimared cosine similarity for alpha and beta at each bootstrap
#' repetition; RSS reports for each configuration the estimated residual sum of squares; finally, evar reports the explained variance.
#' @export nmfLassoBootstrap
#' @import NMF
#' @import nnlasso
#' @import nnls
#' @import parallel
#'
"nmfLassoBootstrap" <- function( x, K = 3:10, starting_beta = NULL, background_signature = NULL, normalize_counts = TRUE, nmf_runs = 10, bootstrap_repetitions = 50, iterations = 30, max_iterations_lasso = 10000, num_processes = Inf, seed = NULL, verbose = TRUE, log_file = "" ) {
# set the seed
set.seed(seed)
# check the input parameters
if(min(K)<2) {
if(verbose) {
cat("The minimum value of K is 2...","\n")
}
K <- K[K>=2]
if(length(K)==0) {
K <- 2
warning("No value of K greater than 2 is provided: setting K to 2...")
}
}
if(nmf_runs<1) {
if(verbose) {
cat("The minimum value of nmf_runs is 1...","\n")
}
nmf_runs <- 1
}
x <- as.matrix(x)
if(normalize_counts) {
x <- (x/rowSums(x))*2500
}
# no Lasso is considered here to speed up computations, i.e., this is an heuristic/approximated result
lambda_values_alpha <- 0.00
lambda_values_beta <- 0.00
# perform a grid search to estimate the best values of K and lambda
if(verbose) {
cat("Performing a total of",bootstrap_repetitions,"bootstrap repetitions to assess nmfLasso solutions for different K ranks...","\n")
}
# setting up parallel execution
parallel <- NULL
close_parallel <- FALSE
if(is.null(parallel)&&bootstrap_repetitions>1) {
if(is.na(num_processes) || is.null(num_processes)) {
parallel <- NULL
}
else if(num_processes==Inf) {
cores <- as.integer((detectCores()-1))
if(cores < 2) {
parallel <- NULL
}
else {
num_processes <- min(num_processes,bootstrap_repetitions)
parallel <- makeCluster(num_processes,outfile=log_file)
close_parallel <- TRUE
}
}
else {
num_processes <- min(num_processes,bootstrap_repetitions)
parallel <- makeCluster(num_processes,outfile=log_file)
close_parallel <- TRUE
}
if(verbose && !is.null(parallel)) {
cat("Executing",num_processes,"processes via parallel...","\n")
}
}
# estimate the background signature
if(is.null(background_signature)&&is.null(starting_beta)) {
warning("No background signature has been specified...")
background_signature_beta <- basis(nmf(t(x),rank=1,nrun=nmf_runs))
background_signature_beta <- t(background_signature_beta)
background_signature_beta <- background_signature_beta / rowSums(background_signature_beta)
background_signature <- as.numeric(background_signature_beta[1,])
}
# structure to save the starting values of beta for each K
if(is.null(starting_beta)) {
background_signature <- as.numeric(background_signature)
background_signature <- background_signature / sum(background_signature)
starting_beta <- array(list(),c(length(K),1))
rownames(starting_beta) <- paste0(as.character(K),"_Signatures")
colnames(starting_beta) <- "Value"
# estimate the contribution of the background to the observed counts
background_signature_beta <- t(background_signature)
background_signature_alpha <- matrix(0,nrow=dim(x)[1],ncol=1)
for(i in 1:dim(x)[1]) {
background_signature_alpha[i,] <- nnls(t(background_signature_beta),as.vector(x[i,]))$x
}
curr_x <- x - (background_signature_alpha %*% background_signature_beta)
curr_x[curr_x<0] <- 0
if(length(which(rowSums(t(curr_x))==0))>0) {
invalid_cols <- as.numeric(which(rowSums(t(curr_x))==0))
for(inv_cols in invalid_cols) {
curr_x[sample(1:length(curr_x[,inv_cols]),size=1),inv_cols] <- 1e-05
}
}
# compute starting values for beta
pos_k <- 0
for(k in K) {
# compute the initial values of beta
if(verbose) {
cat(paste0("Computing the initial values of beta by standard NMF for K equals to ",k,"..."),"\n")
}
pos_k <- pos_k + 1
beta <- NULL
beta <- basis(nmf(t(curr_x),rank=(k-1),nrun=nmf_runs))
beta <- t(beta)
beta <- rbind(background_signature,beta)
# normalize and save beta for the current value of K
rownames(beta) <- c("Background",paste0("S",1:(nrow(beta)-1)))
colnames(beta) <- colnames(x)
beta <- beta / rowSums(beta)
starting_beta[[pos_k,1]] <- beta
}
}
if(verbose) {
cat("Starting bootstrap for a total of",bootstrap_repetitions,"repetitions...","\n")
}
# structure to save the results of the grid search
bootstrap_rss <- array(list(),c(length(K),2))
rownames(bootstrap_rss) <- paste0(as.character(K),"_Signatures")
colnames(bootstrap_rss) <- c("RSS bootstrapped data","RSS randomized data")
bootstrap_evar <- bootstrap_rss
colnames(bootstrap_evar) <- c("Explained Variance bootstrapped data","Explained Variance randomized data")
bootstrap_stability <- array(list(),c(length(K),4))
rownames(bootstrap_stability) <- paste0(as.character(K),"_Signatures")
colnames(bootstrap_stability) <- c("Similarity alpha bootstrapped data","Similarity beta bootstrapped data","Similarity alpha randomized data","Similarity beta randomized data")
starting_values_bootstrap = bootstrap_stability
# generate a set of randomized data from x
set.seed(round(runif(1)*100000))
randomized_x <- x
for(i in 1:ncol(randomized_x)) {
randomized_x[,i] <- randomized_x[sample(1:dim(randomized_x)[1],size=dim(randomized_x)[1],replace=FALSE),i]
}
for(j in 1:nrow(randomized_x)) {
randomized_x[j,] <- randomized_x[j,sample(1:dim(randomized_x)[2],size=dim(randomized_x)[2],replace=FALSE)]
}
# compute starting values of alpha and beta in order to estimate stability of the considered solutions (and ranks)
pos_k <- 0
for(k in K) {
pos_k <- pos_k + 1
is.valid <- FALSE
while(!is.valid) {
curr_results <- nmfLasso(x = x,
K = k,
beta = starting_beta[[pos_k,1]],
background_signature = background_signature,
normalize_counts = normalize_counts,
nmf_runs = 10,
lambda_rate_alpha = lambda_values_alpha,
lambda_rate_beta = lambda_values_beta,
iterations = iterations,
max_iterations_lasso = max_iterations_lasso,
seed = round(runif(1)*100000),
verbose = FALSE)
if(!is.na(curr_results$best_loglik)) {
is.valid <- TRUE
}
}
starting_values_bootstrap[[pos_k,1]] <- curr_results$alpha
starting_values_bootstrap[[pos_k,2]] <- curr_results$beta
is.valid <- FALSE
while(!is.valid) {
curr_results <- nmfLasso(x = randomized_x,
K = k,
beta = starting_beta[[pos_k,1]],
background_signature = background_signature,
normalize_counts = normalize_counts,
nmf_runs = 10,
lambda_rate_alpha = lambda_values_alpha,
lambda_rate_beta = lambda_values_beta,
iterations = iterations,
max_iterations_lasso = max_iterations_lasso,
seed = round(runif(1)*100000),
verbose = FALSE)
if(!is.na(curr_results$best_loglik)) {
is.valid <- TRUE
}
}
starting_values_bootstrap[[pos_k,3]] <- curr_results$alpha
starting_values_bootstrap[[pos_k,4]] <- curr_results$beta
}
# now starting cross validation
if(is.null(parallel)) {
# perform a total of bootstrap_repetitions repetitions of bootstrap
for(nboot in 1:bootstrap_repetitions) {
if(verbose) {
cat(paste0("Performing repetition ",nboot," out of ",bootstrap_repetitions,"..."),"\n")
}
# generate bootstrapped dataset from data
bootstrapped_data <- x
for(i in 1:nrow(x)) {
num_mutations <- sum(x[i,])
mut_distribution <- as.numeric(x[i,]/sum(x[i,]))
sampling <- sample(1:96,size=num_mutations,replace=TRUE,prob=mut_distribution)
bootstrapped_data[i,] <- 0
for(j in sampling) {
bootstrapped_data[i,j] <- bootstrapped_data[i,j] + 1
}
}
# generate randomized data from the bootstrapped data
randomized_data <- bootstrapped_data
for(i in 1:ncol(randomized_data)) {
randomized_data[,i] <- randomized_data[sample(1:dim(randomized_data)[1],size=dim(randomized_data)[1],replace=FALSE),i]
}
for(j in 1:nrow(randomized_data)) {
randomized_data[j,] <- randomized_data[j,sample(1:dim(randomized_data)[2],size=dim(randomized_data)[2],replace=FALSE)]
}
# perform inference on bootstrapped and randomized data
pos_k <- 0
for(k in K) {
pos_k <- pos_k + 1
# perform the analysis for bootstrapped data
res <- nmfLasso(x=bootstrapped_data,K=k,beta=starting_beta[[pos_k,1]],lambda_rate_alpha=lambda_values_alpha,lambda_rate_beta=lambda_values_beta,verbose=FALSE)
if(!is.na(res$best_loglik)) {
# compute cosine similarity of alpha for bootstrapped data
similarity <- NULL
for(i in 1:ncol(res$alpha)) {
curr_similarity <- ((sum(starting_values_bootstrap[[pos_k,1]][,i]*res$alpha[,i]))/sqrt(sum(starting_values_bootstrap[[pos_k,1]][,i]^2)*sum(res$alpha[,i]^2)))
similarity <- c(similarity,curr_similarity)
}
bootstrap_stability[[pos_k,"Similarity alpha bootstrapped data"]] <- c(unlist(bootstrap_stability[[pos_k,"Similarity alpha bootstrapped data"]]),mean(similarity))
# compute cosine similarity of beta for bootstrapped data
similarity <- NULL
for(i in 1:nrow(res$beta)) {
curr_similarity <- ((sum(starting_values_bootstrap[[pos_k,2]][i,]*res$beta[i,]))/sqrt(sum(starting_values_bootstrap[[pos_k,2]][i,]^2)*sum(res$beta[i,]^2)))
similarity <- c(similarity,curr_similarity)
}
bootstrap_stability[[pos_k,"Similarity beta bootstrapped data"]] <- c(unlist(bootstrap_stability[[pos_k,"Similarity beta bootstrapped data"]]),mean(similarity))
# compute RSS for bootstrapped data
predictions <- res$alpha%*%res$beta
mse <- NULL
for(i in 1:nrow(predictions)) {
for(j in 1:ncol(predictions)) {
mse <- c(mse,((bootstrapped_data[i,j]-predictions[i,j])^2))
}
}
mse <- sum(mse)
bootstrap_rss[[pos_k,"RSS bootstrapped data"]] <- c(unlist(bootstrap_rss[[pos_k,"RSS bootstrapped data"]]),mse)
# compute Explained Variance for bootstrapped data
evar <- (1 - (mse/sum(bootstrapped_data^2)))
bootstrap_evar[[pos_k,"Explained Variance bootstrapped data"]] <- c(unlist(bootstrap_evar[[pos_k,"Explained Variance bootstrapped data"]]),evar)
}
else {
bootstrap_stability[[pos_k,"Similarity alpha bootstrapped data"]] <- c(unlist(bootstrap_stability[[pos_k,"Similarity alpha bootstrapped data"]]),NA)
bootstrap_stability[[pos_k,"Similarity beta bootstrapped data"]] <- c(unlist(bootstrap_stability[[pos_k,"Similarity beta bootstrapped data"]]),NA)
bootstrap_rss[[pos_k,"RSS bootstrapped data"]] <- c(unlist(bootstrap_rss[[pos_k,"RSS bootstrapped data"]]),NA)
bootstrap_evar[[pos_k,"Explained Variance bootstrapped data"]] <- c(unlist(bootstrap_evar[[pos_k,"Explained Variance bootstrapped data"]]),NA)
}
# perform the analysis for randomized data
res <- nmfLasso(x=randomized_data,K=k,beta=starting_beta[[pos_k,1]],lambda_rate_alpha=lambda_values_alpha,lambda_rate_beta=lambda_values_beta,verbose=FALSE)
if(!is.na(res$best_loglik)) {
# compute cosine similarity of alpha for randomized data
similarity <- NULL
for(i in 1:ncol(res$alpha)) {
curr_similarity <- ((sum(starting_values_bootstrap[[pos_k,3]][,i]*res$alpha[,i]))/sqrt(sum(starting_values_bootstrap[[pos_k,3]][,i]^2)*sum(res$alpha[,i]^2)))
similarity <- c(similarity,curr_similarity)
}
bootstrap_stability[[pos_k,"Similarity alpha randomized data"]] <- c(unlist(bootstrap_stability[[pos_k,"Similarity alpha randomized data"]]),mean(similarity))
# compute cosine similarity of beta for randomized data
similarity <- NULL
for(i in 1:nrow(res$beta)) {
curr_similarity <- ((sum(starting_values_bootstrap[[pos_k,4]][i,]*res$beta[i,]))/sqrt(sum(starting_values_bootstrap[[pos_k,4]][i,]^2)*sum(res$beta[i,]^2)))
similarity <- c(similarity,curr_similarity)
}
bootstrap_stability[[pos_k,"Similarity beta randomized data"]] <- c(unlist(bootstrap_stability[[pos_k,"Similarity beta randomized data"]]),mean(similarity))
# compute RSS for randomized data
predictions <- res$alpha%*%res$beta
mse <- NULL
for(i in 1:nrow(predictions)) {
for(j in 1:ncol(predictions)) {
mse <- c(mse,((randomized_data[i,j]-predictions[i,j])^2))
}
}
mse <- sum(mse)
bootstrap_rss[[pos_k,"RSS randomized data"]] <- c(unlist(bootstrap_rss[[pos_k,"RSS randomized data"]]),mse)
# compute Explained Variance for randomized data
evar <- (1 - (mse/sum(randomized_data^2)))
bootstrap_evar[[pos_k,"Explained Variance randomized data"]] <- c(unlist(bootstrap_evar[[pos_k,"Explained Variance randomized data"]]),evar)
}
else {
bootstrap_stability[[pos_k,"Similarity alpha randomized data"]] <- c(unlist(bootstrap_stability[[pos_k,"Similarity alpha randomized data"]]),NA)
bootstrap_stability[[pos_k,"Similarity beta randomized data"]] <- c(unlist(bootstrap_stability[[pos_k,"Similarity beta randomized data"]]),NA)
bootstrap_rss[[pos_k,"RSS randomized data"]] <- c(unlist(bootstrap_rss[[pos_k,"RSS randomized data"]]),NA)
bootstrap_evar[[pos_k,"Explained Variance randomized data"]] <- c(unlist(bootstrap_evar[[pos_k,"Explained Variance randomized data"]]),NA)
}
}
if(verbose) {
cat("Progress",paste0(round((nboot/bootstrap_repetitions)*100,digits=3),"%..."),"\n")
}
}
# save the results
results <- list(stability=bootstrap_stability,RSS=bootstrap_rss,evar=bootstrap_evar)
}
else {
# perform the inference
res_clusterEvalQ <- clusterEvalQ(parallel,library("nnls"))
res_clusterEvalQ <- clusterEvalQ(parallel,library("nnlasso"))
clusterExport(parallel,varlist=c("x","K","starting_beta","background_signature","normalize_counts"),envir=environment())
clusterExport(parallel,varlist=c("lambda_values_alpha","lambda_values_beta","iterations","max_iterations_lasso"),envir=environment())
clusterExport(parallel,varlist=c("bootstrap_stability","bootstrap_rss","bootstrap_evar","bootstrap_repetitions","verbose"),envir=environment())
clusterExport(parallel,c('nmfLasso','nmfLassoDecomposition','basis','nmf'),envir=environment())
clusterSetRNGStream(parallel,iseed=round(runif(1)*100000))
curr_results <- parLapply(parallel,1:bootstrap_repetitions,function(nboot) {
if(verbose) {
cat(paste0("Performing repetition ",nboot," out of ",bootstrap_repetitions,"..."),"\n")
}
# generate bootstrapped dataset from data
bootstrapped_data <- x
for(i in 1:nrow(x)) {
num_mutations <- sum(x[i,])
mut_distribution <- as.numeric(x[i,]/sum(x[i,]))
sampling <- sample(1:96,size=num_mutations,replace=TRUE,prob=mut_distribution)
bootstrapped_data[i,] <- 0
for(j in sampling) {
bootstrapped_data[i,j] <- bootstrapped_data[i,j] + 1
}
}
# generate randomized data from the bootstrapped data
randomized_data <- bootstrapped_data
for(i in 1:ncol(randomized_data)) {
randomized_data[,i] <- randomized_data[sample(1:dim(randomized_data)[1],size=dim(randomized_data)[1],replace=FALSE),i]
}
for(j in 1:nrow(randomized_data)) {
randomized_data[j,] <- randomized_data[j,sample(1:dim(randomized_data)[2],size=dim(randomized_data)[2],replace=FALSE)]
}
# perform inference on bootstrapped and randomized data
pos_k <- 0
for(k in K) {
pos_k <- pos_k + 1
# perform the analysis for bootstrapped data
res <- nmfLasso(x=bootstrapped_data,K=k,beta=starting_beta[[pos_k,1]],lambda_rate_alpha=lambda_values_alpha,lambda_rate_beta=lambda_values_beta,verbose=FALSE)
if(!is.na(res$best_loglik)) {
# compute cosine similarity of alpha for bootstrapped data
similarity <- NULL
for(i in 1:ncol(res$alpha)) {
curr_similarity <- ((sum(starting_values_bootstrap[[pos_k,1]][,i]*res$alpha[,i]))/sqrt(sum(starting_values_bootstrap[[pos_k,1]][,i]^2)*sum(res$alpha[,i]^2)))
similarity <- c(similarity,curr_similarity)
}
bootstrap_stability[[pos_k,"Similarity alpha bootstrapped data"]] <- c(unlist(bootstrap_stability[[pos_k,"Similarity alpha bootstrapped data"]]),mean(similarity))
# compute cosine similarity of beta for bootstrapped data
similarity <- NULL
for(i in 1:nrow(res$beta)) {
curr_similarity <- ((sum(starting_values_bootstrap[[pos_k,2]][i,]*res$beta[i,]))/sqrt(sum(starting_values_bootstrap[[pos_k,2]][i,]^2)*sum(res$beta[i,]^2)))
similarity <- c(similarity,curr_similarity)
}
bootstrap_stability[[pos_k,"Similarity beta bootstrapped data"]] <- c(unlist(bootstrap_stability[[pos_k,"Similarity beta bootstrapped data"]]),mean(similarity))
# compute RSS for bootstrapped data
predictions <- res$alpha%*%res$beta
mse <- NULL
for(i in 1:nrow(predictions)) {
for(j in 1:ncol(predictions)) {
mse <- c(mse,((bootstrapped_data[i,j]-predictions[i,j])^2))
}
}
mse <- sum(mse)
bootstrap_rss[[pos_k,"RSS bootstrapped data"]] <- c(unlist(bootstrap_rss[[pos_k,"RSS bootstrapped data"]]),mse)
# compute Explained Variance for bootstrapped data
evar <- (1 - (mse/sum(bootstrapped_data^2)))
bootstrap_evar[[pos_k,"Explained Variance bootstrapped data"]] <- c(unlist(bootstrap_evar[[pos_k,"Explained Variance bootstrapped data"]]),evar)
}
else {
bootstrap_stability[[pos_k,"Similarity alpha bootstrapped data"]] <- c(unlist(bootstrap_stability[[pos_k,"Similarity alpha bootstrapped data"]]),NA)
