BioQC (version 1.0.0)

entropy: Shannon entropy and related concepts

Description

These functions calculate Shannon entropy and related concepts, including diversity, specificity, and specialization. They can be used to quantify gene expression profiles.

Usage

entropy(vector)
entropyDiversity(mat, norm=FALSE)
entropySpecificity(mat, norm=FALSE)
sampleSpecialization(mat, norm=TRUE)

Arguments

vector

A vector of numbers, or characters. Discrete probability of each item is calculated and the Shannon entropy is returned.

mat

A matrix (usually an expression matrix), with genes (features) in rows and samples in columns.

norm

Logical value. If set to TRUE the scores will be normalized between 0 and 1.

Value

entropy returns one entropy value. entropyDiversity and sampleSpecialization returns a vector as long as the column number of the input matrix. entropySpecificity returns a vector of the length of the row number of the input matrix, namely the specificity score of genes.

Details

Shannon entropy can be used as measures of gene expression specificity, as well as measures of tissue diversity and specialization. See references below.

We use 2 as base for the entropy calculation, because in this base the unit of entropy is bit.

References

Martinez and Reyes-Valdes (2008) Defining diversity, specialization, and gene specificity in transcriptomes through information theory. PNAS 105(28):9709--9714

Examples

myVec0 <- 1:9
entropy(myVec0) ## log2(9)
myVec1 <- rep(1, 9)
entropy(myVec1)

myMat <- rbind(c(3,4,5),c(6,6,6), c(0,2,4))
entropySpecificity(myMat)
entropySpecificity(myMat, norm=TRUE)
entropyDiversity(myMat)
entropyDiversity(myMat, norm=TRUE)
sampleSpecialization(myMat)
sampleSpecialization(myMat,norm=TRUE)

myRandomMat <- matrix(runif(1000), ncol=20)
entropySpecificity(myRandomMat)
entropySpecificity(myRandomMat, norm=TRUE)
entropyDiversity(myRandomMat)
entropyDiversity(myRandomMat, norm=TRUE)
sampleSpecialization(myRandomMat)
sampleSpecialization(myRandomMat,norm=TRUE)