mjcasy / infohet

Information in Heterogeneity

infohet

Package for the quantification of the information content of single-cell RNA-sequencing data-sets, and how much of this information has been explained by clustering. Based on the quantification of information in heterogeneity (infohet). Preprint - https://www.biorxiv.org/content/10.1101/2020.10.01.322255v2

The package can be used for the calculation of several information theoretic quantities, most importantly:

1. Het - gene-wise measure of information obtained
2. Net Information - measure of the information explained by a given clustering, penalised by the complexity of the clustering

Het and net information can be used for feature selection and clustering evaluation, as presented below:

Installation

install.packages("devtools")
devtools::install_github("mjcasy/infohet")

Workflow

We will use a dataset with a known cluster structure for this example. ScMixology (https://github.com/LuyiTian/sc_mixology) has several datasets that consist of mixtures of cancer cell lines, enabling the identity of each cell to be identified by genotyping. We will be using the mixture of three cell lines (sincell_with_class.RDat).

Setup. Load in Data and filter low expressing genes (less than 100 transcripts total). Note that infohet works off of the sparse matrix format (“dgCMatrix”). This is the same object type as used in the popular Seurat package, and a normal numeric matrix can be converted to the sparse format using the Seurat function as.sparse().

library(infohet)
library(RColorBrewer)
library(Matrix)

load("../Data/Tian2018/ThreeClasses/CountsMatrix")
CountsMatrix <- CountsMatrix[rowSums(CountsMatrix) > 100,]

Feature Selection

We can determine the amount of information in the heterogeneity of each genes expression pattern. This is the number of bits required to encode the deviation of observed gene expression from homogeneity, i.e. equal gene expression in each cell.

We then select highly informative genes by thresholding, choosing those genes with more than 1 bit of information.

Information <- getHet(CountsMatrix)

HighlyInformative <- Information > 1

N <- CountsMatrix@Dim[2]
Mean <- log10(rowMeans(CountsMatrix))

HetDataFrame <- data.frame(Mean, Information)

ColourSelected <- brewer.pal(9, "Blues")[8]
ColourNotSelected <- brewer.pal(9, "Blues")[4]

plot(HetDataFrame$Mean, 
     HetDataFrame$Information,
     col = ifelse(HighlyInformative, ColourSelected, ColourNotSelected),
     ylim = c(0, log2(N)),
     pch = 20)

Clustering Evaluation

Information is additively decomposable based on a given clustering of cells into that information explained by the differential expression of a gene between clusters, and that which remains unexplained.

Given the goal of clustering is to explain the heterogeneity in gene expression, information explained is a natural measure for cluster evaluation.

Further, information is additive between independent sources. Taking each gene as independent, the total information explained by a given clustering can be found.

Finally, note that information will never increase with increasing cluster number. We account for this increase by quantifying the amount of information required to encode a given cluster structure, (H(S)) and penalizing clusterings accordingly. We can therefore calcuate the net information explained by a given clustering.

Being a global measure of cluster quality, independent of cluster number, net information can serve as a powerful basis of hyperparameter selection. For instance, determining that there are three discrete cellular identities in the scMixology data set.

library(Seurat)

load("../Data/Tian2018/ThreeClasses/Identity")

SeuObj <- Seurat::CreateSeuratObject(CountsMatrix)
SeuObj <- Seurat::SCTransform(SeuObj)
Data <- SeuObj@assays$[e-mail]

SeuObj <- RunPCA(SeuObj, verbose = FALSE)
SeuObj <- FindNeighbors(SeuObj, dims = 1:30, verbose = FALSE)

Resolutions <- c(seq(0.0001, 0.001, 0.0001), seq(0.002, 0.01, 0.001), seq(0.02, 0.2, 0.01), seq(0.3, 1, 0.1))

NumClusters <- c()
NetInformation <- c()

for(i in 1:length(Resolutions)){
  Idents(SeuObj) <- NA
  
  SeuObj <- FindClusters(SeuObj, verbose = FALSE, resolution = Resolutions[i])
  
  Identity <- Idents(SeuObj)
  
  NetInformation[i] <- netInformation(CountsMatrix, Identity, Information)
  
  NumClusters[i] <- length(levels(Identity))
}

Elbow <- cbind(Resolutions, NumClusters, NetInformation)