bootstrap_stability[[pos_k,"Similarity beta bootstrapped data"]] <- c(unlist(bootstrap_stability[[pos_k,"Similarity beta bootstrapped data"]]),NA)
bootstrap_rss[[pos_k,"RSS bootstrapped data"]] <- c(unlist(bootstrap_rss[[pos_k,"RSS bootstrapped data"]]),NA)
bootstrap_evar[[pos_k,"Explained Variance bootstrapped data"]] <- c(unlist(bootstrap_evar[[pos_k,"Explained Variance bootstrapped data"]]),NA)
}
# perform the analysis for randomized data
res <- nmfLasso(x=randomized_data,K=k,beta=starting_beta[[pos_k,1]],lambda_rate_alpha=lambda_values_alpha,lambda_rate_beta=lambda_values_beta,verbose=FALSE)
if(!is.na(res$best_loglik)) {
# compute cosine similarity of alpha for randomized data
similarity <- NULL
for(i in 1:ncol(res$alpha)) {
curr_similarity <- ((sum(starting_values_bootstrap[[pos_k,3]][,i]*res$alpha[,i]))/sqrt(sum(starting_values_bootstrap[[pos_k,3]][,i]^2)*sum(res$alpha[,i]^2)))
similarity <- c(similarity,curr_similarity)
}
bootstrap_stability[[pos_k,"Similarity alpha randomized data"]] <- c(unlist(bootstrap_stability[[pos_k,"Similarity alpha randomized data"]]),mean(similarity))
# compute cosine similarity of beta for randomized data
similarity <- NULL
for(i in 1:nrow(res$beta)) {
curr_similarity <- ((sum(starting_values_bootstrap[[pos_k,4]][i,]*res$beta[i,]))/sqrt(sum(starting_values_bootstrap[[pos_k,4]][i,]^2)*sum(res$beta[i,]^2)))
similarity <- c(similarity,curr_similarity)
}
bootstrap_stability[[pos_k,"Similarity beta randomized data"]] <- c(unlist(bootstrap_stability[[pos_k,"Similarity beta randomized data"]]),mean(similarity))
# compute RSS for randomized data
predictions <- res$alpha%*%res$beta
mse <- NULL
for(i in 1:nrow(predictions)) {
for(j in 1:ncol(predictions)) {
mse <- c(mse,((randomized_data[i,j]-predictions[i,j])^2))
}
}
mse <- sum(mse)
bootstrap_rss[[pos_k,"RSS randomized data"]] <- c(unlist(bootstrap_rss[[pos_k,"RSS randomized data"]]),mse)
# compute Explained Variance for randomized data
evar <- (1 - (mse/sum(randomized_data^2)))
bootstrap_evar[[pos_k,"Explained Variance randomized data"]] <- c(unlist(bootstrap_evar[[pos_k,"Explained Variance randomized data"]]),evar)
}
else {
bootstrap_stability[[pos_k,"Similarity alpha randomized data"]] <- c(unlist(bootstrap_stability[[pos_k,"Similarity alpha randomized data"]]),NA)
bootstrap_stability[[pos_k,"Similarity beta randomized data"]] <- c(unlist(bootstrap_stability[[pos_k,"Similarity beta randomized data"]]),NA)
bootstrap_rss[[pos_k,"RSS randomized data"]] <- c(unlist(bootstrap_rss[[pos_k,"RSS randomized data"]]),NA)
bootstrap_evar[[pos_k,"Explained Variance randomized data"]] <- c(unlist(bootstrap_evar[[pos_k,"Explained Variance randomized data"]]),NA)
}
}
# save the results
curr_results <- list(stability=bootstrap_stability,RSS=bootstrap_rss,evar=bootstrap_evar)
return(curr_results)
})
# save the results
results <- list(stability=bootstrap_stability,RSS=bootstrap_rss,evar=bootstrap_evar)
for(par_res in 1:length(curr_results)) {
curr_par_res <- curr_results[[par_res]]
curr_par_res_stability <- curr_par_res$stability
curr_par_res_rss <- curr_par_res$RSS
curr_par_res_evar <- curr_par_res$evar
for(a in 1:dim(curr_par_res_stability)[1]) {
for(b in 1:dim(curr_par_res_stability)[2]) {
results$stability[[a,b]] <- c(unlist(results$stability[a,b]),unlist(curr_par_res_stability[a,b]))
}
}
for(a in 1:dim(curr_par_res_rss)[1]) {
for(b in 1:dim(curr_par_res_rss)[2]) {
results$RSS[[a,b]] <- c(unlist(results$RSS[a,b]),unlist(curr_par_res_rss[a,b]))
results$evar[[a,b]] <- c(unlist(results$evar[a,b]),unlist(curr_par_res_evar[a,b]))
}
}
}
}
# close parallel
if(close_parallel) {
stopCluster(parallel)
}
return(results)
}
#' Perform a robust estimation of the starting betas for the nmfLasso method
#'
#' @examples
#' data(background)
#' data(patients)
#' res = startingBetaEstimation(x=patients[1:100,],
#' K=3:5,
#' background_signature=background,
#' nmf_runs=1,
#' seed=12345)
#'
#' @title startingBetaEstimation
#' @param x count matrix for a set of n patients and 96 trinucleotides.
#' @param K numeric value (minimum 2) indicating the number of signatures to be discovered.
#' @param background_signature background signature to be used. If not provided, a warning is thrown and an initial value for it is
#' estimated by NMF. If beta is not NULL, this parameter is ignored.
#' @param normalize_counts if true, the input count matrix x is normalize such that the patients have the same number of mutation.
#' @param nmf_runs number of iteration (minimum 1) of NMF to be performed for a robust estimation of starting beta. If beta is not NULL,
#' this parameter is ignored.
#' @param seed Seed for reproducibility.
#' @param verbose boolean; Shall I print all messages?
#' @return A list containing the starting beta values for each configuration of K.
#' @export startingBetaEstimation
#' @import NMF
#' @import nnls
#'
"startingBetaEstimation" <- function( x, K = 3:10, background_signature = NULL, normalize_counts = TRUE, nmf_runs = 10, seed = NULL, verbose = TRUE ) {
# set the seed
set.seed(seed)
# check the input parameters
if(min(K)<2) {
if(verbose) {
cat("The minimum value of K is 2...","\n")
}
K <- K[K>=2]
if(length(K)==0) {
K <- 2
warning("No value of K greater than 2 is provided: setting K to 2...")
}
}
if(nmf_runs<1) {
if(verbose) {
cat("The minimum value of nmf_runs is 1...","\n")
}
nmf_runs <- 1
}
x <- as.matrix(x)
if(normalize_counts) {
x <- (x/rowSums(x))*2500
}
# estimate the background signature
if(is.null(background_signature)) {
warning("No background signature has been specified...")
background_signature_beta <- basis(nmf(t(x),rank=1,nrun=nmf_runs))
background_signature_beta <- t(background_signature_beta)
background_signature_beta <- background_signature_beta / rowSums(background_signature_beta)
background_signature <- as.numeric(background_signature_beta[1,])
}
background_signature <- as.numeric(background_signature)
background_signature <- background_signature / sum(background_signature)
# estimate the contribution of the background to the observed counts
background_signature_beta <- t(background_signature)
background_signature_alpha <- matrix(0,nrow=dim(x)[1],ncol=1)
for(i in 1:dim(x)[1]) {
background_signature_alpha[i,] <- nnls(t(background_signature_beta),as.vector(x[i,]))$x
}
curr_x <- x - (background_signature_alpha %*% background_signature_beta)
curr_x[curr_x<0] <- 0
if(length(which(rowSums(t(curr_x))==0))>0) {
invalid_cols <- as.numeric(which(rowSums(t(curr_x))==0))
for(inv_cols in invalid_cols) {
curr_x[sample(1:length(curr_x[,inv_cols]),size=1),inv_cols] <- 1e-05
}
}
# perform a robust estimation of the starting beta for the nmfLasso method
if(verbose) {
cat("Performing a robust estimation of the starting betas for the nmfLasso method...","\n")
}
# structure to save the starting values of beta for each K
starting_beta <- array(list(),c(length(K),1))
rownames(starting_beta) <- paste0(as.character(K),"_signatures")
colnames(starting_beta) <- "Value"
# consider all the values of K
pos_k <- 0
for(k in K) {
pos_k <- pos_k + 1
beta <- NULL
# compute the initial values of beta
if(verbose) {
cat("Computing the initial values of beta by standard NMF...","\n")
}
beta <- basis(nmf(t(curr_x),rank=(k-1),nrun=nmf_runs))
beta <- t(beta)
beta <- rbind(background_signature,beta)
# normalize and save beta for the current value of K
beta <- beta / rowSums(beta)
rownames(beta) <- c("Background",paste0("S",1:(nrow(beta)-1)))
colnames(beta) <- colnames(x)
starting_beta[[pos_k,1]] <- beta
if(verbose) {
cat("Progress",paste0(round((pos_k/length(K))*100,digits=3),"%..."),"\n")
}
}
return(starting_beta)
}
#' Estimate the range of lambda values for alpha to be considered in the signature inference. Note that too small values of lambda
#' result in dense exposures, but too large values lead to bad fit of the counts.
#'
#' @examples
#' data(background)
#' data(patients)
#' res = lambdaRangeAlphaEvaluation(x=patients[1:100,],
#' K=5,background_signature=background,
#' nmf_runs=1,lambda_values=c(0.01,0.05),
#' num_processes=NA,
#' seed=12345)
#'
#' @title lambdaRangeAlphaEvaluation
#' @param x count matrix for a set of n patients and 96 trinucleotides.
#' @param K numeric value (minimum 2) indicating the number of signatures to be discovered.
#' @param beta starting beta for the estimation. If it is NULL, starting beta is estimated by NMF.
#' @param background_signature background signature to be used. If not provided, a warning is thrown and an initial value for it is
#' estimated by NMF. If beta is not NULL, this parameter is ignored.
#' @param normalize_counts if true, the input count matrix x is normalize such that the patients have the same number of mutation.
#' @param nmf_runs number of iteration (minimum 1) of NMF to be performed for a robust estimation of starting beta. If beta is not NULL,
#' this parameter is ignored.
#' @param lambda_values value of LASSO to be used for alpha between 0 and 1. This value should be greater than 0. 1 is the value of LASSO
#' that would shrink all the signatures to 0 within one step. The higher lambda_values is, the sparser are the resulting exposures,
#' but too large values may result in a reduced fit of the observed counts.
#' @param iterations Number of iterations to be performed. Each iteration corresponds to a first step where beta is fitted
#' and a second step where alpha is fitted.
#' @param max_iterations_lasso Number of maximum iterations to be performed during the sparsification via Lasso.
#' @param num_processes Number of processes to be used during parallel execution. To execute in single process mode,
#' this parameter needs to be set to either NA or NULL.
#' @param seed Seed for reproducibility.
#' @param verbose boolean; Shall I print all messages?
#' @param log_file log file where to print outputs when using parallel. If parallel execution is disabled, this parameter is ignored.
#' @return A list corresponding to results of the function nmfLasso for each value of lambda to be tested. This function allows
#' to test a good range of lambda values for alpha to be considered. One should keep in mind that too small values generate dense solution,
#' while too high ones leads to poor fit. This behavior is resampled in the values of loglik_progression, which should be increasing:
#' too small values of lambda results in unstable log-likelihood through the iterations, while too large values make log-likelihood
#' drop.
#' @export lambdaRangeAlphaEvaluation
#' @import NMF
#' @import nnlasso
#' @import nnls
#' @import parallel
#'
"lambdaRangeAlphaEvaluation" <- function( x, K = 5, beta = NULL, background_signature = NULL, normalize_counts = TRUE, nmf_runs = 10, lambda_values = c(0.01, 0.05, 0.10, 0.20), iterations = 30, max_iterations_lasso = 10000, num_processes = Inf, seed = NULL, verbose = TRUE, log_file = "" ) {
# set the seed
set.seed(seed)
# check the input parameters
if(K<2) {
if(verbose) {
cat("The minimum value of K is 2...","\n")
}
K <- 2
}
if(nmf_runs<1) {
if(verbose) {
cat("The minimum value of nmf_runs is 1...","\n")
}
nmf_runs <- 1
}
x <- as.matrix(x)
if(normalize_counts) {
x_not_normalized <- x
x <- (x/rowSums(x))*2500
}
lambda_values <- sort(unique(lambda_values))
# compute the initial values of beta
if(is.null(beta)) {
if(verbose) {
cat("Computing the initial values of beta by standard NMF...","\n")
}
# add a signature to beta (leading to K signatures in total) to explicitly model background noise
if(is.null(background_signature)) {
warning("No background signature has been specified...")
background_signature_beta <- basis(nmf(t(x),rank=1,nrun=nmf_runs))
background_signature_beta <- t(background_signature_beta)
background_signature_beta <- background_signature_beta / rowSums(background_signature_beta)
background_signature <- as.numeric(background_signature_beta[1,])
}
else {
background_signature <- as.numeric(background_signature)
background_signature <- background_signature / sum(background_signature)
background_signature_beta <- t(background_signature)
}
background_signature_alpha <- matrix(0,nrow=dim(x)[1],ncol=1)
for(i in 1:dim(x)[1]) {
background_signature_alpha[i,] <- nnls(t(background_signature_beta),as.vector(x[i,]))$x
}
curr_x <- x - (background_signature_alpha %*% background_signature_beta)
curr_x[curr_x<0] <- 0
if(length(which(rowSums(t(curr_x))==0))>0) {
invalid_cols <- as.numeric(which(rowSums(t(curr_x))==0))
for(inv_cols in invalid_cols) {
curr_x[sample(1:length(curr_x[,inv_cols]),size=1),inv_cols] <- 1e-05
}
}
beta <- basis(nmf(t(curr_x),rank=(K-1),nrun=nmf_runs))
beta <- t(beta)
beta <- rbind(background_signature,beta)
}
beta <- beta / rowSums(beta)
rownames(beta) <- c("Background",paste0("S",1:(nrow(beta)-1)))
colnames(beta) <- colnames(x)
# setting up parallel execution
parallel <- NULL
close_parallel <- FALSE
if(is.null(parallel)&&length(lambda_values)>1) {
if(is.na(num_processes) || is.null(num_processes)) {
parallel <- NULL
}
else if(num_processes==Inf) {
cores <- as.integer((detectCores()-1))
if(cores < 2) {
parallel <- NULL
}
else {
num_processes <- min(num_processes,length(lambda_values))
parallel <- makeCluster(num_processes,outfile=log_file)
close_parallel <- TRUE
}
}
else {
num_processes <- min(num_processes,length(lambda_values))
parallel <- makeCluster(num_processes,outfile=log_file)
close_parallel <- TRUE
}
if(verbose && !is.null(parallel)) {
cat("Executing",num_processes,"processes via parallel...","\n")
}
}
# structure to save the estimated signatures
lambda_results <- array(list(),c(length(K),length(lambda_values)))
rownames(lambda_results) <- paste0(as.character(K),"_signatures")
colnames(lambda_results) <- paste0(as.character(lambda_values),"_lambda")
if(verbose) {
cat("Performing estimation of lambda range for alpha...","\n")
}
# perform signature discovery for all the values of lambda
if(is.null(parallel)) {
set.seed(round(runif(1)*100000))
cont <- 0
for(l in lambda_values) {
# perform the inference
curr_results <- nmfLasso(x = x,
K = K,
beta = beta,
normalize_counts = normalize_counts,
lambda_rate_alpha = l,
lambda_rate_beta = 0.0,
iterations = iterations,
max_iterations_lasso = max_iterations_lasso,
seed = round(runif(1)*100000),
verbose = FALSE)
# save the results for the current configuration
cont <- cont + 1
# rescale alpha to the original magnitude
if(normalize_counts) {
curr_results$starting_alpha <- curr_results$starting_alpha * (rowSums(x_not_normalized)/2500)
curr_results$alpha <- curr_results$alpha * (rowSums(x_not_normalized)/2500)
}
lambda_results[[1,cont]] <- curr_results
if(verbose) {
cat("Progress",paste0(round((cont/(length(K)*length(lambda_values)))*100,digits=3),"%..."),"\n")
}
}
}
else {
res_clusterEvalQ <- clusterEvalQ(parallel,library("nnls"))
res_clusterEvalQ <- clusterEvalQ(parallel,library("nnlasso"))
clusterExport(parallel,varlist=c("x","K","beta","normalize_counts","iterations","max_iterations_lasso"),envir=environment())
clusterExport(parallel,c('nmfLasso','nmfLassoDecomposition','basis','nmf'),envir=environment())
clusterSetRNGStream(parallel,iseed=round(runif(1)*100000))
lambda_results_res <- parLapply(parallel,lambda_values,function(l) {
# perform the inference
curr_results <- nmfLasso(x = x,
K = K,
beta = beta,
normalize_counts = normalize_counts,
lambda_rate_alpha = l,
lambda_rate_beta = 0.0,
iterations = iterations,
max_iterations_lasso = max_iterations_lasso,
seed = round(runif(1)*100000),
verbose = FALSE)
return(curr_results)
})
for(i in 1:ncol(lambda_results)) {
# rescale alpha to the original magnitude
if(normalize_counts) {
lambda_results_res[[i]]$starting_alpha <- lambda_results_res[[i]]$starting_alpha * (rowSums(x_not_normalized)/2500)
lambda_results_res[[i]]$alpha <- lambda_results_res[[i]]$alpha * (rowSums(x_not_normalized)/2500)
}
lambda_results[[1,i]] <- lambda_results_res[[i]]
}
}
# close parallel
if(close_parallel) {
stopCluster(parallel)
}
return(lambda_results)
}
#' Estimate the range of lambda values for beta to be considered in the signature inference. Note that too small values of lambda
#' result in dense signatures, but too large values lead to bad fit of the counts.
