Running cor() (or any variant) over a sparse matrix in R

Question

When trying to run the cor() function on sparse matrices (of either type dgCMatrix or dgTMatrix) I get the following error:

Error in cor(x) : su         


        

Answer 1

The answer was solved elegantly by @Ron but a slight modification to the solution is a little cleaner and also returns the sample covariance matrix.

sparse.cor4 <- function(x){
    n <- nrow(x)
    cMeans <- colMeans(x)
    covmat <- (as.matrix(crossprod(x)) - n*tcrossprod(cMeans))/(n-1)
    sdvec <- sqrt(diag(covmat)) 
    cormat <- covmat/tcrossprod(sdvec)
    list(cov=covmat,cor=cormat)
}

The simplification comes from this: with an n x p matrix X, and an n x p matrix M of the column means of X:

cov(X) = E[(X-M)'(X-M)] = E[X'X - M'X - X'M + M'M] 

M'X = X'M = M'M, which have (i,j) elements = sum(column i) * sum(column j) / n

= n * mean(column i) * mean(column j)

or written with a row vector m of the column means,

= n * m'm

Then cov(X) = E[X'X - n m'm]

---

and it is now a smidge faster.

> X <- sample(0:10,1e7,replace=T,p=c(0.9,rep(0.01,10)))
> x <- Matrix(X,ncol=10)
> system.time(corx <- sparse.cor(x))
   user  system elapsed 
  1.139   0.196   1.334 
> system.time(corx3 <- sparse.cor3(x))
   user  system elapsed 
  0.194   0.007   0.201 
> system.time(corx4 <- sparse.cor4(x))
   user  system elapsed 
  0.187   0.007   0.194 
> system.time(correg <-cor(as.matrix(x)))
   user  system elapsed 
  0.341   0.067   0.407 
> system.time(covreg <- cov(as.matrix(x)))
   user  system elapsed 
  0.314   0.016   0.330 
> all.equal(c(as.matrix(corx)),c(as.matrix(correg)))
[1] TRUE
> all.equal(c(as.matrix(corx3)),c(as.matrix(correg)))
[1] TRUE
> all.equal(c(as.matrix(corx4$cor)),c(as.matrix(correg)))
[1] TRUE
> all.equal(c(as.matrix(corx4$cov)),c(as.matrix(covreg)))
[1] TRUE