Re: efficient normalization of matrix columns?

[Joachim De Beule]

Me again,

It seems that the following function solves my problem:

function Xn = normalizeX (X)
   norms = spdiag(1./sqrt(sumsq(X)));
   Xn = X*norms;
endfunction

It is fast and relatively cheap on memory. 

Best, Joachim. 

On Tuesday 26 October 2010 12:25:55 pm Joachim De Beule wrote:
> Hi all,
>
> 1) I have the following function that normalizes the columns in a sparse
> matrix X and returns the result as a sparse matrix Xn:
>
> function Xn = normalizeX (X)
>     norms = sqrt(sumsq(X));
>     [i,j,v] = find (X);
>     [n, m] = size(X);
>     v = v./full(norms(j'))';
>     Xn = sparse(i,j,v,n,m);
> endfunction
>
> On my computer, this function takes about 0.7 seconds when applied to a
> random (sparse) matrix of 1000 by 1000.
>
> It uses a huge amount of memory however, and becomes unfeasible to use on
> really large matrices (I need to apply it to matrices of size 3206978  by
> 18846)
>
> 2) On the other hand, the following function performs better on memory, but
> takes over 27 seconds to terminate on the same random matrix as mentioned
> above:
>
> function Xn = normalizeX (X)
>    norms = sqrt(sumsq(X));
>    for c = 1:size(X)(2)
>       Xn(:,c) = X(:,c)./norms(c);
>    endfor
> endfunction
>
> 3) In short, it seems that it is not possible to normalize a large sparse
> matrix in octave, either because it requires too much memory or else
> because it takes too long too compute. Any ideas?
>
>
> Thanks, Joachim.
>
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