R/dreval.R
In csoneson/dreval: Evaluate Reduced Dimension Representations
Defines functions
dreval
Documented in
dreval
#' Evaluate structure preservation in reduced dimension representations
#'
#' Calculates a collection of metrics comparing one or more reduced dimension
#' representations to a reference representation. The function takes a
#' \code{SingleCellExperiment} object as input. The reference representation can
#' be either one of the included assays or one of the reduced dimension
#' representations. If an assay is used, reference distances can be calculated
#' based on all or a subset of the features (rows). These distances are then
#' compared to distances calculated from the specified reduced dimension
#' representations, and several scores are returned. The execution time of the
#' function depends strongly on both the number of retained variables (which
#' affects the distance calculation in the reference space) and the number of
#' samples that are randomly selected to use as the basis for the comparison.
#' Since subsampling of the columns (via the \code{nSamples} argument) is
#' random, setting the random seed is recommended to obtain reproducible
#' results.
#'
#' The following metrics are calculated:
#' \itemize{
#' \item SpearmanCorrDist - The Spearman correlation between the reference
#' distances and the Euclidean distances in the low-dimensional
#' representation. Ranges from -1 to 1, higher values are better.
#' \item PearsonCorrDist - The Pearson correlation between the reference
#' distances and the Euclidean distances in the low-dimensional
#' representation. Ranges from -1 to 1, higher values are better.
#' \item KSstatDist - The Kolmogorov-Smirnov statistic comparing the
#' distribution of distances in the reference space and in the low-dimensional
#' representation. Ranges from 0 to 1, lower values are better.
#' \item EuclDistBetweenDists - The Euclidean distance between the vector of
#' distances in the reference space and those in the low-dimensional
#' representation. Depending on the value of \code{distNorm}, distances are
#' scaled before they are compared. Lower values are better.
#' \item SammonStress - The Sammon stress (Sammon 1969). Depending on the
#' value of \code{distNorm}, distances are scaled before they are compared.
#' Lower values are better.
#' \item Trustworthiness_kNN - The trustworthiness score (Venna & Kaski 2001),
#' using NN nearest neighbors. The trustworthiness indicates to which degree
#' we can trust that the points placed closest to a given sample in the
#' low-dimensional representation are really close to the sample also in the
#' reference space. Ranges from 0 to 1, higher values are better.
#' \item Continuity_kNN - The continuity score (Venna & Kaski 2001), using NN
#' nearest neighbors. The continuity indicates to which degree we can trust
#' that the points closest to a given sample in the reference space are placed
#' close to the sample also in the low-dimensional representation. Ranges from
#' 0 to 1, higher values are better.
#' \item MeanJaccard_kNN - The mean Jaccard index (over all samples),
#' comparing the set of NN nearest neighbors in the reference space and those
#' in the low-dimensional representation. Ranges from 0 to 1, higher values
#' are better.
#' \item MeanSilhouette_X - If a \code{labelColumn} X is supplied, the mean
#' silhouette score (Rousseeuw 1987) across all samples, with the grouping
#' given by this column and the distances obtained from the low-dimensional
#' representation. Ranges from -1 to 1, higher values are better.
#' \item coRankingQlocal - Q_local, defined as the average LCMC over the
#' values to the left of the maximum, following the dimRed/coRanking package
#' implementations (Kraemer et al 2018, Lee and Verleysen 2009, Chen and Buja
#' 2009). Measures the preservation of local distances, higher values are
#' better.
#' \item coRankingQglobal - Q_global, defined as the average LCMC over the
#' values to the right of the maximum, following the dimRed/coRanking package
#' implementations (Kraemer et al 2018, Lee and Verleysen 2009, Chen and Buja
#' 2009). Measures the preservation of global distances, higher values are
#' better.
#' }
#'
#' @param sce A \code{SingleCellExperiment} object.
#' @param dimReds A character vector with the names of the reduced dimension
#' representations from \code{sce} to include in the evaluation. If
#' \code{NULL}, all reduced dimension representations are included.
#' @param refType A character scalar, either "assay" or "dimred", specifying
#' whether to use an assay or a reduced dimension representation of \code{sce}
#' as the reference data source.
#' @param refAssay A character scalar giving the name of the assay from
#' \code{sce} to use as the basis for the distance calculations in the
#' reference space, if \code{refType} if \code{"assay"}.
#' @param refDimRed A character scalar specifying the reduced dimension
#' representation to use as the reference data representation if
#' \code{refType} is \code{"dimred"}.
#' @param features A character vector giving the IDs of the features to use for
#' distance calculations from the chosen assay. Will be matched to the row
#' names of \code{sce}.
#' @param nSamples A numeric scalar, giving the number of columns to subsample
#' (randomly) from \code{sce}.
#' @param distNorm A character scalar, indicating how the distance vectors in
#' the reference and low-dimensional spaces should be normalized before they
#' are compared. If set to "l2", the vectors are L2 normalized, if set to
#' "median" they are divided by the median value times the square root of
#' their length, and if set to any other value they are divided by the square
#' root of their length, to avoid metrics scaling with the number of retained
#' samples.
