make_compositional_variance {PoissonPCA} | R Documentation |
Given a covariance matrix, removes multiplicative noise
make_compositional_variance(Sigma) make_compositional_min_var(Sigma)
Sigma |
the uncorrected covariance matrix |
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
.
The compositionally corrected covariance matrix.
Toby Kenney tkenney@mathstat.dal.ca and Tianshu Huang
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)