corr() with sparse matrix - MATLAB - matlab

Question

I wonder whether MATLAB has a toolbox to do common matrixial operation with sparse matrices.
Using a dense matrix, I can compute the correlogram matrix doing:
R = rand(10,100)
[r,p] = corr(R)
With sparse matrix I would love to do:
S = sprand(10,100,.2)
[r,p] = corr(S)
However, the following error is elicited:
Error using betainc
Inputs must be real, full, and double or single.
Error in tcdf (line 70)
p(t) = betainc(xsq(t) ./ (v(t) + xsq(t)), 0.5, v(t)/2, 'upper') / 2;
Error in corr>pvalPearson (line 720)
p = 2*tcdf(-abs(t),n-2);
Error in corr>corrPearson (line 321)
pval(ltri) = pvalPearson(tail, coef(ltri), n);
Error in corr (line 204)
[coef,pval] = corrFun(rows,tail,x);
Can anyone help me?

Answer 1

Cmon ppl, let's do some math! Let x be a random vector. An entry in the correlation matrix CORR(x_i, x_j) is given by:
CORR(x_i, x_j) = COV(x_i, x_j) / (SQRT(VAR(x_i)) *SQRT(VAR(x_j));
That is, to build our correlation matrix, we need the covariance matrix, which also gives us the individual variances. Formula for covariance: COV(x) = E[x*x'] - E[x]E[x]'. We can then approximate the the population moments E[x*x'] with the sample moments (i.e. X'*X/n and mean(X))
Hence the following Matlab code:
[n, k] = size(X);
Exxprim = full(X'*X)/n; %I'm shocked if this isn't full so let's drop sparse now
Ex = full(mean(X))'; %same deal
COVX = (Exxprim - Ex*Ex');
STDEVX = sqrt(diag(COVX));
CORRX = COVX ./ (STDEVX * STDEVX');
This may help if X'*X and mean(X) can be done more efficiently because X is sparse.