#' @param refDistMethod A character scalar defining the distance measure to use
#' in the reference space. Must be one of "euclidean", "manhattan", "maximum",
#' "canberra" or "cosine". The distance in the low-dimensional representation
#' will always be Euclidean.
#' @param kTM An integer vector giving the number of neighbors to use for
#' trustworthiness, continuity and Jaccard index calculations.
#' @param labelColumn A character scalar defining a column of
#' \code{colData(sce)} to use as the group assignments in the silhouette width
#' calculations. If not provided, the silhouette widths are not calculated.
#' @param verbose A logical scalar, indicating whether to print out progress
#' messages.
#'
#' @author Charlotte Soneson
#'
#' @export
#'
#' @return A list with two elements:
#' \itemize{
#' \item scores - A \code{data.frame} with values of all evaluation metrics,
#' across the dimension reduction methods. In addition to the metrics, it
#' contains the dimensionality of the respective reduced dimension
#' representations, and the value of K giving the highest value of LCMC (used
#' for the calculations of Qlocal and Qglobal, see Kraemer et al 2018, Lee and
#' Verleysen 2009, Chen and Buja 2009).
#' \item plots - A list of ggplot objects, representing diagnostic plots.
#' }
#'
#' @references
#' Venna J., Kaski S. (2001). Neighborhood preservation in nonlinear
#' projection methods: An experimental study. In Dorffner G., Bischof H.,
#' Hornik K., editors, Proceedings of ICANN 2001, pp 485–491. Springer,
#' Berlin.
#'
#' Lee J.A., Verleysen M. (2009). Quality assessment of
#' dimensionality reduction: Rank-based criteria. Neurocomputing 72
#' (7-9):1431-1443.
#'
#' Chen L., Buja A. (2009). Local multidimensional scaling for nonlinear
#' dimension reduction, graph drawing, and proximity analysis. Journal of the
#' American Statistical Association 104:209-219.
#'
#' Kraemer G., Reichstein M., Mahecha M.D. (2018). dimRed and coRanking -
#' Unifying dimensionality reduction in R. The R Journal 10 (1):342-358.
#'
#' Sammon J.W. Jr (1969). A nonlinear mapping for data structure analysis.
#' IEEE Transactions on Computers C18(5):401-409.
#'
#' Rousseeuw, P.J. (1987). Silhouettes: A graphical aid to the interpretation
#' and validation of cluster analysis. Journal of Computational and Applied
#' Mathematics 20:53-65.
#'
#' @importFrom SingleCellExperiment reducedDims reducedDimNames
#' @importFrom SummarizedExperiment assays colData assayNames
#' @importFrom cluster silhouette
#' @importFrom stats cor ks.test median
#' @importFrom dplyr bind_rows
#' @importFrom wordspace dist.matrix
#' @importFrom coRanking coranking LCMC
#' @importFrom methods is
#' @importFrom ggplot2 ggplot aes geom_hex theme_bw labs scale_fill_gradient
#' geom_abline stat_ecdf
#' @importFrom tidyr gather
#' @importFrom magrittr %>%
#'
#' @examples
#' data(pbmc3ksub)
#' dre <- dreval(sce = pbmc3ksub, nSamples = 150)
#'
dreval <- function(
sce, dimReds = NULL, refType = "assay",
refAssay = "logcounts", refDimRed = NULL,
features = NULL, nSamples = NULL, distNorm = "none",
refDistMethod = "euclidean", kTM = c(10, 100),
labelColumn = NULL, verbose = FALSE) {
## --------------------------------------------------------------------- ##
## Check input arguments
## --------------------------------------------------------------------- ##
if (!methods::is(sce, "SingleCellExperiment")) {
stop("sce must be a SingleCellExperiment object")
}
## If dimReds is NULL, use all dimReds
if (is.null(dimReds)) {
dimReds <- SingleCellExperiment::reducedDimNames(sce)
} else {
dimReds <- intersect(
dimReds, SingleCellExperiment::reducedDimNames(sce)
)
}
## If refType is dimred, don't compare the reference dimred to itself
if (refType == "dimred") {
dimReds <- setdiff(dimReds, refDimRed)
}
if (length(dimReds) == 0) (
stop("No valid reduced dimension representations found")
)
if (!(refType %in% c("assay", "dimred"))) {
stop("'refType' must be either 'assay' or 'dimred'")
}
if (refType == "assay" &&
!(refAssay %in% SummarizedExperiment::assayNames(sce))) {
stop("There is no assay named ", refAssay, " in sce")
}
if (refType == "dimred" &&
!(refDimRed %in% SingleCellExperiment::reducedDimNames(sce))) {
stop("There is no reduced dimension representation named ",
refDimRed, " in sce")
}
if (!is.character(distNorm)) {
stop("distNorm must be a character string")
}
if (!(refDistMethod %in% c("euclidean", "manhattan", "maximum",
"canberra", "cosine"))) {
stop("refDistMethod must be one of ",
"'euclidean', 'manhattan', 'maximum', 'canberra' or 'cosine'")
}
if (!is.numeric(kTM)) {
stop("kTM must be a numeric vector")
}
if (!is.logical(verbose)) {
stop("verbose must be a logical value")
}
## If features is not NULL, subset to provided features
if (refType == "assay" && !is.null(features)) {
if (verbose) message("Subsampling rows...")
features <- intersect(features, rownames(sce))
if (length(features) == 0) {
stop("No features remaining after subsetting. ",
"Make sure that the provided features correspond ",
"to the row names of sce.")
