intersectGraphs: Intersect two graphs

In LTLA/mumosa: Multi-Modal Single-Cell Analysis Methods

Intersect two graphs

Description

Intersect two graphs by taking the product of their edge weights.

Usage

intersectGraphs(..., mixing = NULL, nominal = 1e-06)

Arguments

...	Any number of graph objects for the same set and order of nodes.
mixing	Numeric vector of length equal to the number of graphs, specifying the mixing weights for the edge weights.
nominal	Numeric scalar specifying the scaling factor to compute the nominal weight.

Details

The idea of taking an intersection of a weighted graph is based on the intersection of simplicial sets in the UMAP algorithm. For each edge that exists in either graph, we compute the product of the weights across all graphs and assign that value as the edge weight in the output graph. This means that edges in the output only have high weight if they are present and highly weighted in all graphs - hence, an intersection.

This approach would make for a very sparse graph if the product was taken directly. To maintain some connectivity, edges that exist in one graph but not the other are assigned nominal weights in the latter to ensure that the product is not zero. The nominal weight for each graph is defined as the product of its smallest non-zero edge weight and nominal. Decreasing this value will yield a more conservative intersection and a less connected graph, usually manifesting as smaller clusters after application of community detection algorithms.

By default, mixing is a vector of length equal to the numbeer of graphs, containing values of 1. This means that edge weights from each graph in ... contribute equally to the product. However, it is possible to increase the contribution of some of the graphs by supplying a higher mixing values for those graphs.

Unweighted graphs are supported and are considered to have edge weights of 1.

Value

A graph object containing the intersection of g1 and g2.

Author(s)

Aaron Lun

Examples

library(scran)

mat1 <- matrix(rnorm(10000), ncol=20)
chosen <- 1:250
mat1[chosen,1] <- mat1[chosen,1] + 10
g1 <- buildSNNGraph(mat1, d=NA, transposed=TRUE)
clusters1 <- igraph::cluster_walktrap(g1)$membership
table(clusters1, chosen=mat1[,1] > 5)

# Pretending we have some other data for the same cells, e.g., ADT.
mat2 <- matrix(rnorm(10000), ncol=20)
chosen <- c(1:125, 251:375)
mat2[chosen,2] <- mat2[chosen,2] + 10
g2 <- buildSNNGraph(mat2, d=NA, transposed=TRUE)
clusters2 <- igraph::cluster_walktrap(g2)$membership
table(clusters2, mat2[,2] > 5)

# Intersecting the graphs and clustering:
gcom <- intersectGraphs(g1, g2)
clustersC <- igraph::cluster_walktrap(gcom)$membership
table(clustersC, mat1[,1] > 5)
table(clustersC, mat2[,2] > 5)

LTLA/mumosa documentation built on Oct. 1, 2024, 8:47 a.m.