#'
#' @examples
#' data(background)
#' data(patients)
#' res = lambdaRangeBetaEvaluation(x=patients[1:100,],
#' K=5,
#' background_signature=background,
#' nmf_runs=1,
#' lambda_values=c(0.01,0.05),
#' num_processes=NA,
#' seed=12345)
#'
#' @title lambdaRangeBetaEvaluation
#' @param x count matrix for a set of n patients and 96 trinucleotides.
#' @param K numeric value (minimum 2) indicating the number of signatures to be discovered.
#' @param beta starting beta for the estimation. If it is NULL, starting beta is estimated by NMF.
#' @param background_signature background signature to be used. If not provided, a warning is thrown and an initial value for it is
#' estimated by NMF. If beta is not NULL, this parameter is ignored.
#' @param normalize_counts if true, the input count matrix x is normalize such that the patients have the same number of mutation.
#' @param nmf_runs number of iteration (minimum 1) of NMF to be performed for a robust estimation of starting beta. If beta is not NULL,
#' this parameter is ignored.
#' @param lambda_values value of LASSO to be used for beta between 0 and 1. This value should be greater than 0. 1 is the value of LASSO
#' that would shrink all the signatures to 0 within one step. The higher lambda_values is, the sparser are the resulting signatures,
#' but too large values may result in a reduced fit of the observed counts.
#' @param iterations Number of iterations to be performed. Each iteration corresponds to a first step where beta is fitted
#' and a second step where alpha is fitted.
#' @param max_iterations_lasso Number of maximum iterations to be performed during the sparsification via Lasso.
#' @param num_processes Number of processes to be used during parallel execution. To execute in single process mode,
#' this parameter needs to be set to either NA or NULL.
#' @param seed Seed for reproducibility.
#' @param verbose boolean; Shall I print all messages?
#' @param log_file log file where to print outputs when using parallel. If parallel execution is disabled, this parameter is ignored.
#' @return A list corresponding to results of the function nmfLasso for each value of lambda to be tested. This function allows
#' to test a good range of lambda values for beta to be considered. One should keep in mind that too small values generate dense solution,
#' while too high ones leads to poor fit. This behavior is resampled in the values of loglik_progression, which should be increasing:
#' too small values of lambda results in unstable log-likelihood through the iterations, while too large values make log-likelihood
#' drop.
#' @export lambdaRangeBetaEvaluation
#' @import NMF
#' @import nnlasso
#' @import nnls
#' @import parallel
#'
"lambdaRangeBetaEvaluation" <- function( x, K = 5, beta = NULL, background_signature = NULL, normalize_counts = TRUE, nmf_runs = 10, lambda_values = c(0.01, 0.05, 0.10, 0.20), iterations = 30, max_iterations_lasso = 10000, num_processes = Inf, seed = NULL, verbose = TRUE, log_file = "" ) {
# set the seed
set.seed(seed)
# check the input parameters
if(K<2) {
if(verbose) {
cat("The minimum value of K is 2...","\n")
}
K <- 2
}
if(nmf_runs<1) {
if(verbose) {
cat("The minimum value of nmf_runs is 1...","\n")
}
nmf_runs <- 1
}
x <- as.matrix(x)
if(normalize_counts) {
x_not_normalized <- x
x <- (x/rowSums(x))*2500
}
lambda_values <- sort(unique(lambda_values))
# compute the initial values of beta
if(is.null(beta)) {
if(verbose) {
cat("Computing the initial values of beta by standard NMF...","\n")
}
# add a signature to beta (leading to K signatures in total) to explicitly model background noise
if(is.null(background_signature)) {
warning("No background signature has been specified...")
background_signature_beta <- basis(nmf(t(x),rank=1,nrun=nmf_runs))
background_signature_beta <- t(background_signature_beta)
background_signature_beta <- background_signature_beta / rowSums(background_signature_beta)
background_signature <- as.numeric(background_signature_beta[1,])
}
else {
background_signature <- as.numeric(background_signature)
background_signature <- background_signature / sum(background_signature)
background_signature_beta <- t(background_signature)
}
background_signature_alpha <- matrix(0,nrow=dim(x)[1],ncol=1)
for(i in 1:dim(x)[1]) {
background_signature_alpha[i,] <- nnls(t(background_signature_beta),as.vector(x[i,]))$x
}
curr_x <- x - (background_signature_alpha %*% background_signature_beta)
curr_x[curr_x<0] <- 0
if(length(which(rowSums(t(curr_x))==0))>0) {
invalid_cols <- as.numeric(which(rowSums(t(curr_x))==0))
for(inv_cols in invalid_cols) {
curr_x[sample(1:length(curr_x[,inv_cols]),size=1),inv_cols] <- 1e-05
}
}
beta <- basis(nmf(t(curr_x),rank=(K-1),nrun=nmf_runs))
beta <- t(beta)
beta <- rbind(background_signature,beta)
}
beta <- beta / rowSums(beta)
rownames(beta) <- c("Background",paste0("S",1:(nrow(beta)-1)))
colnames(beta) <- colnames(x)
# setting up parallel execution
parallel <- NULL
close_parallel <- FALSE
if(is.null(parallel)&&length(lambda_values)>1) {
if(is.na(num_processes) || is.null(num_processes)) {
parallel <- NULL
}
else if(num_processes==Inf) {
cores <- as.integer((detectCores()-1))
if(cores < 2) {
parallel <- NULL
}
else {
num_processes <- min(num_processes,length(lambda_values))
parallel <- makeCluster(num_processes,outfile=log_file)
close_parallel <- TRUE
}
}
else {
num_processes <- min(num_processes,length(lambda_values))
parallel <- makeCluster(num_processes,outfile=log_file)
close_parallel <- TRUE
}
if(verbose && !is.null(parallel)) {
cat("Executing",num_processes,"processes via parallel...","\n")
}
}
# structure to save the estimated signatures
lambda_results <- array(list(),c(length(K),length(lambda_values)))
rownames(lambda_results) <- paste0(as.character(K),"_signatures")
colnames(lambda_results) <- paste0(as.character(lambda_values),"_lambda")
if(verbose) {
cat("Performing estimation of lambda range for beta...","\n")
}
# perform signature discovery for all the values of lambda
if(is.null(parallel)) {
set.seed(round(runif(1)*100000))
cont <- 0
for(l in lambda_values) {
# perform the inference
curr_results <- nmfLasso(x = x,
K = K,
beta = beta,
normalize_counts = normalize_counts,
lambda_rate_alpha = 0.0,
lambda_rate_beta = l,
iterations = iterations,
max_iterations_lasso = max_iterations_lasso,
seed = round(runif(1)*100000),
verbose = FALSE)
# save the results for the current configuration
cont <- cont + 1
# rescale alpha to the original magnitude
if(normalize_counts) {
curr_results$starting_alpha <- curr_results$starting_alpha * (rowSums(x_not_normalized)/2500)
curr_results$alpha <- curr_results$alpha * (rowSums(x_not_normalized)/2500)
}
lambda_results[[1,cont]] <- curr_results
if(verbose) {
cat("Progress",paste0(round((cont/(length(K)*length(lambda_values)))*100,digits=3),"%..."),"\n")
}
}
}
else {
res_clusterEvalQ <- clusterEvalQ(parallel,library("nnls"))
res_clusterEvalQ <- clusterEvalQ(parallel,library("nnlasso"))
clusterExport(parallel,varlist=c("x","K","beta","normalize_counts","iterations","max_iterations_lasso"),envir=environment())
clusterExport(parallel,c('nmfLasso','nmfLassoDecomposition','basis','nmf'),envir=environment())
clusterSetRNGStream(parallel,iseed=round(runif(1)*100000))
lambda_results_res <- parLapply(parallel,lambda_values,function(l) {
# perform the inference
curr_results <- nmfLasso(x = x,
K = K,
beta = beta,
normalize_counts = normalize_counts,
lambda_rate_alpha = 0.0,
lambda_rate_beta = l,
iterations = iterations,
max_iterations_lasso = max_iterations_lasso,
seed = round(runif(1)*100000),
verbose = FALSE)
return(curr_results)
})
for(i in 1:ncol(lambda_results)) {
# rescale alpha to the original magnitude
if(normalize_counts) {
lambda_results_res[[i]]$starting_alpha <- lambda_results_res[[i]]$starting_alpha * (rowSums(x_not_normalized)/2500)
lambda_results_res[[i]]$alpha <- lambda_results_res[[i]]$alpha * (rowSums(x_not_normalized)/2500)
}
lambda_results[[1,i]] <- lambda_results_res[[i]]
}
}
# close parallel
if(close_parallel) {
stopCluster(parallel)
}
return(lambda_results)
}
#' Perform the discovery of K somatic mutational signatures given a set of observed counts x.
#'
#' @examples
#' data(patients)
#' data(starting_betas_example)
#' beta = starting_betas_example[["5_signatures","Value"]]
#' res = nmfLasso(x=patients[1:100,],
#' K=5,
#' beta=beta,
#' lambda_rate_alpha=0.05,
#' lambda_rate_beta=0.05,
#' iterations=5,
#' seed=12345)
#'
#' @title nmfLasso
#' @param x count matrix for a set of n patients and 96 trinucleotides.
#' @param K numeric value (minimum 2) indicating the number of signatures to be discovered.
#' @param beta starting beta for the estimation. If it is NULL, starting beta is estimated by NMF.
#' @param background_signature background signature to be used. If not provided, a warning is thrown and an initial value for it is
#' estimated by NMF. If beta is not NULL, this parameter is ignored.
#' @param normalize_counts if true, the input count matrix x is normalize such that the patients have the same number of mutation.
#' @param nmf_runs number of iteration (minimum 1) of NMF to be performed for a robust estimation of starting beta. If beta is not NULL,
#' this parameter is ignored.
#' @param lambda_rate_alpha value of LASSO to be used for alpha between 0 and 1. This value should be greater than 0. 1 is the value of LASSO
#' that would shrink all the exposure values to 0 within one step. The higher lambda_rate_alpha is, the sparser are the resulting exposure values,
#' but too large values may result in a reduced fit of the observed counts.
#' @param lambda_rate_beta value of LASSO to be used for beta between 0 and 1. This value should be greater than 0. 1 is the value of LASSO
#' that would shrink all the signatures to 0 within one step. The higher lambda_rate_beta is, the sparser are the resulting signatures,
#' but too large values may result in a reduced fit of the observed counts.
#' @param iterations Number of iterations to be performed. Each iteration corresponds to a first step where beta is fitted
#' and a second step where alpha is fitted.
#' @param max_iterations_lasso Number of maximum iterations to be performed during the sparsification via Lasso.
#' @param seed Seed for reproducibility.
#' @param verbose boolean; Shall I print all messages?
#' @return A list with the discovered signatures. It includes 6 elements:
#' alpha: matrix of the discovered exposure values
#' beta: matrix of the discovered signatures
#' starting_alpha: initial alpha on which the method has been applied
#' starting_beta: initial beta on which the method has been applied
#' loglik_progression: log-likelihood values during the iterations. This values should be increasing, if not the selected value of lambda is too high
#' best_loglik: log-likelihood of the best signatures configuration
#' @export nmfLasso
#' @import NMF
#' @import nnls
#' @import nnlasso
#'
"nmfLasso" <- function( x, K, beta = NULL, background_signature = NULL, normalize_counts = TRUE, nmf_runs = 10, lambda_rate_alpha = 0.05, lambda_rate_beta = 0.05, iterations = 30, max_iterations_lasso = 10000, seed = NULL, verbose = TRUE ) {
# set the seed
set.seed(seed)
# check the input parameters
if(K<2) {
if(verbose) {
cat("The minimum value of K is 2...","\n")
}
K <- 2
}
if(nmf_runs<1) {
if(verbose) {
cat("The minimum value of nmf_runs is 1...","\n")
}
nmf_runs <- 1
}
if(lambda_rate_alpha<0) {
if(verbose) {
cat("The minimum value of lambda_rate_alpha is 0...","\n")
}
lambda_rate_alpha <- 0
}
if(lambda_rate_alpha>1) {
if(verbose) {
cat("The maximum value of lambda_rate_alpha is 1...","\n")
}
lambda_rate_alpha <- 1
}
if(lambda_rate_beta<0) {
if(verbose) {
cat("The minimum value of lambda_rate_beta is 0...","\n")
}
lambda_rate_beta <- 0
}
if(lambda_rate_beta>1) {
if(verbose) {
cat("The maximum value of lambda_rate_beta is 1...","\n")
}
lambda_rate_beta <- 1
}
x <- as.matrix(x)
if(normalize_counts) {
x_not_normalized <- x
x <- (x/rowSums(x))*2500
}
# compute the initial values of beta
if(is.null(beta)) {
if(verbose) {
cat("Computing the initial values of beta by standard NMF...","\n")
}
# add a signature to beta (leading to K signatures in total) to explicitly model background noise
if(is.null(background_signature)) {
warning("No background signature has been specified...")
background_signature_beta <- basis(nmf(t(x),rank=1,nrun=nmf_runs))
background_signature_beta <- t(background_signature_beta)
background_signature_beta <- background_signature_beta / rowSums(background_signature_beta)
background_signature <- as.numeric(background_signature_beta[1,])
}
else {
background_signature <- as.numeric(background_signature)
background_signature <- background_signature / sum(background_signature)
background_signature_beta <- t(background_signature)
}
background_signature_alpha <- matrix(0,nrow=dim(x)[1],ncol=1)
for(i in 1:dim(x)[1]) {
background_signature_alpha[i,] <- nnls(t(background_signature_beta),as.vector(x[i,]))$x
}
curr_x <- x - (background_signature_alpha %*% background_signature_beta)
curr_x[curr_x<0] <- 0
if(length(which(rowSums(t(curr_x))==0))>0) {
invalid_cols <- as.numeric(which(rowSums(t(curr_x))==0))
for(inv_cols in invalid_cols) {
curr_x[sample(1:length(curr_x[,inv_cols]),size=1),inv_cols] <- 1e-05
}
}
beta <- basis(nmf(t(curr_x),rank=(K-1),nrun=nmf_runs))
beta <- t(beta)
beta <- rbind(background_signature,beta)
}
beta <- beta / rowSums(beta)
rownames(beta) <- c("Background",paste0("S",1:(nrow(beta)-1)))
colnames(beta) <- colnames(x)
if(verbose) {
cat("Performing the discovery of the signatures by NMF with Lasso...","\n")
}
# perform the discovery of the signatures
results = tryCatch({
results = nmfLassoDecomposition(x,beta,lambda_rate_alpha,lambda_rate_beta,iterations,max_iterations_lasso,round(runif(1)*100000),verbose)
# rescale alpha to the original magnitude
if(normalize_counts) {
results$starting_alpha <- results$starting_alpha * (rowSums(x_not_normalized)/2500)
results$alpha <- results$alpha * (rowSums(x_not_normalized)/2500)
}
return(results)
}, error = function(e) {
warning("Lasso did not converge, you should try a lower value of lambda! Current settings: K = ",K,", lambda_rate_alpha = ",lambda_rate_alpha,", lambda_rate_beta = ",lambda_rate_beta,"...")