}
sce <- sce[features, ]
}
## If nSamples is not NULL, subsample columns for increased speed
if (!is.null(nSamples)) {
if (verbose) message("Subsampling columns...")
nSamples <- min(nSamples, ncol(sce))
if (nSamples == 0) {
stop("nSamples must be >0")
}
keep <- sample(seq_len(ncol(sce)), nSamples, replace = FALSE)
sce <- sce[, keep]
}
if (!is.null(labelColumn)) {
if (!(labelColumn %in%
colnames(SummarizedExperiment::colData(sce)))) {
stop("labelColumn must be one of the columns in colData(sce)")
}
tmp <- SummarizedExperiment::colData(sce)[[labelColumn]]
if (length(unique(tmp)) < 2) {
stop("labelColumn must correspond to a column ",
"with at least two unique values")
}
if (length(unique(tmp)) == ncol(sce)) {
stop("labelColumn must correspond to a column ",
"where not all values are different")
}
}
## --------------------------------------------------------------------- ##
## Initialize list to hold results
## --------------------------------------------------------------------- ##
results <- lapply(dimReds, function(m) list())
names(results) <- dimReds
plots <- list(disthex = list())
## --------------------------------------------------------------------- ##
## Calculate distances and ranks for the high-dimensional data
## --------------------------------------------------------------------- ##
if (verbose) message("Calculating distances in high-dimensional space...")
if (refType == "assay") {
mat <- as.matrix(SummarizedExperiment::assays(sce)[[refAssay]])
distReference <- wordspace::dist.matrix(
mat, method = refDistMethod,
as.dist = TRUE, byrow = FALSE, convert = FALSE
)
} else if (refType == "dimred") {
mat <- SingleCellExperiment::reducedDims(sce)[[refDimRed]]
distReference <- wordspace::dist.matrix(
mat, method = refDistMethod,
as.dist = TRUE, byrow = TRUE, convert = FALSE
)
} else {
stop("Invalid 'refType'")
}
## Get the rank for each sample compared to each other sample. In each
## column, the row with the value 1 corresponds to the nearest neighbor,
## the one with the value 2 to the second nearest neighbor, etc.
if (verbose) message("Getting ranks in high-dimensional space...")
drm <- as.matrix(distReference)
diag(drm) <- NA
rankReference <- apply(drm, 2, function(w) order(order(w)))
diag(rankReference) <- 0
rownames(rankReference) <- rownames(distReference)
## Define normalization constant for distances
if (distNorm == "l2") {
distNormReference <- sqrt(sum(distReference^2))
} else if (distNorm == "median") {
distNormReference <- stats::median(distReference) *
sqrt(length(distReference))
} else {
distNormReference <- sqrt(length(distReference))
}
distdf <- data.frame(reference = c(distReference/distNormReference))
## --------------------------------------------------------------------- ##
## For each dimRed, calculate scores
## --------------------------------------------------------------------- ##
for (dr in dimReds) {
if (verbose) message(dr, ":")
dimRedMat <- SingleCellExperiment::reducedDims(sce)[[dr]]
## Get dimensionality
results[[dr]]$dimensionality <- ncol(dimRedMat)
## ----------------------------------------------------------------- ##
## Calculate distances and ranks for the low-dimensional data
## ----------------------------------------------------------------- ##
if (verbose)
message(" Calculating distances in low-dimensional space...")
distLowDim <- wordspace::dist.matrix(
as.matrix(dimRedMat), method = "euclidean",
as.dist = TRUE, byrow = TRUE, convert = FALSE
)
## Get the rank for each sample compared to each other sample. In each
## column, the row with the value 1 corresponds to the nearest neighbor,
## the one with the value 2 to the second nearest neighbor, etc.
if (verbose) message(" Getting ranks in low-dimensional space...")
dlm <- as.matrix(distLowDim)
diag(dlm) <- NA
rankLowDim <- apply(dlm, 2, function(w) order(order(w)))
diag(rankLowDim) <- 0
rownames(rankLowDim) <- rownames(distLowDim)
if (distNorm == "l2") {
distNormLowDim <- sqrt(sum(distLowDim^2))
} else if (distNorm == "median") {
distNormLowDim <- stats::median(distLowDim) *
sqrt(length(distLowDim))
} else {
distNormLowDim <- sqrt(length(distLowDim))
}
distdf[[dr]] <- c(distLowDim/distNormLowDim)
## ----------------------------------------------------------------- ##
## Correlation between distance vectors
## ----------------------------------------------------------------- ##
if (verbose) message(" Calculating Spearman correlations...")
