make_compositional_variance {PoissonPCA}

Converts a covariance matrix to compositional form

Description

Given a covariance matrix, removes multiplicative noise

Usage

make_compositional_variance(Sigma)
make_compositional_min_var(Sigma)

Arguments

Sigma

the uncorrected covariance matrix

Details

The two functions use different methods. make_compositional_variance calculates the variance of compositional data that agrees with Sigma (viewed as a bilinear form) on compositional vectors. That is, the return value Sigma_c is a symmetric matrix which satisfies t(u)%*%Sigma_c%*%v=t(u)%*%Sigma%*%v for any compositional vectors u and v, and also rowSums(Sigma_c)=0.

Value

The compositionally corrected covariance matrix.

Author(s)

Toby Kenney [e-mail] and Tianshu Huang

Examples

n<-10
p<-5

X<-rnorm(n*p)

dim(X)<-c(n,p)
Sigma<-t(X)%*%X/(n-1)

SigmaComp<-make_compositional_variance(Sigma)

SigmaCompMin<-make_compositional_min_var(Sigma)