return(list(alpha=NA,beta=NA,starting_alpha=NA,starting_beta=NA,loglik_progression=rep(NA,iterations),best_loglik=NA))
})
return(results)
}
# perform de novo discovery of somatic mutational signatures using NMF with Lasso to ensure sparsity
"nmfLassoDecomposition" <- function( x, starting_beta, lambda_rate_alpha = 0.05, lambda_rate_beta = 0.05, iterations = 30, max_iterations_lasso = 10000, seed = NULL, verbose = TRUE ) {
# set the seed
set.seed(seed)
# n is the number of observations in x, i.e., the patients
n <- dim(x)[1]
# J is the number of trinucleotides, i.e., 96 categories
J <- dim(x)[2]
# K is the number of signatures to be called
K <- dim(starting_beta)[1]
# initialize beta
starting_beta <- starting_beta / rowSums(starting_beta)
rownames(starting_beta) <- c("Background",paste0("S",1:(nrow(starting_beta)-1)))
colnames(starting_beta) <- colnames(x)
beta <- starting_beta
# initialize alpha
alpha <- matrix(0,nrow=n,ncol=K)
rownames(alpha) <- 1:nrow(alpha)
colnames(alpha) <- rownames(beta)
for(i in 1:n) {
alpha[i,] <- nnls(t(beta),as.vector(x[i,]))$x
}
starting_alpha <- alpha
# rescale the two matrices of a factor of 50 for numerical reasons
beta <- beta * 50
for(i in 1:n) {
alpha[i,] <- nnls(t(beta),as.vector(x[i,]))$x
}
# structure where to save the log-likelihood at each iteration
loglik <- rep(NA,iterations)
# structure where to save the lambda values for alpha and beta
lambda_values_alpha <- rep(NA,n) # sparsity over the patients (reduce the number of signatures per patient)
lambda_values_beta <- rep(NA,J) # sparsity over the signatures (produce sparse signatures)
if(verbose) {
cat("Performing a total of",iterations,"iterations...","\n")
}
# start the learning procedure
best_loglik <- NA
best_alpha <- NA
best_beta <- NA
for(i in 1:iterations) {
# initialize the value of the log-likelihood for the current iteration
loglik[i] <- 0
# configuration 1 (turn off sparsity): repeat a 2 step algorithm iteratively, where
# first beta is estimated by Non-Negative Linear Least Squares and, then, alpha is also estimated by Non-Negative Linear Least Squares
if(lambda_rate_alpha==0&&lambda_rate_beta==0) {
# update beta by Non-Negative Linear Least Squares
for(k in 1:J) {
# the first signature represents the background model, thus it is not changed
beta[2:K,k] <- nnls(alpha[,2:K,drop=FALSE],as.vector(x[,k]-(alpha[,1]*beta[1,k])))$x
}
# update alpha by Non-Negative Linear Least Squares
for(j in 1:n) {
alpha[j,] <- nnls(t(beta),as.vector(x[j,]))$x
}
# update the log-likelihood for the current iteration
loglik[i] <- -sum((x - alpha %*% beta)^2)
}
# configuration 2 (sparsity only on beta): repeat a 2 step algorithm iteratively, where
# first beta is estimated by Non-Negative Lasso and, then, alpha is estimated by Non-Negative Linear Least Squares
if(lambda_rate_alpha==0&&lambda_rate_beta>0) {
# update beta by Non-Negative Lasso
for(k in 1:J) {
# compute independently for each trinucleotide the difference between the observed counts, i.e., x,
# and the counts predicted by considering only the first signature (i.e., which represents the background model)
target <- x[,k] - (alpha[,1] * beta[1,k])
# estimate beta for the remaining signatues by Non-Negative Lasso to ensure sparsity
if(is.na(lambda_values_beta[k])) {
max_lambda_value <- max(abs(t(alpha[,2:K,drop=FALSE]) %*% target))
lambda_values_beta[k] <- max_lambda_value * lambda_rate_beta
}
beta[2:K,k] <- as.vector(nnlasso(x = alpha[,2:K,drop=FALSE],
y = target,
family = "normal",
lambda = lambda_values_beta[k],
intercept = FALSE,
normalize = FALSE,
tol = 1e-05,
maxiter = max_iterations_lasso,
path = FALSE)$coef[2,])
}
# update alpha by Non-Negative Linear Least Squares
for(j in 1:n) {
alpha[j,] <- nnls(t(beta),as.vector(x[j,]))$x
}
# update the log-likelihood for the current iteration
for(k in 1:J) {
curr_loglik <- -sum((x[,k] - alpha %*% beta[,k])^2) - (lambda_values_beta[k] * sum(beta[2:K,k]))
loglik[i] <- loglik[i] + curr_loglik
}
}
# configuration 3 (sparsity only on alpha): repeat a 2 step algorithm iteratively, where
# first beta is estimated by Non-Negative Linear Least Squares and, then, alpha is estimated by Non-Negative Lasso
if(lambda_rate_alpha>0&&lambda_rate_beta==0) {
# update beta by Non-Negative Linear Least Squares
for(k in 1:J) {
# the first signature represents the background model, thus it is not changed
beta[2:K,k] <- nnls(alpha[,2:K,drop=FALSE],as.vector(x[,k]-(alpha[,1]*beta[1,k])))$x
}
# update alpha by Non-Negative Lasso
for(j in 1:n) {
# compute independently for each patient the counts to be approximted
target <- x[j,]
# estimate alpha by Non-Negative Lasso to ensure sparsity
if(is.na(lambda_values_alpha[j])) {
max_lambda_value <- max(abs(beta %*% target))
lambda_values_alpha[j] <- max_lambda_value * lambda_rate_alpha
}
alpha[j,] <- as.vector(nnlasso(x = t(beta),
y = target,
family = "normal",
lambda = lambda_values_alpha[j],
intercept = FALSE,
normalize = FALSE,
tol = 1e-05,
maxiter = max_iterations_lasso,
path = FALSE)$coef[2,])
}
# update the log-likelihood for the current iteration
for(j in 1:n) {
curr_loglik <- -sum((x[j,] - alpha[j,] %*% beta)^2) - (lambda_values_alpha[j] * sum(alpha[j,]))
loglik[i] <- loglik[i] + curr_loglik
}
}
# configuration 4 (sparsity on both alpha and beta): repeat a 2 step algorithm iteratively, where
# first beta is estimated by Non-Negative Lasso and, then, also alpha is estimated by Non-Negative Lasso
if(lambda_rate_alpha>0&&lambda_rate_beta>0) {
# update beta by Non-Negative Lasso
for(k in 1:J) {
# compute independently for each trinucleotide the difference between the observed counts, i.e., x,
# and the counts predicted by considering only the first signature (i.e., which represents the background model)
target <- x[,k] - (alpha[,1] * beta[1,k])
# estimate beta for the remaining signatues by Non-Negative Lasso to ensure sparsity
if(is.na(lambda_values_beta[k])) {
max_lambda_value <- max(abs(t(alpha[,2:K,drop=FALSE]) %*% target))
lambda_values_beta[k] <- max_lambda_value * lambda_rate_beta
}
beta[2:K,k] <- as.vector(nnlasso(x = alpha[,2:K,drop=FALSE],
y = target,
family = "normal",
lambda = lambda_values_beta[k],
intercept = FALSE,
normalize = FALSE,
tol = 1e-05,
maxiter = max_iterations_lasso,
path = FALSE)$coef[2,])
}
# update alpha by Non-Negative Lasso
for(j in 1:n) {
# compute independently for each patient the counts to be approximted
target <- x[j,]
# estimate alpha by Non-Negative Lasso to ensure sparsity
if(is.na(lambda_values_alpha[j])) {
max_lambda_value <- max(abs(beta %*% target))
lambda_values_alpha[j] <- max_lambda_value * lambda_rate_alpha
}
alpha[j,] <- as.vector(nnlasso(x = t(beta),
y = target,
family = "normal",
lambda = lambda_values_alpha[j],
intercept = FALSE,
normalize = FALSE,
tol = 1e-05,
maxiter = max_iterations_lasso,
path = FALSE)$coef[2,])
}
# update the log-likelihood for the current iteration
for(k in 1:J) {
for(j in 1:n) {
curr_loglik <- -((x[j,k] - alpha[j,] %*% beta[,k])^2) - (lambda_values_alpha[j] * sum(alpha[j,])) - (lambda_values_beta[k] * sum(beta[2:K,k]))
loglik[i] <- loglik[i] + curr_loglik
}
}
}
# save the results at maximum log-likelihood
if(is.na(best_loglik)||loglik[i]>best_loglik) {
best_alpha <- alpha
best_beta <- beta
best_loglik <- loglik[i]
}
if(verbose) {
cat("Progress",paste0((i/iterations)*100,"%..."),"\n")
}
}
alpha <- best_alpha
beta <- best_beta
# check if the likelihood is increasing
if(length(loglik)>1) {
cont <- 1
for(i in 2:length(loglik)) {
if(loglik[i]>loglik[(i-1)]) {
cont <- cont + 1
}
}
if(cont/iterations<0.5) {
warning("The likelihood is not increasing, you should try a lower value of lambda! Current settings: K = ",K,", lambda_rate_alpha = ",lambda_rate_alpha,", lambda_rate_beta = ",lambda_rate_beta,"...")
}
}
# normalize the rate of the signatures to sum to 1
beta <- beta / rowSums(beta)
# final computation of alpha using the normalized version of beta
if(lambda_rate_alpha>0) {
# update alpha by Non-Negative Lasso
for(j in 1:n) {
# compute independently for each patient the counts to be approximted
target <- x[j,]
# estimate alpha by Non-Negative Lasso to ensure sparsity
alpha[j,] <- as.vector(nnlasso(x = t(beta),
y = target,
family = "normal",
lambda = (max(abs(beta %*% target)) * lambda_rate_alpha),
intercept = FALSE,
normalize = FALSE,
tol = 1e-05,
maxiter = max_iterations_lasso,
path = FALSE)$coef[2,])
}
}
else {
# update alpha by Non-Negative Linear Least Squares
for(j in 1:n) {
alpha[j,] <- nnls(t(beta),as.vector(x[j,]))$x
}
}
# save the results
results <- list(alpha=alpha,beta=beta,starting_alpha=starting_alpha,starting_beta=starting_beta,loglik_progression=loglik,best_loglik=best_loglik)
return(results)
}
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#' Perform the assessment of different nmfLasso solutions by cross validation for K (unknown) somatic mutational signatures given a set of observations x. The estimation can slow down because of
#' memory usage and intensive computations, when a big number of cross validation repetitions is asked and when the grid search is performed for a lot of configurations. In this case,
#' an advice may be to split the computation into multiple smaller sets.
#'
#' @examples
#' data(background)
#' data(patients)
#' res = nmfLassoCV(x=patients[1:100,],
#' K=3:5,
#' background_signature=background,
#' nmf_runs=1,
#' lambda_values_alpha=c(0.00),
#' lambda_values_beta=c(0.00),
#' cross_validation_repetitions=2,
#' num_processes=NA,
#' seed=12345)
#'
#' @title nmfLassoCV
#' @param x count matrix for a set of n patients and 96 trinucleotides.
#' @param K a range of numeric value (each of them greater than 1) indicating the number of signatures to be discovered.
#' @param starting_beta a list of starting beta value for each configuration of K. If it is NULL, starting betas are estimated by
#' NMF.
#' @param background_signature background signature to be used. If not provided, a warning is thrown and an initial value for it is
#' estimated by NMF. If beta is not NULL, this parameter is ignored.
#' @param normalize_counts if true, the input count matrix x is normalize such that the patients have the same number of mutation.
#' @param nmf_runs number of iteration (minimum 1) of NMF to be performed for a robust estimation of starting beta. If beta is not NULL,
#' this parameter is ignored.
#' @param lambda_values_alpha value of LASSO to be used for alpha between 0 and 1. This value should be greater than 0. 1 is the value of LASSO
#' that would shrink all the signatures to 0 within one step. The higher lambda_rate_alpha is, the sparser are the resulting exposures,
#' but too large values may result in a reduced fit of the observed counts.
#' @param lambda_values_beta value of LASSO to be used for beta between 0 and 1. This value should be greater than 0. 1 is the value of LASSO
#' that would shrink all the signatures to 0 within one step. The higher lambda_rate_beta is, the sparser are the resulting exposures,
#' but too large values may result in a reduced fit of the observed counts.
#' @param cross_validation_entries Percentage of cells in the count matrix to be replaced by 0s during cross validation.
#' @param cross_validation_iterations For each configuration, the first time the signatures are discovered form a matrix with a
#' percentage of values replaced by 0s. This may result in poor fit/results. Then, we perform predictions of these entries and replace them with
#' such predicted values. This parameter is the number of restarts to be performed to improve this estimate and obtain more stable solutions.
#' @param cross_validation_repetitions Number of time cross-validation should be repeated. Higher values result in better estimate, but are computationally more expensive.
#' @param iterations Number of iterations to be performed. Each iteration corresponds to a first step where beta is fitted
#' and a second step where alpha is fitted.
#' @param max_iterations_lasso Number of maximum iterations to be performed during the sparsification via Lasso.
#' @param num_processes Number of processes to be used during parallel execution. To execute in single process mode,
#' this parameter needs to be set to either NA or NULL.
#' @param seed Seed for reproducibility.
#' @param verbose boolean; Shall I print all messages?
#' @param log_file log file where to print outputs when using parallel. If parallel execution is disabled, this parameter is ignored.
#' @return A list of 2 elements: grid_search_mse and and grid_search_loglik. Here, grid_search_mse reports the mean squared error for each configuration of performed
#' cross validation; grid_search_loglik reports for each configuration the number of times the algorithm converged.
#' @export nmfLassoCV
#' @import NMF
#' @import nnlasso
#' @import nnls
#' @import parallel
#'
"nmfLassoCV" <- function( x, K = 3:10, starting_beta = NULL, background_signature = NULL, normalize_counts = TRUE, nmf_runs = 10, lambda_values_alpha = c(0.00, 0.01, 0.05, 0.10), lambda_values_beta = c(0.00, 0.01, 0.05, 0.10), cross_validation_entries = 0.01, cross_validation_iterations = 5, cross_validation_repetitions = 50, iterations = 30, max_iterations_lasso = 10000, num_processes = Inf, seed = NULL, verbose = TRUE, log_file = "" ) {
# set the seed
set.seed(seed)
# check the input parameters
if(min(K)<2) {
if(verbose) {
cat("The minimum value of K is 2...","\n")
}
K <- K[K>=2]
if(length(K)==0) {
K <- 2
warning("No value of K greater than 2 is provided: setting K to 2...")
}
}
if(nmf_runs<1) {
if(verbose) {
cat("The minimum value of nmf_runs is 1...","\n")
}
nmf_runs <- 1
}
x <- as.matrix(x)
if(normalize_counts) {
x <- (x/rowSums(x))*2500
}
lambda_values_alpha <- sort(unique(lambda_values_alpha))
lambda_values_beta <- sort(unique(lambda_values_beta))
# perform a grid search to estimate the best values of K and lambda
if(verbose) {
cat("Performing a grid search to estimate the best values of K and lambda with a total of",cross_validation_repetitions,"cross validation repetitions...","\n")
}
# setting up parallel execution
parallel <- NULL
close_parallel <- FALSE
if(is.null(parallel)&&cross_validation_repetitions>1) {
if(is.na(num_processes) || is.null(num_processes)) {
parallel <- NULL
}
else if(num_processes==Inf) {
cores <- as.integer((detectCores()-1))
if(cores < 2) {
parallel <- NULL
}
else {
num_processes <- min(num_processes,cross_validation_repetitions)
parallel <- makeCluster(num_processes,outfile=log_file)
close_parallel <- TRUE
}
}
else {
num_processes <- min(num_processes,cross_validation_repetitions)
parallel <- makeCluster(num_processes,outfile=log_file)
close_parallel <- TRUE
}
if(verbose && !is.null(parallel)) {
cat("Executing",num_processes,"processes via parallel...","\n")
}
}
# estimate the background signature
if(is.null(background_signature)&&is.null(starting_beta)) {
warning("No background signature has been specified...")