results[[dr]]$SpearmanCorrDist <- stats::cor(
distReference, distLowDim,
method = "spearman"
)
if (verbose) message(" Calculating Pearson correlations...")
results[[dr]]$PearsonCorrDist <- stats::cor(
distReference, distLowDim,
method = "pearson"
)
plots$disthex[[dr]] <-
ggplot2::ggplot(
data.frame(reference = c(distReference/distNormReference),
lowdim = c(distLowDim/distNormLowDim)),
ggplot2::aes(x = reference, y = lowdim)
) +
ggplot2::geom_hex(bins = 100, ggplot2::aes(fill = stat(density))) +
ggplot2::scale_fill_gradient(
name = "", low = "bisque2", high = "darkblue"
) +
ggplot2::theme_bw() +
ggplot2::labs(
title = dr, x = "Scaled distance in reference space",
y = "Scaled distance in low-dimensional space"
) +
ggplot2::geom_abline(slope = 1, intercept = 0)
## ----------------------------------------------------------------- ##
## Kolmogorov-Smirnov statistic comparing distance distributions
## ----------------------------------------------------------------- ##
if (verbose) message(" Calculating KS statistic")
results[[dr]]$KSStatDist <- stats::ks.test(
distReference/distNormReference,
distLowDim/distNormLowDim
)$statistic
## ----------------------------------------------------------------- ##
## Euclidean distance to reference-space (scaled) distances
## ----------------------------------------------------------------- ##
if (verbose) message(" Calculating distances between distances...")
results[[dr]]$EuclDistBetweenDists <-
sqrt(sum(((distReference/distNormReference) -
(distLowDim/distNormLowDim))^2))
## ----------------------------------------------------------------- ##
## Sammon stress
## ----------------------------------------------------------------- ##
if (verbose) message(" Calculating Sammon stress...")
results[[dr]]$SammonStress <-
1/sum(distReference/distNormReference) *
sum(((distReference/distNormReference -
distLowDim/distNormLowDim) ^ 2) /
(distReference/distNormReference))
## ----------------------------------------------------------------- ##
## Trustworthiness and continuity
## ----------------------------------------------------------------- ##
for (k in kTM) {
if (verbose) message(" Calculating trustworthiness, k=", k)
tm <- calcTrustworthinessFromRank(
rankReference = rankReference,
rankLowDim = rankLowDim,
kTM = k
)
results[[dr]][[paste0("Trustworthiness_k", k)]] <- tm
if (verbose) message(" Calculating continuity, k=", k)
ct <- calcContinuityFromRank(
rankReference = rankReference,
rankLowDim = rankLowDim,
kTM = k
)
results[[dr]][[paste0("Continuity_k", k)]] <- ct
}
## ----------------------------------------------------------------- ##
## Jaccard index of nearest neighbors
## ----------------------------------------------------------------- ##
for (k in kTM) {
if (verbose) message(" Calculating Jaccard index ",
"of nearest neighbors, k=", k)
intrs <- colSums((rankReference <= k) * (rankLowDim <= k))
unin <- colSums(sign((rankReference <= k) + (rankLowDim <= k)))
jaccs <- intrs/unin
results[[dr]][[paste0("MeanJaccard_k", k)]] <- mean(jaccs)
}
## ----------------------------------------------------------------- ##
## Silhouette index relative to known labels
## ----------------------------------------------------------------- ##
if (!is.null(labelColumn)) {
silh <- cluster::silhouette(
x = as.numeric(as.factor(
SummarizedExperiment::colData(sce)[[labelColumn]]
)),
dist = distLowDim
)
results[[dr]][[paste0("MeanSilhouette_", labelColumn)]] <-
summary(silh)$avg.width
}
## ----------------------------------------------------------------- ##
## Coranking (with the coRanking package)
## ----------------------------------------------------------------- ##
qt <- coRanking::coranking(
Xi = as.matrix(distReference),
X = as.matrix(distLowDim),
input_Xi = "dist",
input_X = "dist",
)
lcmc <- coRanking::LCMC(qt)
## We follow the implementation in the dimRed package, where Qlocal and
## Qglobal are calculated as averages of LCMC values (not Q_NX values)
Kmax <- which.max(lcmc)
qlocal <- mean(lcmc[seq(from = 1, to = Kmax, by = 1)])
qglobal <- mean(lcmc[seq(from = Kmax + 1, to = length(lcmc), by = 1)])
results[[dr]][["coRankingQlocal"]] <- qlocal
results[[dr]][["coRankingQglobal"]] <- qglobal
results[[dr]][["KmaxLCMC"]] <- Kmax
}
plots$distcdf <-
ggplot2::ggplot(
distdf %>% tidyr::gather(key = "dr", value = "distance"),
ggplot2::aes(x = distance, color = dr)
) +
ggplot2::stat_ecdf() + ggplot2::theme_bw()
results <- do.call(dplyr::bind_rows, lapply(names(results), function(nm) {
data.frame(
Method = nm, as.data.frame(results[[nm]]),
stringsAsFactors = FALSE
)
}))
list(scores = results, plots = plots)
}
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Defines functions dreval
Documented in dreval
#' Evaluate structure preservation in reduced dimension representations
#'
#' Calculates a collection of metrics comparing one or more reduced dimension
#' representations to a reference representation. The function takes a
#' \code{SingleCellExperiment} object as input. The reference representation can
#' be either one of the included assays or one of the reduced dimension
#' representations. If an assay is used, reference distances can be calculated
#' based on all or a subset of the features (rows). These distances are then
#' compared to distances calculated from the specified reduced dimension
#' representations, and several scores are returned. The execution time of the
#' function depends strongly on both the number of retained variables (which
#' affects the distance calculation in the reference space) and the number of
#' samples that are randomly selected to use as the basis for the comparison.
#' Since subsampling of the columns (via the \code{nSamples} argument) is
#' random, setting the random seed is recommended to obtain reproducible
#' results.
#'
#' The following metrics are calculated:
#' \itemize{
#' \item SpearmanCorrDist - The Spearman correlation between the reference
#' distances and the Euclidean distances in the low-dimensional
#' representation. Ranges from -1 to 1, higher values are better.
#' \item PearsonCorrDist - The Pearson correlation between the reference
#' distances and the Euclidean distances in the low-dimensional
#' representation. Ranges from -1 to 1, higher values are better.
#' \item KSstatDist - The Kolmogorov-Smirnov statistic comparing the
#' distribution of distances in the reference space and in the low-dimensional
#' representation. Ranges from 0 to 1, lower values are better.
#' \item EuclDistBetweenDists - The Euclidean distance between the vector of
#' distances in the reference space and those in the low-dimensional
#' representation. Depending on the value of \code{distNorm}, distances are
#' scaled before they are compared. Lower values are better.
#' \item SammonStress - The Sammon stress (Sammon 1969). Depending on the
#' value of \code{distNorm}, distances are scaled before they are compared.
#' Lower values are better.
#' \item Trustworthiness_kNN - The trustworthiness score (Venna & Kaski 2001),
#' using NN nearest neighbors. The trustworthiness indicates to which degree
#' we can trust that the points placed closest to a given sample in the
#' low-dimensional representation are really close to the sample also in the
#' reference space. Ranges from 0 to 1, higher values are better.
#' \item Continuity_kNN - The continuity score (Venna & Kaski 2001), using NN
#' nearest neighbors. The continuity indicates to which degree we can trust
#' that the points closest to a given sample in the reference space are placed
#' close to the sample also in the low-dimensional representation. Ranges from
#' 0 to 1, higher values are better.
#' \item MeanJaccard_kNN - The mean Jaccard index (over all samples),
#' comparing the set of NN nearest neighbors in the reference space and those
#' in the low-dimensional representation. Ranges from 0 to 1, higher values
#' are better.
#' \item MeanSilhouette_X - If a \code{labelColumn} X is supplied, the mean
#' silhouette score (Rousseeuw 1987) across all samples, with the grouping
#' given by this column and the distances obtained from the low-dimensional
#' representation. Ranges from -1 to 1, higher values are better.
#' \item coRankingQlocal - Q_local, defined as the average LCMC over the
#' values to the left of the maximum, following the dimRed/coRanking package
#' implementations (Kraemer et al 2018, Lee and Verleysen 2009, Chen and Buja
#' 2009). Measures the preservation of local distances, higher values are
#' better.
#' \item coRankingQglobal - Q_global, defined as the average LCMC over the
#' values to the right of the maximum, following the dimRed/coRanking package
#' implementations (Kraemer et al 2018, Lee and Verleysen 2009, Chen and Buja
#' 2009). Measures the preservation of global distances, higher values are
#' better.
#' }
#'
#' @param sce A \code{SingleCellExperiment} object.
#' @param dimReds A character vector with the names of the reduced dimension
#' representations from \code{sce} to include in the evaluation. If
#' \code{NULL}, all reduced dimension representations are included.
#' @param refType A character scalar, either "assay" or "dimred", specifying
#' whether to use an assay or a reduced dimension representation of \code{sce}
#' as the reference data source.
#' @param refAssay A character scalar giving the name of the assay from
#' \code{sce} to use as the basis for the distance calculations in the
#' reference space, if \code{refType} if \code{"assay"}.
#' @param refDimRed A character scalar specifying the reduced dimension
#' representation to use as the reference data representation if
#' \code{refType} is \code{"dimred"}.
#' @param features A character vector giving the IDs of the features to use for
#' distance calculations from the chosen assay. Will be matched to the row
#' names of \code{sce}.
#' @param nSamples A numeric scalar, giving the number of columns to subsample
#' (randomly) from \code{sce}.
#' @param distNorm A character scalar, indicating how the distance vectors in
#' the reference and low-dimensional spaces should be normalized before they
#' are compared. If set to "l2", the vectors are L2 normalized, if set to
#' "median" they are divided by the median value times the square root of
#' their length, and if set to any other value they are divided by the square
#' root of their length, to avoid metrics scaling with the number of retained
#' samples.