background_signature_beta <- basis(nmf(t(x),rank=1,nrun=nmf_runs))
background_signature_beta <- t(background_signature_beta)
background_signature_beta <- background_signature_beta / rowSums(background_signature_beta)
background_signature <- as.numeric(background_signature_beta[1,])
}
# structure to save the starting values of beta for each K
if(is.null(starting_beta)) {
background_signature <- as.numeric(background_signature)
background_signature <- background_signature / sum(background_signature)
starting_beta <- array(list(),c(length(K),1))
rownames(starting_beta) <- paste0(as.character(K),"_Signatures")
colnames(starting_beta) <- "Value"
# estimate the contribution of the background to the observed counts
background_signature_beta <- t(background_signature)
background_signature_alpha <- matrix(0,nrow=dim(x)[1],ncol=1)
for(i in 1:dim(x)[1]) {
background_signature_alpha[i,] <- nnls(t(background_signature_beta),as.vector(x[i,]))$x
}
curr_x <- x - (background_signature_alpha %*% background_signature_beta)
curr_x[curr_x<0] <- 0
if(length(which(rowSums(t(curr_x))==0))>0) {
invalid_cols <- as.numeric(which(rowSums(t(curr_x))==0))
for(inv_cols in invalid_cols) {
curr_x[sample(1:length(curr_x[,inv_cols]),size=1),inv_cols] <- 1e-05
}
}
# compute starting values for beta
pos_k <- 0
for(k in K) {
# compute the initial values of beta
if(verbose) {
cat(paste0("Computing the initial values of beta by standard NMF for K equals to ",k,"..."),"\n")
}
pos_k <- pos_k + 1
beta <- NULL
beta <- basis(nmf(t(curr_x),rank=(k-1),nrun=nmf_runs))
beta <- t(beta)
beta <- rbind(background_signature,beta)
# normalize and save beta for the current value of K
rownames(beta) <- c("Background",paste0("S",1:(nrow(beta)-1)))
colnames(beta) <- colnames(x)
beta <- beta / rowSums(beta)
starting_beta[[pos_k,1]] <- beta
}
}
if(verbose) {
cat("Starting cross validation with a total of",cross_validation_repetitions,"repetitions...","\n")
}
# structure to save the results of the grid search
grid_search_mse <- array(list(),c(length(lambda_values_alpha),length(lambda_values_beta),length(K)),dimnames=list(paste0(as.character(lambda_values_alpha),"_Lambda_Alpha"),paste0(as.character(lambda_values_beta),"_Lambda_Beta"),paste0(as.character(K),"_Signatures")))
grid_search_loglik <- array(list(),c(length(lambda_values_alpha),length(lambda_values_beta),length(K)),dimnames=list(paste0(as.character(lambda_values_alpha),"_Lambda_Alpha"),paste0(as.character(lambda_values_beta),"_Lambda_Beta"),paste0(as.character(K),"_Signatures")))
# now starting cross validation
if(is.null(parallel)) {
# perform a total of cross_validation_repetitions repetitions of cross validation
set.seed(round(runif(1)*100000))
for(cv_repetitions in 1:cross_validation_repetitions) {
if(verbose) {
cat(paste0("Performing repetition ",cv_repetitions," out of ",cross_validation_repetitions,"..."),"\n")
}
# randomly set the cross validation entries for the current iteration
valid_entries <- which(x>0,arr.ind=TRUE)
cv_entries <- valid_entries[sample(1:nrow(valid_entries),size=round(nrow(valid_entries)*cross_validation_entries),replace=FALSE),]
# consider all the values for K
cont <- 0
pos_k <- 0
for(k in K) {
# consider the first k signatures to be used for the current configuration
pos_k <- pos_k + 1
# consider all the values for lambda
pos_l_alpha <- 0
for(l_alpha in lambda_values_alpha) {
pos_l_alpha <- pos_l_alpha + 1
pos_l_beta <- 0
for(l_beta in lambda_values_beta) {
pos_l_beta <- pos_l_beta + 1
# repeat the estimation for a number of cross_validation_iterations
x_cv <- NULL
cont <- cont + 1
for(cv_iteration in 1:cross_validation_iterations) {
if(verbose) {
cat(paste0("Performing cross validation iteration ",cv_iteration," out of ",cross_validation_iterations,"..."),"\n")
}
# set a percentage of cross_validation_entries entries to 0 in order to perform cross validation
if(cv_iteration==1) {
x_cv <- x
x_cv[cv_entries] <- 0
}
else {
if(!is.na(curr_iter_alpha[1])&&!is.na(curr_iter_beta[1])) {
predicted_counts <- curr_iter_alpha %*% curr_iter_beta
x_cv[cv_entries] <- predicted_counts[cv_entries]
}
}
# perform the inference
curr_results <- nmfLasso(x = x_cv,
K = k,
beta = starting_beta[[pos_k,1]],
background_signature = background_signature,
normalize_counts = normalize_counts,
nmf_runs = 10,
lambda_rate_alpha = l_alpha,
lambda_rate_beta = l_beta,
iterations = iterations,
max_iterations_lasso = max_iterations_lasso,
seed = round(runif(1)*100000),
verbose = FALSE)
curr_iter_alpha <- curr_results[["alpha"]]
curr_iter_beta <- curr_results[["beta"]]
curr_iter_loglik <- curr_results[["loglik_progression"]]
}
# save an estimate of mean squared error and stability of the solution
if(!is.na(curr_iter_alpha[1])&&!is.na(curr_iter_beta[1])) {
curr_predicted_counts <- round(curr_iter_alpha%*%curr_iter_beta)
curr_true_considered_counts <- as.vector(x[cv_entries])
curr_predicted_considered_counts <- as.vector(curr_predicted_counts[cv_entries])
error <- mean((curr_true_considered_counts-curr_predicted_considered_counts)^2)
grid_search_mse[pos_l_alpha,pos_l_beta,pos_k][[1]] <- c(grid_search_mse[pos_l_alpha,pos_l_beta,pos_k][[1]],error)
}
if((!is.na(curr_iter_loglik)[1])&&(curr_iter_loglik[1]<curr_iter_loglik[length(curr_iter_loglik)])) {
grid_search_loglik[pos_l_alpha,pos_l_beta,pos_k][[1]] <- c(grid_search_loglik[pos_l_alpha,pos_l_beta,pos_k][[1]],"increasing")
}
else if((!is.na(curr_iter_loglik)[1])&&(curr_iter_loglik[1]>=curr_iter_loglik[length(curr_iter_loglik)])) {
grid_search_loglik[pos_l_alpha,pos_l_beta,pos_k][[1]] <- c(grid_search_loglik[pos_l_alpha,pos_l_beta,pos_k][[1]],"decreasing")
}
if(verbose) {
cat("Progress",paste0(round((cont/(length(K)*length(lambda_values_alpha)*length(lambda_values_beta)))*100,digits=3),"%..."),"\n")
}
}
}
}
}
# save the results
results <- list(grid_search_mse=grid_search_mse,grid_search_loglik=grid_search_loglik)
}
else {
# perform the inference
res_clusterEvalQ <- clusterEvalQ(parallel,library("nnls"))
res_clusterEvalQ <- clusterEvalQ(parallel,library("nnlasso"))
clusterExport(parallel,varlist=c("x","K","starting_beta","background_signature","normalize_counts","cross_validation_entries"),envir=environment())
clusterExport(parallel,varlist=c("lambda_values_alpha","lambda_values_beta","cross_validation_iterations","iterations","max_iterations_lasso"),envir=environment())
clusterExport(parallel,varlist=c("grid_search_mse","grid_search_loglik","cross_validation_repetitions","verbose"),envir=environment())
clusterExport(parallel,c('nmfLasso','nmfLassoDecomposition','basis','nmf'),envir=environment())
clusterSetRNGStream(parallel,iseed=round(runif(1)*100000))
curr_results <- parLapply(parallel,1:cross_validation_repetitions,function(cv_rep) {
if(verbose) {
cat(paste0("Performing repetition ",cv_rep," out of ",cross_validation_repetitions,"..."),"\n")
}
# randomly set the cross validation entries for the current iteration
valid_entries <- which(x>0,arr.ind=TRUE)
cv_entries <- valid_entries[sample(1:nrow(valid_entries),size=round(nrow(valid_entries)*cross_validation_entries),replace=FALSE),]
# consider all the values for K
cont <- 0
pos_k <- 0
for(k in K) {
# consider the first k signatures to be used for the current configuration
pos_k <- pos_k + 1
# consider all the values for lambda
pos_l_alpha <- 0
for(l_alpha in lambda_values_alpha) {
pos_l_alpha <- pos_l_alpha + 1
pos_l_beta <- 0
for(l_beta in lambda_values_beta) {
pos_l_beta <- pos_l_beta + 1
# repeat the estimation for a number of cross_validation_iterations
x_cv <- NULL
cont <- cont + 1
for(cv_iteration in 1:cross_validation_iterations) {
# set a percentage of cross_validation_entries entries to 0 in order to perform cross validation
if(cv_iteration==1) {
x_cv <- x
x_cv[cv_entries] <- 0
}
else {
if(!is.na(curr_iter_alpha[1])&&!is.na(curr_iter_beta[1])) {
predicted_counts <- curr_iter_alpha %*% curr_iter_beta
x_cv[cv_entries] <- predicted_counts[cv_entries]
}
}
# perform the inference
curr_results <- nmfLasso(x = x_cv,
K = k,
beta = starting_beta[[pos_k,1]],
background_signature = background_signature,
normalize_counts = normalize_counts,
nmf_runs = 10,
lambda_rate_alpha = l_alpha,
lambda_rate_beta = l_beta,
iterations = iterations,
max_iterations_lasso = max_iterations_lasso,
seed = round(runif(1)*100000),
verbose = FALSE)
curr_iter_alpha <- curr_results[["alpha"]]
curr_iter_beta <- curr_results[["beta"]]
curr_iter_loglik <- curr_results[["loglik_progression"]]
}
# save an estimate of mean squared error and stability of the solution
if(!is.na(curr_iter_alpha[1])&&!is.na(curr_iter_beta[1])) {
curr_predicted_counts <- round(curr_iter_alpha%*%curr_iter_beta)
curr_true_considered_counts <- as.vector(x[cv_entries])
curr_predicted_considered_counts <- as.vector(curr_predicted_counts[cv_entries])
error <- mean((curr_true_considered_counts-curr_predicted_considered_counts)^2)
grid_search_mse[pos_l_alpha,pos_l_beta,pos_k][[1]] <- c(grid_search_mse[pos_l_alpha,pos_l_beta,pos_k][[1]],error)
}
if((!is.na(curr_iter_loglik)[1])&&(curr_iter_loglik[1]<curr_iter_loglik[length(curr_iter_loglik)])) {
grid_search_loglik[pos_l_alpha,pos_l_beta,pos_k][[1]] <- c(grid_search_loglik[pos_l_alpha,pos_l_beta,pos_k][[1]],"increasing")
}
else if((!is.na(curr_iter_loglik)[1])&&(curr_iter_loglik[1]>=curr_iter_loglik[length(curr_iter_loglik)])) {
grid_search_loglik[pos_l_alpha,pos_l_beta,pos_k][[1]] <- c(grid_search_loglik[pos_l_alpha,pos_l_beta,pos_k][[1]],"decreasing")
}
}
}
}
# save the results
curr_results <- list(grid_search_mse=grid_search_mse,grid_search_loglik=grid_search_loglik)
return(curr_results)
})
# save the results
results <- list(grid_search_mse=grid_search_mse,grid_search_loglik=grid_search_loglik)
for(par_res in 1:length(curr_results)) {
curr_par_res <- curr_results[[par_res]]
curr_par_res_grid_search_mse <- curr_par_res$grid_search_mse
curr_par_res_grid_search_loglik <- curr_par_res$grid_search_loglik
for(a in 1:dim(curr_par_res_grid_search_mse)[1]) {
for(b in 1:dim(curr_par_res_grid_search_mse)[2]) {
for(c in 1:dim(curr_par_res_grid_search_mse)[3]) {
if(!is.null(unlist(curr_par_res_grid_search_mse[a,b,c]))) {
results$grid_search_mse[[a,b,c]] <- c(unlist(results$grid_search_mse[a,b,c]),unlist(curr_par_res_grid_search_mse[a,b,c]))
results$grid_search_loglik[[a,b,c]] <- c(unlist(results$grid_search_loglik[a,b,c]),unlist(curr_par_res_grid_search_loglik[a,b,c]))
}
}
}
}
}
}
# close parallel
if(close_parallel) {
stopCluster(parallel)
}
return(results)
}
#' Perform the evaluation of different nmfLasso solutions by bootstrap for K (unknown) somatic mutational signatures given a set of observations x. The estimation can slow down because of
#' memory usage and intensive computations, when a big number of bootstrap repetitions is asked and when the analysis is performed for a big range of signatures (K). In this case,
#' an advice may be to split the computation into multiple smaller sets.
#'
#' @examples
#' data(background)
#' data(patients)
#' res = nmfLassoBootstrap(x=patients[1:100,],
#' K=3:5,
#' background_signature=background,
#' nmf_runs=1,
#' bootstrap_repetitions=2,
#' num_processes=NA,
#' seed=12345)
#'
#' @title nmfLassoBootstrap
#' @param x count matrix for a set of n patients and 96 trinucleotides.
#' @param K a range of numeric value (each of them greater than 1) indicating the number of signatures to be discovered.
#' @param starting_beta a list of starting beta value for each configuration of K. If it is NULL, starting betas are estimated by
#' NMF.
#' @param background_signature background signature to be used. If not provided, a warning is thrown and an initial value for it is
#' estimated by NMF. If beta is not NULL, this parameter is ignored.
#' @param normalize_counts if true, the input count matrix x is normalize such that the patients have the same number of mutation.
#' @param nmf_runs number of iteration (minimum 1) of NMF to be performed for a robust estimation of starting beta. If beta is not NULL,
#' this parameter is ignored.
#' @param bootstrap_repetitions Number of time bootstrap should be repeated. Higher values result in better estimate, but are computationally more expensive.
#' @param iterations Number of iterations to be performed. Each iteration corresponds to a first step where beta is fitted
#' and a second step where alpha is fitted.
#' @param max_iterations_lasso Number of maximum iterations to be performed during the sparsification via Lasso.
#' @param num_processes Number of processes to be used during parallel execution. To execute in single process mode,
#' this parameter needs to be set to either NA or NULL.
#' @param seed Seed for reproducibility.
#' @param verbose boolean; Shall I print all messages?
#' @param log_file log file where to print outputs when using parallel. If parallel execution is disabled, this parameter is ignored.
#' @return A list of 3 elements: stability, RSS and evar. Here, stability reports the estimared cosine similarity for alpha and beta at each bootstrap
#' repetition; RSS reports for each configuration the estimated residual sum of squares; finally, evar reports the explained variance.
#' @export nmfLassoBootstrap
#' @import NMF
#' @import nnlasso
#' @import nnls
#' @import parallel
#'
"nmfLassoBootstrap" <- function( x, K = 3:10, starting_beta = NULL, background_signature = NULL, normalize_counts = TRUE, nmf_runs = 10, bootstrap_repetitions = 50, iterations = 30, max_iterations_lasso = 10000, num_processes = Inf, seed = NULL, verbose = TRUE, log_file = "" ) {
# set the seed
set.seed(seed)
# check the input parameters
if(min(K)<2) {
if(verbose) {
cat("The minimum value of K is 2...","\n")
}
K <- K[K>=2]
if(length(K)==0) {
K <- 2
warning("No value of K greater than 2 is provided: setting K to 2...")
}
}
if(nmf_runs<1) {
if(verbose) {
cat("The minimum value of nmf_runs is 1...","\n")
}
nmf_runs <- 1
}
x <- as.matrix(x)
if(normalize_counts) {
x <- (x/rowSums(x))*2500
}
# no Lasso is considered here to speed up computations, i.e., this is an heuristic/approximated result
lambda_values_alpha <- 0.00
lambda_values_beta <- 0.00
# perform a grid search to estimate the best values of K and lambda
if(verbose) {
cat("Performing a total of",bootstrap_repetitions,"bootstrap repetitions to assess nmfLasso solutions for different K ranks...","\n")
}
# setting up parallel execution
parallel <- NULL
close_parallel <- FALSE
if(is.null(parallel)&&bootstrap_repetitions>1) {
if(is.na(num_processes) || is.null(num_processes)) {
parallel <- NULL
}
else if(num_processes==Inf) {
cores <- as.integer((detectCores()-1))
if(cores < 2) {
parallel <- NULL
}
else {
num_processes <- min(num_processes,bootstrap_repetitions)
parallel <- makeCluster(num_processes,outfile=log_file)
close_parallel <- TRUE
}
}
else {
num_processes <- min(num_processes,bootstrap_repetitions)
parallel <- makeCluster(num_processes,outfile=log_file)
close_parallel <- TRUE
}
if(verbose && !is.null(parallel)) {
cat("Executing",num_processes,"processes via parallel...","\n")
}
}
# estimate the background signature
if(is.null(background_signature)&&is.null(starting_beta)) {
warning("No background signature has been specified...")
background_signature_beta <- basis(nmf(t(x),rank=1,nrun=nmf_runs))
background_signature_beta <- t(background_signature_beta)
background_signature_beta <- background_signature_beta / rowSums(background_signature_beta)
background_signature <- as.numeric(background_signature_beta[1,])
}
# structure to save the starting values of beta for each K
if(is.null(starting_beta)) {
background_signature <- as.numeric(background_signature)
background_signature <- background_signature / sum(background_signature)
starting_beta <- array(list(),c(length(K),1))
rownames(starting_beta) <- paste0(as.character(K),"_Signatures")
colnames(starting_beta) <- "Value"
# estimate the contribution of the background to the observed counts
background_signature_beta <- t(background_signature)
background_signature_alpha <- matrix(0,nrow=dim(x)[1],ncol=1)
for(i in 1:dim(x)[1]) {
background_signature_alpha[i,] <- nnls(t(background_signature_beta),as.vector(x[i,]))$x
}
curr_x <- x - (background_signature_alpha %*% background_signature_beta)
curr_x[curr_x<0] <- 0
if(length(which(rowSums(t(curr_x))==0))>0) {
invalid_cols <- as.numeric(which(rowSums(t(curr_x))==0))
for(inv_cols in invalid_cols) {
curr_x[sample(1:length(curr_x[,inv_cols]),size=1),inv_cols] <- 1e-05
}
}
# compute starting values for beta
pos_k <- 0
for(k in K) {
# compute the initial values of beta
if(verbose) {
cat(paste0("Computing the initial values of beta by standard NMF for K equals to ",k,"..."),"\n")
}
pos_k <- pos_k + 1
beta <- NULL
beta <- basis(nmf(t(curr_x),rank=(k-1),nrun=nmf_runs))
beta <- t(beta)
beta <- rbind(background_signature,beta)
# normalize and save beta for the current value of K
rownames(beta) <- c("Background",paste0("S",1:(nrow(beta)-1)))
colnames(beta) <- colnames(x)
beta <- beta / rowSums(beta)
starting_beta[[pos_k,1]] <- beta
}
}
if(verbose) {
cat("Starting bootstrap for a total of",bootstrap_repetitions,"repetitions...","\n")
}
# structure to save the results of the grid search
bootstrap_rss <- array(list(),c(length(K),2))