#' @param refDistMethod A character scalar defining the distance measure to use
#' in the reference space. Must be one of "euclidean", "manhattan", "maximum",
#' "canberra" or "cosine". The distance in the low-dimensional representation
#' will always be Euclidean.
#' @param kTM An integer vector giving the number of neighbors to use for
#' trustworthiness, continuity and Jaccard index calculations.
#' @param labelColumn A character scalar defining a column of
#' \code{colData(sce)} to use as the group assignments in the silhouette width
#' calculations. If not provided, the silhouette widths are not calculated.
#' @param verbose A logical scalar, indicating whether to print out progress
#' messages.
#'
#' @author Charlotte Soneson
#'
#' @export
#'
#' @return A list with two elements:
#' \itemize{
#' \item scores - A \code{data.frame} with values of all evaluation metrics,
#' across the dimension reduction methods. In addition to the metrics, it
#' contains the dimensionality of the respective reduced dimension
#' representations, and the value of K giving the highest value of LCMC (used
#' for the calculations of Qlocal and Qglobal, see Kraemer et al 2018, Lee and
#' Verleysen 2009, Chen and Buja 2009).
#' \item plots - A list of ggplot objects, representing diagnostic plots.
#' }
#'
#' @references
#' Venna J., Kaski S. (2001). Neighborhood preservation in nonlinear
#' projection methods: An experimental study. In Dorffner G., Bischof H.,
#' Hornik K., editors, Proceedings of ICANN 2001, pp 485–491. Springer,
#' Berlin.
#'
#' Lee J.A., Verleysen M. (2009). Quality assessment of
#' dimensionality reduction: Rank-based criteria. Neurocomputing 72
#' (7-9):1431-1443.
#'
#' Chen L., Buja A. (2009). Local multidimensional scaling for nonlinear
#' dimension reduction, graph drawing, and proximity analysis. Journal of the
#' American Statistical Association 104:209-219.
#'
#' Kraemer G., Reichstein M., Mahecha M.D. (2018). dimRed and coRanking -
#' Unifying dimensionality reduction in R. The R Journal 10 (1):342-358.
#'
#' Sammon J.W. Jr (1969). A nonlinear mapping for data structure analysis.
#' IEEE Transactions on Computers C18(5):401-409.
#'
#' Rousseeuw, P.J. (1987). Silhouettes: A graphical aid to the interpretation
#' and validation of cluster analysis. Journal of Computational and Applied
#' Mathematics 20:53-65.
#'
#' @importFrom SingleCellExperiment reducedDims reducedDimNames
#' @importFrom SummarizedExperiment assays colData assayNames
#' @importFrom cluster silhouette
#' @importFrom stats cor ks.test median
#' @importFrom dplyr bind_rows
#' @importFrom wordspace dist.matrix
#' @importFrom coRanking coranking LCMC
#' @importFrom methods is
#' @importFrom ggplot2 ggplot aes geom_hex theme_bw labs scale_fill_gradient
#' geom_abline stat_ecdf
#' @importFrom tidyr gather
#' @importFrom magrittr %>%
#'
#' @examples
#' data(pbmc3ksub)
#' dre <- dreval(sce = pbmc3ksub, nSamples = 150)
#'
dreval <- function(
sce, dimReds = NULL, refType = "assay",
refAssay = "logcounts", refDimRed = NULL,
features = NULL, nSamples = NULL, distNorm = "none",
refDistMethod = "euclidean", kTM = c(10, 100),
labelColumn = NULL, verbose = FALSE) {
## --------------------------------------------------------------------- ##
## Check input arguments
## --------------------------------------------------------------------- ##
if (!methods::is(sce, "SingleCellExperiment")) {
stop("sce must be a SingleCellExperiment object")
}
## If dimReds is NULL, use all dimReds
if (is.null(dimReds)) {
dimReds <- SingleCellExperiment::reducedDimNames(sce)
} else {
dimReds <- intersect(
dimReds, SingleCellExperiment::reducedDimNames(sce)
)
}
## If refType is dimred, don't compare the reference dimred to itself
if (refType == "dimred") {
dimReds <- setdiff(dimReds, refDimRed)
}
if (length(dimReds) == 0) (
stop("No valid reduced dimension representations found")
)
if (!(refType %in% c("assay", "dimred"))) {
stop("'refType' must be either 'assay' or 'dimred'")
}
if (refType == "assay" &&
!(refAssay %in% SummarizedExperiment::assayNames(sce))) {
stop("There is no assay named ", refAssay, " in sce")
}
if (refType == "dimred" &&
!(refDimRed %in% SingleCellExperiment::reducedDimNames(sce))) {
stop("There is no reduced dimension representation named ",
refDimRed, " in sce")
}
if (!is.character(distNorm)) {
stop("distNorm must be a character string")
}
if (!(refDistMethod %in% c("euclidean", "manhattan", "maximum",
"canberra", "cosine"))) {
stop("refDistMethod must be one of ",
"'euclidean', 'manhattan', 'maximum', 'canberra' or 'cosine'")
}
if (!is.numeric(kTM)) {
stop("kTM must be a numeric vector")
}
if (!is.logical(verbose)) {
stop("verbose must be a logical value")
}
## If features is not NULL, subset to provided features
if (refType == "assay" && !is.null(features)) {
if (verbose) message("Subsampling rows...")
features <- intersect(features, rownames(sce))
if (length(features) == 0) {
stop("No features remaining after subsetting. ",
"Make sure that the provided features correspond ",
"to the row names of sce.")
}
sce <- sce[features, ]
}
## If nSamples is not NULL, subsample columns for increased speed
if (!is.null(nSamples)) {
if (verbose) message("Subsampling columns...")
nSamples <- min(nSamples, ncol(sce))
if (nSamples == 0) {
stop("nSamples must be >0")
}
keep <- sample(seq_len(ncol(sce)), nSamples, replace = FALSE)
sce <- sce[, keep]
}
if (!is.null(labelColumn)) {
if (!(labelColumn %in%
colnames(SummarizedExperiment::colData(sce)))) {
stop("labelColumn must be one of the columns in colData(sce)")
}
tmp <- SummarizedExperiment::colData(sce)[[labelColumn]]
if (length(unique(tmp)) < 2) {
stop("labelColumn must correspond to a column ",
"with at least two unique values")
}
if (length(unique(tmp)) == ncol(sce)) {
stop("labelColumn must correspond to a column ",
"where not all values are different")
}
}
## --------------------------------------------------------------------- ##
## Initialize list to hold results
## --------------------------------------------------------------------- ##
results <- lapply(dimReds, function(m) list())
names(results) <- dimReds
plots <- list(disthex = list())
## --------------------------------------------------------------------- ##
## Calculate distances and ranks for the high-dimensional data
## --------------------------------------------------------------------- ##
if (verbose) message("Calculating distances in high-dimensional space...")
if (refType == "assay") {
mat <- as.matrix(SummarizedExperiment::assays(sce)[[refAssay]])
distReference <- wordspace::dist.matrix(
mat, method = refDistMethod,
as.dist = TRUE, byrow = FALSE, convert = FALSE
)
} else if (refType == "dimred") {
mat <- SingleCellExperiment::reducedDims(sce)[[refDimRed]]
distReference <- wordspace::dist.matrix(
mat, method = refDistMethod,
as.dist = TRUE, byrow = TRUE, convert = FALSE
)
} else {
stop("Invalid 'refType'")
}
## Get the rank for each sample compared to each other sample. In each
## column, the row with the value 1 corresponds to the nearest neighbor,
## the one with the value 2 to the second nearest neighbor, etc.
if (verbose) message("Getting ranks in high-dimensional space...")
drm <- as.matrix(distReference)
diag(drm) <- NA
rankReference <- apply(drm, 2, function(w) order(order(w)))
diag(rankReference) <- 0
rownames(rankReference) <- rownames(distReference)
## Define normalization constant for distances
if (distNorm == "l2") {
distNormReference <- sqrt(sum(distReference^2))
} else if (distNorm == "median") {
distNormReference <- stats::median(distReference) *
sqrt(length(distReference))
} else {
distNormReference <- sqrt(length(distReference))
}
distdf <- data.frame(reference = c(distReference/distNormReference))
## --------------------------------------------------------------------- ##
## For each dimRed, calculate scores
## --------------------------------------------------------------------- ##
for (dr in dimReds) {
if (verbose) message(dr, ":")
dimRedMat <- SingleCellExperiment::reducedDims(sce)[[dr]]
## Get dimensionality
results[[dr]]$dimensionality <- ncol(dimRedMat)
## ----------------------------------------------------------------- ##
## Calculate distances and ranks for the low-dimensional data
## ----------------------------------------------------------------- ##
if (verbose)
message(" Calculating distances in low-dimensional space...")
distLowDim <- wordspace::dist.matrix(
as.matrix(dimRedMat), method = "euclidean",
as.dist = TRUE, byrow = TRUE, convert = FALSE
)
## Get the rank for each sample compared to each other sample. In each
## column, the row with the value 1 corresponds to the nearest neighbor,
## the one with the value 2 to the second nearest neighbor, etc.
if (verbose) message(" Getting ranks in low-dimensional space...")
dlm <- as.matrix(distLowDim)
diag(dlm) <- NA
rankLowDim <- apply(dlm, 2, function(w) order(order(w)))
diag(rankLowDim) <- 0
rownames(rankLowDim) <- rownames(distLowDim)
if (distNorm == "l2") {
distNormLowDim <- sqrt(sum(distLowDim^2))
} else if (distNorm == "median") {
distNormLowDim <- stats::median(distLowDim) *
sqrt(length(distLowDim))
} else {
distNormLowDim <- sqrt(length(distLowDim))
}
distdf[[dr]] <- c(distLowDim/distNormLowDim)
## ----------------------------------------------------------------- ##
## Correlation between distance vectors
## ----------------------------------------------------------------- ##
if (verbose) message(" Calculating Spearman correlations...")