rownames(bootstrap_rss) <- paste0(as.character(K),"_Signatures")
colnames(bootstrap_rss) <- c("RSS bootstrapped data","RSS randomized data")
bootstrap_evar <- bootstrap_rss
colnames(bootstrap_evar) <- c("Explained Variance bootstrapped data","Explained Variance randomized data")
bootstrap_stability <- array(list(),c(length(K),4))
rownames(bootstrap_stability) <- paste0(as.character(K),"_Signatures")
colnames(bootstrap_stability) <- c("Similarity alpha bootstrapped data","Similarity beta bootstrapped data","Similarity alpha randomized data","Similarity beta randomized data")
starting_values_bootstrap = bootstrap_stability
# generate a set of randomized data from x
set.seed(round(runif(1)*100000))
randomized_x <- x
for(i in 1:ncol(randomized_x)) {
randomized_x[,i] <- randomized_x[sample(1:dim(randomized_x)[1],size=dim(randomized_x)[1],replace=FALSE),i]
}
for(j in 1:nrow(randomized_x)) {
randomized_x[j,] <- randomized_x[j,sample(1:dim(randomized_x)[2],size=dim(randomized_x)[2],replace=FALSE)]
}
# compute starting values of alpha and beta in order to estimate stability of the considered solutions (and ranks)
pos_k <- 0
for(k in K) {
pos_k <- pos_k + 1
is.valid <- FALSE
while(!is.valid) {
curr_results <- nmfLasso(x = x,
K = k,
beta = starting_beta[[pos_k,1]],
background_signature = background_signature,
normalize_counts = normalize_counts,
nmf_runs = 10,
lambda_rate_alpha = lambda_values_alpha,
lambda_rate_beta = lambda_values_beta,
iterations = iterations,
max_iterations_lasso = max_iterations_lasso,
seed = round(runif(1)*100000),
verbose = FALSE)
if(!is.na(curr_results$best_loglik)) {
is.valid <- TRUE
}
}
starting_values_bootstrap[[pos_k,1]] <- curr_results$alpha
starting_values_bootstrap[[pos_k,2]] <- curr_results$beta
is.valid <- FALSE
while(!is.valid) {
curr_results <- nmfLasso(x = randomized_x,
K = k,
beta = starting_beta[[pos_k,1]],
background_signature = background_signature,
normalize_counts = normalize_counts,
nmf_runs = 10,
lambda_rate_alpha = lambda_values_alpha,
lambda_rate_beta = lambda_values_beta,
iterations = iterations,
max_iterations_lasso = max_iterations_lasso,
seed = round(runif(1)*100000),
verbose = FALSE)
if(!is.na(curr_results$best_loglik)) {
is.valid <- TRUE
}
}
starting_values_bootstrap[[pos_k,3]] <- curr_results$alpha
starting_values_bootstrap[[pos_k,4]] <- curr_results$beta
}
# now starting cross validation
if(is.null(parallel)) {
# perform a total of bootstrap_repetitions repetitions of bootstrap
for(nboot in 1:bootstrap_repetitions) {
if(verbose) {
cat(paste0("Performing repetition ",nboot," out of ",bootstrap_repetitions,"..."),"\n")
}
# generate bootstrapped dataset from data
bootstrapped_data <- x
for(i in 1:nrow(x)) {
num_mutations <- sum(x[i,])
mut_distribution <- as.numeric(x[i,]/sum(x[i,]))
sampling <- sample(1:96,size=num_mutations,replace=TRUE,prob=mut_distribution)
bootstrapped_data[i,] <- 0
for(j in sampling) {
bootstrapped_data[i,j] <- bootstrapped_data[i,j] + 1
}
}
# generate randomized data from the bootstrapped data
randomized_data <- bootstrapped_data
for(i in 1:ncol(randomized_data)) {
randomized_data[,i] <- randomized_data[sample(1:dim(randomized_data)[1],size=dim(randomized_data)[1],replace=FALSE),i]
}
for(j in 1:nrow(randomized_data)) {
randomized_data[j,] <- randomized_data[j,sample(1:dim(randomized_data)[2],size=dim(randomized_data)[2],replace=FALSE)]
}
# perform inference on bootstrapped and randomized data
pos_k <- 0
for(k in K) {
pos_k <- pos_k + 1
# perform the analysis for bootstrapped data
res <- nmfLasso(x=bootstrapped_data,K=k,beta=starting_beta[[pos_k,1]],lambda_rate_alpha=lambda_values_alpha,lambda_rate_beta=lambda_values_beta,verbose=FALSE)
if(!is.na(res$best_loglik)) {
# compute cosine similarity of alpha for bootstrapped data
similarity <- NULL
for(i in 1:ncol(res$alpha)) {
curr_similarity <- ((sum(starting_values_bootstrap[[pos_k,1]][,i]*res$alpha[,i]))/sqrt(sum(starting_values_bootstrap[[pos_k,1]][,i]^2)*sum(res$alpha[,i]^2)))
similarity <- c(similarity,curr_similarity)
}
bootstrap_stability[[pos_k,"Similarity alpha bootstrapped data"]] <- c(unlist(bootstrap_stability[[pos_k,"Similarity alpha bootstrapped data"]]),mean(similarity))
# compute cosine similarity of beta for bootstrapped data
similarity <- NULL
for(i in 1:nrow(res$beta)) {
curr_similarity <- ((sum(starting_values_bootstrap[[pos_k,2]][i,]*res$beta[i,]))/sqrt(sum(starting_values_bootstrap[[pos_k,2]][i,]^2)*sum(res$beta[i,]^2)))
similarity <- c(similarity,curr_similarity)
}
bootstrap_stability[[pos_k,"Similarity beta bootstrapped data"]] <- c(unlist(bootstrap_stability[[pos_k,"Similarity beta bootstrapped data"]]),mean(similarity))
# compute RSS for bootstrapped data
predictions <- res$alpha%*%res$beta
mse <- NULL
for(i in 1:nrow(predictions)) {
for(j in 1:ncol(predictions)) {
mse <- c(mse,((bootstrapped_data[i,j]-predictions[i,j])^2))
}
}
mse <- sum(mse)
bootstrap_rss[[pos_k,"RSS bootstrapped data"]] <- c(unlist(bootstrap_rss[[pos_k,"RSS bootstrapped data"]]),mse)
# compute Explained Variance for bootstrapped data
evar <- (1 - (mse/sum(bootstrapped_data^2)))
bootstrap_evar[[pos_k,"Explained Variance bootstrapped data"]] <- c(unlist(bootstrap_evar[[pos_k,"Explained Variance bootstrapped data"]]),evar)
}
else {
bootstrap_stability[[pos_k,"Similarity alpha bootstrapped data"]] <- c(unlist(bootstrap_stability[[pos_k,"Similarity alpha bootstrapped data"]]),NA)
bootstrap_stability[[pos_k,"Similarity beta bootstrapped data"]] <- c(unlist(bootstrap_stability[[pos_k,"Similarity beta bootstrapped data"]]),NA)
bootstrap_rss[[pos_k,"RSS bootstrapped data"]] <- c(unlist(bootstrap_rss[[pos_k,"RSS bootstrapped data"]]),NA)
bootstrap_evar[[pos_k,"Explained Variance bootstrapped data"]] <- c(unlist(bootstrap_evar[[pos_k,"Explained Variance bootstrapped data"]]),NA)
}
# perform the analysis for randomized data
res <- nmfLasso(x=randomized_data,K=k,beta=starting_beta[[pos_k,1]],lambda_rate_alpha=lambda_values_alpha,lambda_rate_beta=lambda_values_beta,verbose=FALSE)
if(!is.na(res$best_loglik)) {
# compute cosine similarity of alpha for randomized data
similarity <- NULL
for(i in 1:ncol(res$alpha)) {
curr_similarity <- ((sum(starting_values_bootstrap[[pos_k,3]][,i]*res$alpha[,i]))/sqrt(sum(starting_values_bootstrap[[pos_k,3]][,i]^2)*sum(res$alpha[,i]^2)))
similarity <- c(similarity,curr_similarity)
}
bootstrap_stability[[pos_k,"Similarity alpha randomized data"]] <- c(unlist(bootstrap_stability[[pos_k,"Similarity alpha randomized data"]]),mean(similarity))
# compute cosine similarity of beta for randomized data
similarity <- NULL
for(i in 1:nrow(res$beta)) {
curr_similarity <- ((sum(starting_values_bootstrap[[pos_k,4]][i,]*res$beta[i,]))/sqrt(sum(starting_values_bootstrap[[pos_k,4]][i,]^2)*sum(res$beta[i,]^2)))
similarity <- c(similarity,curr_similarity)
}
bootstrap_stability[[pos_k,"Similarity beta randomized data"]] <- c(unlist(bootstrap_stability[[pos_k,"Similarity beta randomized data"]]),mean(similarity))
# compute RSS for randomized data
predictions <- res$alpha%*%res$beta
mse <- NULL
for(i in 1:nrow(predictions)) {
for(j in 1:ncol(predictions)) {
mse <- c(mse,((randomized_data[i,j]-predictions[i,j])^2))
}
}
mse <- sum(mse)
bootstrap_rss[[pos_k,"RSS randomized data"]] <- c(unlist(bootstrap_rss[[pos_k,"RSS randomized data"]]),mse)
# compute Explained Variance for randomized data
evar <- (1 - (mse/sum(randomized_data^2)))
bootstrap_evar[[pos_k,"Explained Variance randomized data"]] <- c(unlist(bootstrap_evar[[pos_k,"Explained Variance randomized data"]]),evar)
}
else {
bootstrap_stability[[pos_k,"Similarity alpha randomized data"]] <- c(unlist(bootstrap_stability[[pos_k,"Similarity alpha randomized data"]]),NA)
bootstrap_stability[[pos_k,"Similarity beta randomized data"]] <- c(unlist(bootstrap_stability[[pos_k,"Similarity beta randomized data"]]),NA)
bootstrap_rss[[pos_k,"RSS randomized data"]] <- c(unlist(bootstrap_rss[[pos_k,"RSS randomized data"]]),NA)
bootstrap_evar[[pos_k,"Explained Variance randomized data"]] <- c(unlist(bootstrap_evar[[pos_k,"Explained Variance randomized data"]]),NA)
}
}
if(verbose) {
cat("Progress",paste0(round((nboot/bootstrap_repetitions)*100,digits=3),"%..."),"\n")
}
}
# save the results
results <- list(stability=bootstrap_stability,RSS=bootstrap_rss,evar=bootstrap_evar)
}
else {
# perform the inference
res_clusterEvalQ <- clusterEvalQ(parallel,library("nnls"))
res_clusterEvalQ <- clusterEvalQ(parallel,library("nnlasso"))
clusterExport(parallel,varlist=c("x","K","starting_beta","background_signature","normalize_counts"),envir=environment())
clusterExport(parallel,varlist=c("lambda_values_alpha","lambda_values_beta","iterations","max_iterations_lasso"),envir=environment())
clusterExport(parallel,varlist=c("bootstrap_stability","bootstrap_rss","bootstrap_evar","bootstrap_repetitions","verbose"),envir=environment())
clusterExport(parallel,c('nmfLasso','nmfLassoDecomposition','basis','nmf'),envir=environment())
clusterSetRNGStream(parallel,iseed=round(runif(1)*100000))
curr_results <- parLapply(parallel,1:bootstrap_repetitions,function(nboot) {
if(verbose) {
cat(paste0("Performing repetition ",nboot," out of ",bootstrap_repetitions,"..."),"\n")
}
# generate bootstrapped dataset from data
bootstrapped_data <- x
for(i in 1:nrow(x)) {
num_mutations <- sum(x[i,])
mut_distribution <- as.numeric(x[i,]/sum(x[i,]))
sampling <- sample(1:96,size=num_mutations,replace=TRUE,prob=mut_distribution)
bootstrapped_data[i,] <- 0
for(j in sampling) {
bootstrapped_data[i,j] <- bootstrapped_data[i,j] + 1
}
}
# generate randomized data from the bootstrapped data
randomized_data <- bootstrapped_data
for(i in 1:ncol(randomized_data)) {
randomized_data[,i] <- randomized_data[sample(1:dim(randomized_data)[1],size=dim(randomized_data)[1],replace=FALSE),i]
}
for(j in 1:nrow(randomized_data)) {
randomized_data[j,] <- randomized_data[j,sample(1:dim(randomized_data)[2],size=dim(randomized_data)[2],replace=FALSE)]
}
# perform inference on bootstrapped and randomized data
pos_k <- 0
for(k in K) {
pos_k <- pos_k + 1
# perform the analysis for bootstrapped data
res <- nmfLasso(x=bootstrapped_data,K=k,beta=starting_beta[[pos_k,1]],lambda_rate_alpha=lambda_values_alpha,lambda_rate_beta=lambda_values_beta,verbose=FALSE)
if(!is.na(res$best_loglik)) {
# compute cosine similarity of alpha for bootstrapped data
similarity <- NULL
for(i in 1:ncol(res$alpha)) {
curr_similarity <- ((sum(starting_values_bootstrap[[pos_k,1]][,i]*res$alpha[,i]))/sqrt(sum(starting_values_bootstrap[[pos_k,1]][,i]^2)*sum(res$alpha[,i]^2)))
similarity <- c(similarity,curr_similarity)
}
bootstrap_stability[[pos_k,"Similarity alpha bootstrapped data"]] <- c(unlist(bootstrap_stability[[pos_k,"Similarity alpha bootstrapped data"]]),mean(similarity))
# compute cosine similarity of beta for bootstrapped data
similarity <- NULL
for(i in 1:nrow(res$beta)) {
curr_similarity <- ((sum(starting_values_bootstrap[[pos_k,2]][i,]*res$beta[i,]))/sqrt(sum(starting_values_bootstrap[[pos_k,2]][i,]^2)*sum(res$beta[i,]^2)))
similarity <- c(similarity,curr_similarity)
}
bootstrap_stability[[pos_k,"Similarity beta bootstrapped data"]] <- c(unlist(bootstrap_stability[[pos_k,"Similarity beta bootstrapped data"]]),mean(similarity))
# compute RSS for bootstrapped data
predictions <- res$alpha%*%res$beta
mse <- NULL
for(i in 1:nrow(predictions)) {
for(j in 1:ncol(predictions)) {
mse <- c(mse,((bootstrapped_data[i,j]-predictions[i,j])^2))
}
}
mse <- sum(mse)
bootstrap_rss[[pos_k,"RSS bootstrapped data"]] <- c(unlist(bootstrap_rss[[pos_k,"RSS bootstrapped data"]]),mse)
# compute Explained Variance for bootstrapped data
evar <- (1 - (mse/sum(bootstrapped_data^2)))
bootstrap_evar[[pos_k,"Explained Variance bootstrapped data"]] <- c(unlist(bootstrap_evar[[pos_k,"Explained Variance bootstrapped data"]]),evar)
}
else {
bootstrap_stability[[pos_k,"Similarity alpha bootstrapped data"]] <- c(unlist(bootstrap_stability[[pos_k,"Similarity alpha bootstrapped data"]]),NA)
bootstrap_stability[[pos_k,"Similarity beta bootstrapped data"]] <- c(unlist(bootstrap_stability[[pos_k,"Similarity beta bootstrapped data"]]),NA)
bootstrap_rss[[pos_k,"RSS bootstrapped data"]] <- c(unlist(bootstrap_rss[[pos_k,"RSS bootstrapped data"]]),NA)
bootstrap_evar[[pos_k,"Explained Variance bootstrapped data"]] <- c(unlist(bootstrap_evar[[pos_k,"Explained Variance bootstrapped data"]]),NA)
}
# perform the analysis for randomized data
res <- nmfLasso(x=randomized_data,K=k,beta=starting_beta[[pos_k,1]],lambda_rate_alpha=lambda_values_alpha,lambda_rate_beta=lambda_values_beta,verbose=FALSE)
if(!is.na(res$best_loglik)) {
# compute cosine similarity of alpha for randomized data
similarity <- NULL
for(i in 1:ncol(res$alpha)) {
curr_similarity <- ((sum(starting_values_bootstrap[[pos_k,3]][,i]*res$alpha[,i]))/sqrt(sum(starting_values_bootstrap[[pos_k,3]][,i]^2)*sum(res$alpha[,i]^2)))
similarity <- c(similarity,curr_similarity)
}
bootstrap_stability[[pos_k,"Similarity alpha randomized data"]] <- c(unlist(bootstrap_stability[[pos_k,"Similarity alpha randomized data"]]),mean(similarity))
# compute cosine similarity of beta for randomized data
similarity <- NULL
for(i in 1:nrow(res$beta)) {
curr_similarity <- ((sum(starting_values_bootstrap[[pos_k,4]][i,]*res$beta[i,]))/sqrt(sum(starting_values_bootstrap[[pos_k,4]][i,]^2)*sum(res$beta[i,]^2)))
similarity <- c(similarity,curr_similarity)
}
bootstrap_stability[[pos_k,"Similarity beta randomized data"]] <- c(unlist(bootstrap_stability[[pos_k,"Similarity beta randomized data"]]),mean(similarity))
# compute RSS for randomized data
predictions <- res$alpha%*%res$beta
mse <- NULL
for(i in 1:nrow(predictions)) {
for(j in 1:ncol(predictions)) {
mse <- c(mse,((randomized_data[i,j]-predictions[i,j])^2))
}
}
mse <- sum(mse)
bootstrap_rss[[pos_k,"RSS randomized data"]] <- c(unlist(bootstrap_rss[[pos_k,"RSS randomized data"]]),mse)
# compute Explained Variance for randomized data
evar <- (1 - (mse/sum(randomized_data^2)))
bootstrap_evar[[pos_k,"Explained Variance randomized data"]] <- c(unlist(bootstrap_evar[[pos_k,"Explained Variance randomized data"]]),evar)
}
else {
bootstrap_stability[[pos_k,"Similarity alpha randomized data"]] <- c(unlist(bootstrap_stability[[pos_k,"Similarity alpha randomized data"]]),NA)
bootstrap_stability[[pos_k,"Similarity beta randomized data"]] <- c(unlist(bootstrap_stability[[pos_k,"Similarity beta randomized data"]]),NA)
bootstrap_rss[[pos_k,"RSS randomized data"]] <- c(unlist(bootstrap_rss[[pos_k,"RSS randomized data"]]),NA)
bootstrap_evar[[pos_k,"Explained Variance randomized data"]] <- c(unlist(bootstrap_evar[[pos_k,"Explained Variance randomized data"]]),NA)
}
}
# save the results
curr_results <- list(stability=bootstrap_stability,RSS=bootstrap_rss,evar=bootstrap_evar)
return(curr_results)
})
# save the results
results <- list(stability=bootstrap_stability,RSS=bootstrap_rss,evar=bootstrap_evar)
for(par_res in 1:length(curr_results)) {
curr_par_res <- curr_results[[par_res]]
curr_par_res_stability <- curr_par_res$stability
curr_par_res_rss <- curr_par_res$RSS
curr_par_res_evar <- curr_par_res$evar
for(a in 1:dim(curr_par_res_stability)[1]) {
for(b in 1:dim(curr_par_res_stability)[2]) {
results$stability[[a,b]] <- c(unlist(results$stability[a,b]),unlist(curr_par_res_stability[a,b]))
}
}
for(a in 1:dim(curr_par_res_rss)[1]) {
for(b in 1:dim(curr_par_res_rss)[2]) {
results$RSS[[a,b]] <- c(unlist(results$RSS[a,b]),unlist(curr_par_res_rss[a,b]))
results$evar[[a,b]] <- c(unlist(results$evar[a,b]),unlist(curr_par_res_evar[a,b]))
}
}
}
}
# close parallel
if(close_parallel) {
stopCluster(parallel)
}
return(results)
}
#' Perform a robust estimation of the starting betas for the nmfLasso method
#'
#' @examples
#' data(background)
#' data(patients)
#' res = startingBetaEstimation(x=patients[1:100,],
#' K=3:5,
#' background_signature=background,
#' nmf_runs=1,
#' seed=12345)
#'
#' @title startingBetaEstimation
#' @param x count matrix for a set of n patients and 96 trinucleotides.
#' @param K numeric value (minimum 2) indicating the number of signatures to be discovered.
#' @param background_signature background signature to be used. If not provided, a warning is thrown and an initial value for it is
#' estimated by NMF. If beta is not NULL, this parameter is ignored.
#' @param normalize_counts if true, the input count matrix x is normalize such that the patients have the same number of mutation.
#' @param nmf_runs number of iteration (minimum 1) of NMF to be performed for a robust estimation of starting beta. If beta is not NULL,
#' this parameter is ignored.
#' @param seed Seed for reproducibility.
#' @param verbose boolean; Shall I print all messages?
#' @return A list containing the starting beta values for each configuration of K.
#' @export startingBetaEstimation
#' @import NMF
#' @import nnls
#'
"startingBetaEstimation" <- function( x, K = 3:10, background_signature = NULL, normalize_counts = TRUE, nmf_runs = 10, seed = NULL, verbose = TRUE ) {
# set the seed
set.seed(seed)
# check the input parameters
if(min(K)<2) {
if(verbose) {
cat("The minimum value of K is 2...","\n")
}
K <- K[K>=2]
if(length(K)==0) {
K <- 2
warning("No value of K greater than 2 is provided: setting K to 2...")
}
}
if(nmf_runs<1) {
if(verbose) {
cat("The minimum value of nmf_runs is 1...","\n")
}
nmf_runs <- 1
}
x <- as.matrix(x)
if(normalize_counts) {
x <- (x/rowSums(x))*2500
}
# estimate the background signature
if(is.null(background_signature)) {
warning("No background signature has been specified...")
background_signature_beta <- basis(nmf(t(x),rank=1,nrun=nmf_runs))
background_signature_beta <- t(background_signature_beta)
background_signature_beta <- background_signature_beta / rowSums(background_signature_beta)
background_signature <- as.numeric(background_signature_beta[1,])
}
background_signature <- as.numeric(background_signature)
background_signature <- background_signature / sum(background_signature)
# estimate the contribution of the background to the observed counts
background_signature_beta <- t(background_signature)
background_signature_alpha <- matrix(0,nrow=dim(x)[1],ncol=1)
for(i in 1:dim(x)[1]) {
background_signature_alpha[i,] <- nnls(t(background_signature_beta),as.vector(x[i,]))$x
}
curr_x <- x - (background_signature_alpha %*% background_signature_beta)
curr_x[curr_x<0] <- 0
if(length(which(rowSums(t(curr_x))==0))>0) {
invalid_cols <- as.numeric(which(rowSums(t(curr_x))==0))
for(inv_cols in invalid_cols) {
curr_x[sample(1:length(curr_x[,inv_cols]),size=1),inv_cols] <- 1e-05
}
}
# perform a robust estimation of the starting beta for the nmfLasso method
if(verbose) {
cat("Performing a robust estimation of the starting betas for the nmfLasso method...","\n")
}
# structure to save the starting values of beta for each K
starting_beta <- array(list(),c(length(K),1))
rownames(starting_beta) <- paste0(as.character(K),"_signatures")
colnames(starting_beta) <- "Value"
# consider all the values of K
pos_k <- 0
for(k in K) {
pos_k <- pos_k + 1
beta <- NULL
# compute the initial values of beta
if(verbose) {
cat("Computing the initial values of beta by standard NMF...","\n")
}
beta <- basis(nmf(t(curr_x),rank=(k-1),nrun=nmf_runs))
beta <- t(beta)
beta <- rbind(background_signature,beta)
# normalize and save beta for the current value of K
beta <- beta / rowSums(beta)
rownames(beta) <- c("Background",paste0("S",1:(nrow(beta)-1)))
colnames(beta) <- colnames(x)
starting_beta[[pos_k,1]] <- beta
if(verbose) {
cat("Progress",paste0(round((pos_k/length(K))*100,digits=3),"%..."),"\n")
}
}
return(starting_beta)
}
#' Estimate the range of lambda values for alpha to be considered in the signature inference. Note that too small values of lambda
#' result in dense exposures, but too large values lead to bad fit of the counts.
#'
#' @examples
#' data(background)
#' data(patients)
#' res = lambdaRangeAlphaEvaluation(x=patients[1:100,],
#' K=5,background_signature=background,
#' nmf_runs=1,lambda_values=c(0.01,0.05),
#' num_processes=NA,
#' seed=12345)
#'
#' @title lambdaRangeAlphaEvaluation
#' @param x count matrix for a set of n patients and 96 trinucleotides.
#' @param K numeric value (minimum 2) indicating the number of signatures to be discovered.
#' @param beta starting beta for the estimation. If it is NULL, starting beta is estimated by NMF.
#' @param background_signature background signature to be used. If not provided, a warning is thrown and an initial value for it is
#' estimated by NMF. If beta is not NULL, this parameter is ignored.
#' @param normalize_counts if true, the input count matrix x is normalize such that the patients have the same number of mutation.
#' @param nmf_runs number of iteration (minimum 1) of NMF to be performed for a robust estimation of starting beta. If beta is not NULL,
#' this parameter is ignored.
#' @param lambda_values value of LASSO to be used for alpha between 0 and 1. This value should be greater than 0. 1 is the value of LASSO
#' that would shrink all the signatures to 0 within one step. The higher lambda_values is, the sparser are the resulting exposures,
#' but too large values may result in a reduced fit of the observed counts.
#' @param iterations Number of iterations to be performed. Each iteration corresponds to a first step where beta is fitted
#' and a second step where alpha is fitted.
#' @param max_iterations_lasso Number of maximum iterations to be performed during the sparsification via Lasso.
#' @param num_processes Number of processes to be used during parallel execution. To execute in single process mode,
#' this parameter needs to be set to either NA or NULL.
#' @param seed Seed for reproducibility.
#' @param verbose boolean; Shall I print all messages?
#' @param log_file log file where to print outputs when using parallel. If parallel execution is disabled, this parameter is ignored.
#' @return A list corresponding to results of the function nmfLasso for each value of lambda to be tested. This function allows
#' to test a good range of lambda values for alpha to be considered. One should keep in mind that too small values generate dense solution,
#' while too high ones leads to poor fit. This behavior is resampled in the values of loglik_progression, which should be increasing:
#' too small values of lambda results in unstable log-likelihood through the iterations, while too large values make log-likelihood
#' drop.
#' @export lambdaRangeAlphaEvaluation
#' @import NMF
#' @import nnlasso
#' @import nnls
#' @import parallel
#'
"lambdaRangeAlphaEvaluation" <- function( x, K = 5, beta = NULL, background_signature = NULL, normalize_counts = TRUE, nmf_runs = 10, lambda_values = c(0.01, 0.05, 0.10, 0.20), iterations = 30, max_iterations_lasso = 10000, num_processes = Inf, seed = NULL, verbose = TRUE, log_file = "" ) {
# set the seed
set.seed(seed)
# check the input parameters
if(K<2) {
if(verbose) {
cat("The minimum value of K is 2...","\n")
}
K <- 2
}
if(nmf_runs<1) {
if(verbose) {
cat("The minimum value of nmf_runs is 1...","\n")
}
nmf_runs <- 1
}
x <- as.matrix(x)
if(normalize_counts) {
x_not_normalized <- x
x <- (x/rowSums(x))*2500
}
lambda_values <- sort(unique(lambda_values))
# compute the initial values of beta
if(is.null(beta)) {
if(verbose) {
cat("Computing the initial values of beta by standard NMF...","\n")
}
# add a signature to beta (leading to K signatures in total) to explicitly model background noise
if(is.null(background_signature)) {
warning("No background signature has been specified...")
background_signature_beta <- basis(nmf(t(x),rank=1,nrun=nmf_runs))
background_signature_beta <- t(background_signature_beta)
background_signature_beta <- background_signature_beta / rowSums(background_signature_beta)
background_signature <- as.numeric(background_signature_beta[1,])
}
else {
background_signature <- as.numeric(background_signature)
background_signature <- background_signature / sum(background_signature)
background_signature_beta <- t(background_signature)
}
background_signature_alpha <- matrix(0,nrow=dim(x)[1],ncol=1)
for(i in 1:dim(x)[1]) {
background_signature_alpha[i,] <- nnls(t(background_signature_beta),as.vector(x[i,]))$x
}
curr_x <- x - (background_signature_alpha %*% background_signature_beta)
curr_x[curr_x<0] <- 0
if(length(which(rowSums(t(curr_x))==0))>0) {
invalid_cols <- as.numeric(which(rowSums(t(curr_x))==0))
for(inv_cols in invalid_cols) {
curr_x[sample(1:length(curr_x[,inv_cols]),size=1),inv_cols] <- 1e-05
}
}
beta <- basis(nmf(t(curr_x),rank=(K-1),nrun=nmf_runs))
beta <- t(beta)
beta <- rbind(background_signature,beta)
}
beta <- beta / rowSums(beta)
rownames(beta) <- c("Background",paste0("S",1:(nrow(beta)-1)))
colnames(beta) <- colnames(x)
# setting up parallel execution
parallel <- NULL
close_parallel <- FALSE
if(is.null(parallel)&&length(lambda_values)>1) {
if(is.na(num_processes) || is.null(num_processes)) {
parallel <- NULL
}
else if(num_processes==Inf) {
cores <- as.integer((detectCores()-1))
if(cores < 2) {
parallel <- NULL
}
else {
num_processes <- min(num_processes,length(lambda_values))
parallel <- makeCluster(num_processes,outfile=log_file)
close_parallel <- TRUE
}
}
else {
num_processes <- min(num_processes,length(lambda_values))
parallel <- makeCluster(num_processes,outfile=log_file)
close_parallel <- TRUE
}
if(verbose && !is.null(parallel)) {
cat("Executing",num_processes,"processes via parallel...","\n")
}
}
# structure to save the estimated signatures
lambda_results <- array(list(),c(length(K),length(lambda_values)))
rownames(lambda_results) <- paste0(as.character(K),"_signatures")
colnames(lambda_results) <- paste0(as.character(lambda_values),"_lambda")
if(verbose) {
cat("Performing estimation of lambda range for alpha...","\n")
}
# perform signature discovery for all the values of lambda
if(is.null(parallel)) {
set.seed(round(runif(1)*100000))
cont <- 0
for(l in lambda_values) {
# perform the inference
curr_results <- nmfLasso(x = x,
K = K,
beta = beta,
normalize_counts = normalize_counts,
lambda_rate_alpha = l,
lambda_rate_beta = 0.0,
iterations = iterations,
max_iterations_lasso = max_iterations_lasso,
seed = round(runif(1)*100000),
verbose = FALSE)
# save the results for the current configuration
cont <- cont + 1
# rescale alpha to the original magnitude
if(normalize_counts) {
curr_results$starting_alpha <- curr_results$starting_alpha * (rowSums(x_not_normalized)/2500)
curr_results$alpha <- curr_results$alpha * (rowSums(x_not_normalized)/2500)
}
lambda_results[[1,cont]] <- curr_results
if(verbose) {
cat("Progress",paste0(round((cont/(length(K)*length(lambda_values)))*100,digits=3),"%..."),"\n")
}
}
}
else {
res_clusterEvalQ <- clusterEvalQ(parallel,library("nnls"))
res_clusterEvalQ <- clusterEvalQ(parallel,library("nnlasso"))
clusterExport(parallel,varlist=c("x","K","beta","normalize_counts","iterations","max_iterations_lasso"),envir=environment())
clusterExport(parallel,c('nmfLasso','nmfLassoDecomposition','basis','nmf'),envir=environment())
clusterSetRNGStream(parallel,iseed=round(runif(1)*100000))
lambda_results_res <- parLapply(parallel,lambda_values,function(l) {
# perform the inference
curr_results <- nmfLasso(x = x,
K = K,
beta = beta,
normalize_counts = normalize_counts,
lambda_rate_alpha = l,
lambda_rate_beta = 0.0,
iterations = iterations,
max_iterations_lasso = max_iterations_lasso,
seed = round(runif(1)*100000),
verbose = FALSE)
return(curr_results)
})
for(i in 1:ncol(lambda_results)) {
# rescale alpha to the original magnitude
if(normalize_counts) {
lambda_results_res[[i]]$starting_alpha <- lambda_results_res[[i]]$starting_alpha * (rowSums(x_not_normalized)/2500)
lambda_results_res[[i]]$alpha <- lambda_results_res[[i]]$alpha * (rowSums(x_not_normalized)/2500)
}
lambda_results[[1,i]] <- lambda_results_res[[i]]
}
}
# close parallel
if(close_parallel) {
stopCluster(parallel)
}
return(lambda_results)
}
#' Estimate the range of lambda values for beta to be considered in the signature inference. Note that too small values of lambda
#' result in dense signatures, but too large values lead to bad fit of the counts.
#'
#' @examples
#' data(background)
#' data(patients)
#' res = lambdaRangeBetaEvaluation(x=patients[1:100,],
#' K=5,
#' background_signature=background,
#' nmf_runs=1,
#' lambda_values=c(0.01,0.05),
#' num_processes=NA,
#' seed=12345)
#'
#' @title lambdaRangeBetaEvaluation
#' @param x count matrix for a set of n patients and 96 trinucleotides.
#' @param K numeric value (minimum 2) indicating the number of signatures to be discovered.
#' @param beta starting beta for the estimation. If it is NULL, starting beta is estimated by NMF.
#' @param background_signature background signature to be used. If not provided, a warning is thrown and an initial value for it is
#' estimated by NMF. If beta is not NULL, this parameter is ignored.
#' @param normalize_counts if true, the input count matrix x is normalize such that the patients have the same number of mutation.
#' @param nmf_runs number of iteration (minimum 1) of NMF to be performed for a robust estimation of starting beta. If beta is not NULL,
#' this parameter is ignored.
#' @param lambda_values value of LASSO to be used for beta between 0 and 1. This value should be greater than 0. 1 is the value of LASSO
#' that would shrink all the signatures to 0 within one step. The higher lambda_values is, the sparser are the resulting signatures,
#' but too large values may result in a reduced fit of the observed counts.
#' @param iterations Number of iterations to be performed. Each iteration corresponds to a first step where beta is fitted
#' and a second step where alpha is fitted.
#' @param max_iterations_lasso Number of maximum iterations to be performed during the sparsification via Lasso.
#' @param num_processes Number of processes to be used during parallel execution. To execute in single process mode,
#' this parameter needs to be set to either NA or NULL.
#' @param seed Seed for reproducibility.
#' @param verbose boolean; Shall I print all messages?
#' @param log_file log file where to print outputs when using parallel. If parallel execution is disabled, this parameter is ignored.
#' @return A list corresponding to results of the function nmfLasso for each value of lambda to be tested. This function allows
#' to test a good range of lambda values for beta to be considered. One should keep in mind that too small values generate dense solution,
#' while too high ones leads to poor fit. This behavior is resampled in the values of loglik_progression, which should be increasing:
#' too small values of lambda results in unstable log-likelihood through the iterations, while too large values make log-likelihood
#' drop.
#' @export lambdaRangeBetaEvaluation
#' @import NMF
#' @import nnlasso
#' @import nnls
#' @import parallel
#'
"lambdaRangeBetaEvaluation" <- function( x, K = 5, beta = NULL, background_signature = NULL, normalize_counts = TRUE, nmf_runs = 10, lambda_values = c(0.01, 0.05, 0.10, 0.20), iterations = 30, max_iterations_lasso = 10000, num_processes = Inf, seed = NULL, verbose = TRUE, log_file = "" ) {
# set the seed
set.seed(seed)
# check the input parameters
if(K<2) {
if(verbose) {
cat("The minimum value of K is 2...","\n")
}
K <- 2
}
if(nmf_runs<1) {
if(verbose) {
cat("The minimum value of nmf_runs is 1...","\n")
}
nmf_runs <- 1
}
x <- as.matrix(x)
if(normalize_counts) {
x_not_normalized <- x
x <- (x/rowSums(x))*2500
}
lambda_values <- sort(unique(lambda_values))
# compute the initial values of beta
if(is.null(beta)) {
if(verbose) {
cat("Computing the initial values of beta by standard NMF...","\n")
}
# add a signature to beta (leading to K signatures in total) to explicitly model background noise
if(is.null(background_signature)) {
warning("No background signature has been specified...")
background_signature_beta <- basis(nmf(t(x),rank=1,nrun=nmf_runs))
background_signature_beta <- t(background_signature_beta)
background_signature_beta <- background_signature_beta / rowSums(background_signature_beta)
background_signature <- as.numeric(background_signature_beta[1,])
}
else {
background_signature <- as.numeric(background_signature)
background_signature <- background_signature / sum(background_signature)
background_signature_beta <- t(background_signature)
}
background_signature_alpha <- matrix(0,nrow=dim(x)[1],ncol=1)
for(i in 1:dim(x)[1]) {
background_signature_alpha[i,] <- nnls(t(background_signature_beta),as.vector(x[i,]))$x
}
curr_x <- x - (background_signature_alpha %*% background_signature_beta)
curr_x[curr_x<0] <- 0
if(length(which(rowSums(t(curr_x))==0))>0) {
invalid_cols <- as.numeric(which(rowSums(t(curr_x))==0))
for(inv_cols in invalid_cols) {
curr_x[sample(1:length(curr_x[,inv_cols]),size=1),inv_cols] <- 1e-05
}
}
beta <- basis(nmf(t(curr_x),rank=(K-1),nrun=nmf_runs))
beta <- t(beta)
beta <- rbind(background_signature,beta)
}
beta <- beta / rowSums(beta)
rownames(beta) <- c("Background",paste0("S",1:(nrow(beta)-1)))
colnames(beta) <- colnames(x)
# setting up parallel execution
parallel <- NULL
close_parallel <- FALSE
if(is.null(parallel)&&length(lambda_values)>1) {
if(is.na(num_processes) || is.null(num_processes)) {
parallel <- NULL
}
else if(num_processes==Inf) {
cores <- as.integer((detectCores()-1))
if(cores < 2) {
parallel <- NULL
}
else {
num_processes <- min(num_processes,length(lambda_values))
parallel <- makeCluster(num_processes,outfile=log_file)
close_parallel <- TRUE
}
}
else {
num_processes <- min(num_processes,length(lambda_values))
parallel <- makeCluster(num_processes,outfile=log_file)
close_parallel <- TRUE
}
if(verbose && !is.null(parallel)) {
cat("Executing",num_processes,"processes via parallel...","\n")
}
}
# structure to save the estimated signatures
lambda_results <- array(list(),c(length(K),length(lambda_values)))
rownames(lambda_results) <- paste0(as.character(K),"_signatures")
colnames(lambda_results) <- paste0(as.character(lambda_values),"_lambda")
if(verbose) {
cat("Performing estimation of lambda range for beta...","\n")
}
# perform signature discovery for all the values of lambda
if(is.null(parallel)) {
set.seed(round(runif(1)*100000))
cont <- 0
for(l in lambda_values) {
# perform the inference
curr_results <- nmfLasso(x = x,
K = K,
beta = beta,
normalize_counts = normalize_counts,
lambda_rate_alpha = 0.0,
lambda_rate_beta = l,
iterations = iterations,
max_iterations_lasso = max_iterations_lasso,
seed = round(runif(1)*100000),
verbose = FALSE)
# save the results for the current configuration
cont <- cont + 1
# rescale alpha to the original magnitude
if(normalize_counts) {
curr_results$starting_alpha <- curr_results$starting_alpha * (rowSums(x_not_normalized)/2500)
curr_results$alpha <- curr_results$alpha * (rowSums(x_not_normalized)/2500)
}
lambda_results[[1,cont]] <- curr_results
if(verbose) {
cat("Progress",paste0(round((cont/(length(K)*length(lambda_values)))*100,digits=3),"%..."),"\n")
}
}
}
else {
res_clusterEvalQ <- clusterEvalQ(parallel,library("nnls"))
res_clusterEvalQ <- clusterEvalQ(parallel,library("nnlasso"))
clusterExport(parallel,varlist=c("x","K","beta","normalize_counts","iterations","max_iterations_lasso"),envir=environment())
clusterExport(parallel,c('nmfLasso','nmfLassoDecomposition','basis','nmf'),envir=environment())
clusterSetRNGStream(parallel,iseed=round(runif(1)*100000))
lambda_results_res <- parLapply(parallel,lambda_values,function(l) {
# perform the inference
curr_results <- nmfLasso(x = x,
K = K,
beta = beta,
normalize_counts = normalize_counts,
lambda_rate_alpha = 0.0,
lambda_rate_beta = l,
iterations = iterations,
max_iterations_lasso = max_iterations_lasso,
seed = round(runif(1)*100000),
verbose = FALSE)
return(curr_results)
})
for(i in 1:ncol(lambda_results)) {
# rescale alpha to the original magnitude
if(normalize_counts) {
lambda_results_res[[i]]$starting_alpha <- lambda_results_res[[i]]$starting_alpha * (rowSums(x_not_normalized)/2500)
lambda_results_res[[i]]$alpha <- lambda_results_res[[i]]$alpha * (rowSums(x_not_normalized)/2500)
}
lambda_results[[1,i]] <- lambda_results_res[[i]]
}
}
# close parallel
if(close_parallel) {
stopCluster(parallel)
}
return(lambda_results)
}
#' Perform the discovery of K somatic mutational signatures given a set of observed counts x.