results[[dr]]$SpearmanCorrDist <- stats::cor(
distReference, distLowDim,
method = "spearman"
)
if (verbose) message(" Calculating Pearson correlations...")
results[[dr]]$PearsonCorrDist <- stats::cor(
distReference, distLowDim,
method = "pearson"
)
plots$disthex[[dr]] <-
ggplot2::ggplot(
data.frame(reference = c(distReference/distNormReference),
lowdim = c(distLowDim/distNormLowDim)),
ggplot2::aes(x = reference, y = lowdim)
) +
ggplot2::geom_hex(bins = 100, ggplot2::aes(fill = stat(density))) +
ggplot2::scale_fill_gradient(
name = "", low = "bisque2", high = "darkblue"
) +
ggplot2::theme_bw() +
ggplot2::labs(
title = dr, x = "Scaled distance in reference space",
y = "Scaled distance in low-dimensional space"
) +
ggplot2::geom_abline(slope = 1, intercept = 0)
## ----------------------------------------------------------------- ##
## Kolmogorov-Smirnov statistic comparing distance distributions
## ----------------------------------------------------------------- ##
if (verbose) message(" Calculating KS statistic")
results[[dr]]$KSStatDist <- stats::ks.test(
distReference/distNormReference,
distLowDim/distNormLowDim
)$statistic
## ----------------------------------------------------------------- ##
## Euclidean distance to reference-space (scaled) distances
## ----------------------------------------------------------------- ##
if (verbose) message(" Calculating distances between distances...")
results[[dr]]$EuclDistBetweenDists <-
sqrt(sum(((distReference/distNormReference) -
(distLowDim/distNormLowDim))^2))
## ----------------------------------------------------------------- ##
## Sammon stress
## ----------------------------------------------------------------- ##
if (verbose) message(" Calculating Sammon stress...")
results[[dr]]$SammonStress <-
1/sum(distReference/distNormReference) *
sum(((distReference/distNormReference -
distLowDim/distNormLowDim) ^ 2) /
(distReference/distNormReference))
## ----------------------------------------------------------------- ##
## Trustworthiness and continuity
## ----------------------------------------------------------------- ##
for (k in kTM) {
if (verbose) message(" Calculating trustworthiness, k=", k)
tm <- calcTrustworthinessFromRank(
rankReference = rankReference,
rankLowDim = rankLowDim,
kTM = k
)
results[[dr]][[paste0("Trustworthiness_k", k)]] <- tm
if (verbose) message(" Calculating continuity, k=", k)
ct <- calcContinuityFromRank(
rankReference = rankReference,
rankLowDim = rankLowDim,
kTM = k
)
results[[dr]][[paste0("Continuity_k", k)]] <- ct
}
## ----------------------------------------------------------------- ##
## Jaccard index of nearest neighbors
## ----------------------------------------------------------------- ##
for (k in kTM) {
if (verbose) message(" Calculating Jaccard index ",
"of nearest neighbors, k=", k)
intrs <- colSums((rankReference <= k) * (rankLowDim <= k))
unin <- colSums(sign((rankReference <= k) + (rankLowDim <= k)))
jaccs <- intrs/unin
results[[dr]][[paste0("MeanJaccard_k", k)]] <- mean(jaccs)
}
## ----------------------------------------------------------------- ##
## Silhouette index relative to known labels
## ----------------------------------------------------------------- ##
if (!is.null(labelColumn)) {
silh <- cluster::silhouette(
x = as.numeric(as.factor(
SummarizedExperiment::colData(sce)[[labelColumn]]
)),
dist = distLowDim
)
results[[dr]][[paste0("MeanSilhouette_", labelColumn)]] <-
summary(silh)$avg.width
}
## ----------------------------------------------------------------- ##
## Coranking (with the coRanking package)
## ----------------------------------------------------------------- ##
qt <- coRanking::coranking(
Xi = as.matrix(distReference),
X = as.matrix(distLowDim),
input_Xi = "dist",
input_X = "dist",
)
lcmc <- coRanking::LCMC(qt)
## We follow the implementation in the dimRed package, where Qlocal and
## Qglobal are calculated as averages of LCMC values (not Q_NX values)
Kmax <- which.max(lcmc)
qlocal <- mean(lcmc[seq(from = 1, to = Kmax, by = 1)])
qglobal <- mean(lcmc[seq(from = Kmax + 1, to = length(lcmc), by = 1)])
results[[dr]][["coRankingQlocal"]] <- qlocal
results[[dr]][["coRankingQglobal"]] <- qglobal
results[[dr]][["KmaxLCMC"]] <- Kmax
}
plots$distcdf <-
ggplot2::ggplot(
distdf %>% tidyr::gather(key = "dr", value = "distance"),
ggplot2::aes(x = distance, color = dr)
) +
ggplot2::stat_ecdf() + ggplot2::theme_bw()
results <- do.call(dplyr::bind_rows, lapply(names(results), function(nm) {
data.frame(
Method = nm, as.data.frame(results[[nm]]),
stringsAsFactors = FALSE
)
}))
list(scores = results, plots = plots)
}
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