#'
#' @examples
#' data(patients)
#' data(starting_betas_example)
#' beta = starting_betas_example[["5_signatures","Value"]]
#' res = nmfLasso(x=patients[1:100,],
#' K=5,
#' beta=beta,
#' lambda_rate_alpha=0.05,
#' lambda_rate_beta=0.05,
#' iterations=5,
#' seed=12345)
#'
#' @title nmfLasso
#' @param x count matrix for a set of n patients and 96 trinucleotides.
#' @param K numeric value (minimum 2) indicating the number of signatures to be discovered.
#' @param beta starting beta for the estimation. If it is NULL, starting beta is estimated by NMF.
#' @param background_signature background signature to be used. If not provided, a warning is thrown and an initial value for it is
#' estimated by NMF. If beta is not NULL, this parameter is ignored.
#' @param normalize_counts if true, the input count matrix x is normalize such that the patients have the same number of mutation.
#' @param nmf_runs number of iteration (minimum 1) of NMF to be performed for a robust estimation of starting beta. If beta is not NULL,
#' this parameter is ignored.
#' @param lambda_rate_alpha value of LASSO to be used for alpha between 0 and 1. This value should be greater than 0. 1 is the value of LASSO
#' that would shrink all the exposure values to 0 within one step. The higher lambda_rate_alpha is, the sparser are the resulting exposure values,
#' but too large values may result in a reduced fit of the observed counts.
#' @param lambda_rate_beta value of LASSO to be used for beta between 0 and 1. This value should be greater than 0. 1 is the value of LASSO
#' that would shrink all the signatures to 0 within one step. The higher lambda_rate_beta is, the sparser are the resulting signatures,
#' but too large values may result in a reduced fit of the observed counts.
#' @param iterations Number of iterations to be performed. Each iteration corresponds to a first step where beta is fitted
#' and a second step where alpha is fitted.
#' @param max_iterations_lasso Number of maximum iterations to be performed during the sparsification via Lasso.
#' @param seed Seed for reproducibility.
#' @param verbose boolean; Shall I print all messages?
#' @return A list with the discovered signatures. It includes 6 elements:
#' alpha: matrix of the discovered exposure values
#' beta: matrix of the discovered signatures
#' starting_alpha: initial alpha on which the method has been applied
#' starting_beta: initial beta on which the method has been applied
#' loglik_progression: log-likelihood values during the iterations. This values should be increasing, if not the selected value of lambda is too high
#' best_loglik: log-likelihood of the best signatures configuration
#' @export nmfLasso
#' @import NMF
#' @import nnls
#' @import nnlasso
#'
"nmfLasso" <- function( x, K, beta = NULL, background_signature = NULL, normalize_counts = TRUE, nmf_runs = 10, lambda_rate_alpha = 0.05, lambda_rate_beta = 0.05, iterations = 30, max_iterations_lasso = 10000, seed = NULL, verbose = TRUE ) {
# set the seed
set.seed(seed)
# check the input parameters
if(K<2) {
if(verbose) {
cat("The minimum value of K is 2...","\n")
}
K <- 2
}
if(nmf_runs<1) {
if(verbose) {
cat("The minimum value of nmf_runs is 1...","\n")
}
nmf_runs <- 1
}
if(lambda_rate_alpha<0) {
if(verbose) {
cat("The minimum value of lambda_rate_alpha is 0...","\n")
}
lambda_rate_alpha <- 0
}
if(lambda_rate_alpha>1) {
if(verbose) {
cat("The maximum value of lambda_rate_alpha is 1...","\n")
}
lambda_rate_alpha <- 1
}
if(lambda_rate_beta<0) {
if(verbose) {
cat("The minimum value of lambda_rate_beta is 0...","\n")
}
lambda_rate_beta <- 0
}
if(lambda_rate_beta>1) {
if(verbose) {
cat("The maximum value of lambda_rate_beta is 1...","\n")
}
lambda_rate_beta <- 1
}
x <- as.matrix(x)
if(normalize_counts) {
x_not_normalized <- x
x <- (x/rowSums(x))*2500
}
# compute the initial values of beta
if(is.null(beta)) {
if(verbose) {
cat("Computing the initial values of beta by standard NMF...","\n")
}
# add a signature to beta (leading to K signatures in total) to explicitly model background noise
if(is.null(background_signature)) {
warning("No background signature has been specified...")
background_signature_beta <- basis(nmf(t(x),rank=1,nrun=nmf_runs))
background_signature_beta <- t(background_signature_beta)
background_signature_beta <- background_signature_beta / rowSums(background_signature_beta)
background_signature <- as.numeric(background_signature_beta[1,])
}
else {
background_signature <- as.numeric(background_signature)
background_signature <- background_signature / sum(background_signature)
background_signature_beta <- t(background_signature)
}
background_signature_alpha <- matrix(0,nrow=dim(x)[1],ncol=1)
for(i in 1:dim(x)[1]) {
background_signature_alpha[i,] <- nnls(t(background_signature_beta),as.vector(x[i,]))$x
}
curr_x <- x - (background_signature_alpha %*% background_signature_beta)
curr_x[curr_x<0] <- 0
if(length(which(rowSums(t(curr_x))==0))>0) {
invalid_cols <- as.numeric(which(rowSums(t(curr_x))==0))
for(inv_cols in invalid_cols) {
curr_x[sample(1:length(curr_x[,inv_cols]),size=1),inv_cols] <- 1e-05
}
}
beta <- basis(nmf(t(curr_x),rank=(K-1),nrun=nmf_runs))
beta <- t(beta)
beta <- rbind(background_signature,beta)
}
beta <- beta / rowSums(beta)
rownames(beta) <- c("Background",paste0("S",1:(nrow(beta)-1)))
colnames(beta) <- colnames(x)
if(verbose) {
cat("Performing the discovery of the signatures by NMF with Lasso...","\n")
}
# perform the discovery of the signatures
results = tryCatch({
results = nmfLassoDecomposition(x,beta,lambda_rate_alpha,lambda_rate_beta,iterations,max_iterations_lasso,round(runif(1)*100000),verbose)
# rescale alpha to the original magnitude
if(normalize_counts) {
results$starting_alpha <- results$starting_alpha * (rowSums(x_not_normalized)/2500)
results$alpha <- results$alpha * (rowSums(x_not_normalized)/2500)
}
return(results)
}, error = function(e) {
warning("Lasso did not converge, you should try a lower value of lambda! Current settings: K = ",K,", lambda_rate_alpha = ",lambda_rate_alpha,", lambda_rate_beta = ",lambda_rate_beta,"...")
return(list(alpha=NA,beta=NA,starting_alpha=NA,starting_beta=NA,loglik_progression=rep(NA,iterations),best_loglik=NA))
})
return(results)
}
# perform de novo discovery of somatic mutational signatures using NMF with Lasso to ensure sparsity
"nmfLassoDecomposition" <- function( x, starting_beta, lambda_rate_alpha = 0.05, lambda_rate_beta = 0.05, iterations = 30, max_iterations_lasso = 10000, seed = NULL, verbose = TRUE ) {
# set the seed
set.seed(seed)
# n is the number of observations in x, i.e., the patients
n <- dim(x)[1]
# J is the number of trinucleotides, i.e., 96 categories
J <- dim(x)[2]
# K is the number of signatures to be called
K <- dim(starting_beta)[1]
# initialize beta
starting_beta <- starting_beta / rowSums(starting_beta)
rownames(starting_beta) <- c("Background",paste0("S",1:(nrow(starting_beta)-1)))
colnames(starting_beta) <- colnames(x)
beta <- starting_beta
# initialize alpha
alpha <- matrix(0,nrow=n,ncol=K)
rownames(alpha) <- 1:nrow(alpha)
colnames(alpha) <- rownames(beta)
for(i in 1:n) {
alpha[i,] <- nnls(t(beta),as.vector(x[i,]))$x
}
starting_alpha <- alpha
# rescale the two matrices of a factor of 50 for numerical reasons
beta <- beta * 50
for(i in 1:n) {
alpha[i,] <- nnls(t(beta),as.vector(x[i,]))$x
}
# structure where to save the log-likelihood at each iteration
loglik <- rep(NA,iterations)
# structure where to save the lambda values for alpha and beta
lambda_values_alpha <- rep(NA,n) # sparsity over the patients (reduce the number of signatures per patient)
lambda_values_beta <- rep(NA,J) # sparsity over the signatures (produce sparse signatures)
if(verbose) {
cat("Performing a total of",iterations,"iterations...","\n")
}
# start the learning procedure
best_loglik <- NA
best_alpha <- NA
best_beta <- NA
for(i in 1:iterations) {
# initialize the value of the log-likelihood for the current iteration
loglik[i] <- 0
# configuration 1 (turn off sparsity): repeat a 2 step algorithm iteratively, where
# first beta is estimated by Non-Negative Linear Least Squares and, then, alpha is also estimated by Non-Negative Linear Least Squares
if(lambda_rate_alpha==0&&lambda_rate_beta==0) {
# update beta by Non-Negative Linear Least Squares
for(k in 1:J) {
# the first signature represents the background model, thus it is not changed
beta[2:K,k] <- nnls(alpha[,2:K,drop=FALSE],as.vector(x[,k]-(alpha[,1]*beta[1,k])))$x
}
# update alpha by Non-Negative Linear Least Squares
for(j in 1:n) {
alpha[j,] <- nnls(t(beta),as.vector(x[j,]))$x
}
# update the log-likelihood for the current iteration
loglik[i] <- -sum((x - alpha %*% beta)^2)
}
# configuration 2 (sparsity only on beta): repeat a 2 step algorithm iteratively, where
# first beta is estimated by Non-Negative Lasso and, then, alpha is estimated by Non-Negative Linear Least Squares
if(lambda_rate_alpha==0&&lambda_rate_beta>0) {
# update beta by Non-Negative Lasso
for(k in 1:J) {
# compute independently for each trinucleotide the difference between the observed counts, i.e., x,
# and the counts predicted by considering only the first signature (i.e., which represents the background model)
target <- x[,k] - (alpha[,1] * beta[1,k])
# estimate beta for the remaining signatues by Non-Negative Lasso to ensure sparsity
if(is.na(lambda_values_beta[k])) {
max_lambda_value <- max(abs(t(alpha[,2:K,drop=FALSE]) %*% target))
lambda_values_beta[k] <- max_lambda_value * lambda_rate_beta
}
beta[2:K,k] <- as.vector(nnlasso(x = alpha[,2:K,drop=FALSE],
y = target,
family = "normal",
lambda = lambda_values_beta[k],
intercept = FALSE,
normalize = FALSE,
tol = 1e-05,
maxiter = max_iterations_lasso,
path = FALSE)$coef[2,])
}
# update alpha by Non-Negative Linear Least Squares
for(j in 1:n) {
alpha[j,] <- nnls(t(beta),as.vector(x[j,]))$x
}
# update the log-likelihood for the current iteration
for(k in 1:J) {
curr_loglik <- -sum((x[,k] - alpha %*% beta[,k])^2) - (lambda_values_beta[k] * sum(beta[2:K,k]))
loglik[i] <- loglik[i] + curr_loglik
}
}
# configuration 3 (sparsity only on alpha): repeat a 2 step algorithm iteratively, where
# first beta is estimated by Non-Negative Linear Least Squares and, then, alpha is estimated by Non-Negative Lasso
if(lambda_rate_alpha>0&&lambda_rate_beta==0) {
# update beta by Non-Negative Linear Least Squares
for(k in 1:J) {
# the first signature represents the background model, thus it is not changed
beta[2:K,k] <- nnls(alpha[,2:K,drop=FALSE],as.vector(x[,k]-(alpha[,1]*beta[1,k])))$x
}
# update alpha by Non-Negative Lasso
for(j in 1:n) {
# compute independently for each patient the counts to be approximted
target <- x[j,]
# estimate alpha by Non-Negative Lasso to ensure sparsity
if(is.na(lambda_values_alpha[j])) {
max_lambda_value <- max(abs(beta %*% target))
lambda_values_alpha[j] <- max_lambda_value * lambda_rate_alpha
}
alpha[j,] <- as.vector(nnlasso(x = t(beta),
y = target,
family = "normal",
lambda = lambda_values_alpha[j],
intercept = FALSE,
normalize = FALSE,
tol = 1e-05,
maxiter = max_iterations_lasso,
path = FALSE)$coef[2,])
}
# update the log-likelihood for the current iteration
for(j in 1:n) {
curr_loglik <- -sum((x[j,] - alpha[j,] %*% beta)^2) - (lambda_values_alpha[j] * sum(alpha[j,]))
loglik[i] <- loglik[i] + curr_loglik
}
}
# configuration 4 (sparsity on both alpha and beta): repeat a 2 step algorithm iteratively, where
# first beta is estimated by Non-Negative Lasso and, then, also alpha is estimated by Non-Negative Lasso
if(lambda_rate_alpha>0&&lambda_rate_beta>0) {
# update beta by Non-Negative Lasso
for(k in 1:J) {
# compute independently for each trinucleotide the difference between the observed counts, i.e., x,
# and the counts predicted by considering only the first signature (i.e., which represents the background model)
target <- x[,k] - (alpha[,1] * beta[1,k])
# estimate beta for the remaining signatues by Non-Negative Lasso to ensure sparsity
if(is.na(lambda_values_beta[k])) {
max_lambda_value <- max(abs(t(alpha[,2:K,drop=FALSE]) %*% target))
lambda_values_beta[k] <- max_lambda_value * lambda_rate_beta
}
beta[2:K,k] <- as.vector(nnlasso(x = alpha[,2:K,drop=FALSE],
y = target,
family = "normal",
lambda = lambda_values_beta[k],
intercept = FALSE,
normalize = FALSE,
tol = 1e-05,
maxiter = max_iterations_lasso,
path = FALSE)$coef[2,])
}
# update alpha by Non-Negative Lasso
for(j in 1:n) {
# compute independently for each patient the counts to be approximted
target <- x[j,]
# estimate alpha by Non-Negative Lasso to ensure sparsity
if(is.na(lambda_values_alpha[j])) {
max_lambda_value <- max(abs(beta %*% target))
lambda_values_alpha[j] <- max_lambda_value * lambda_rate_alpha
}
alpha[j,] <- as.vector(nnlasso(x = t(beta),
y = target,
family = "normal",
lambda = lambda_values_alpha[j],
intercept = FALSE,
normalize = FALSE,
tol = 1e-05,
maxiter = max_iterations_lasso,
path = FALSE)$coef[2,])
}
# update the log-likelihood for the current iteration
for(k in 1:J) {
for(j in 1:n) {
curr_loglik <- -((x[j,k] - alpha[j,] %*% beta[,k])^2) - (lambda_values_alpha[j] * sum(alpha[j,])) - (lambda_values_beta[k] * sum(beta[2:K,k]))
loglik[i] <- loglik[i] + curr_loglik
}
}
}
# save the results at maximum log-likelihood
if(is.na(best_loglik)||loglik[i]>best_loglik) {
best_alpha <- alpha
best_beta <- beta
best_loglik <- loglik[i]
}
if(verbose) {
cat("Progress",paste0((i/iterations)*100,"%..."),"\n")
}
}
alpha <- best_alpha
beta <- best_beta
# check if the likelihood is increasing
if(length(loglik)>1) {
cont <- 1
for(i in 2:length(loglik)) {
if(loglik[i]>loglik[(i-1)]) {
cont <- cont + 1
}
}
if(cont/iterations<0.5) {
warning("The likelihood is not increasing, you should try a lower value of lambda! Current settings: K = ",K,", lambda_rate_alpha = ",lambda_rate_alpha,", lambda_rate_beta = ",lambda_rate_beta,"...")
}
}
# normalize the rate of the signatures to sum to 1
beta <- beta / rowSums(beta)
# final computation of alpha using the normalized version of beta
if(lambda_rate_alpha>0) {
# update alpha by Non-Negative Lasso
for(j in 1:n) {
# compute independently for each patient the counts to be approximted
target <- x[j,]
# estimate alpha by Non-Negative Lasso to ensure sparsity
alpha[j,] <- as.vector(nnlasso(x = t(beta),
y = target,
family = "normal",
lambda = (max(abs(beta %*% target)) * lambda_rate_alpha),
intercept = FALSE,
normalize = FALSE,
tol = 1e-05,
maxiter = max_iterations_lasso,
path = FALSE)$coef[2,])
}
}
else {
# update alpha by Non-Negative Linear Least Squares
for(j in 1:n) {
alpha[j,] <- nnls(t(beta),as.vector(x[j,]))$x
}
}
# save the results
results <- list(alpha=alpha,beta=beta,starting_alpha=starting_alpha,starting_beta=starting_beta,loglik_progression=loglik,best_loglik=best_loglik)
return(results)
}
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