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From Dmitriy Lyubimov <>
Subject Re: SSVD compute U * Sigma
Date Fri, 07 Sep 2012 16:18:15 GMT
Yes you got it, thats what i was proposing before. A very easy patch.
On Sep 7, 2012 9:11 AM, "Pat Ferrel" <> wrote:

> U*Sigma[i,j]=U[i,j]*sv[j] is what I meant by "write your own multiply".
> WRT using U * Sigma vs. U * Sigma^(1/2) I do want to retain distance
> proportions for doing clustering and similarity (though not sure if this is
> strictly required with cosine distance) I probably want to use U * Sigma
> instead of sqrt Sigma.
> Since I have no other reason to load U row by row I could write another
> transform and keep it out of the mahout core but doing this in a patch
> seems trivial. Just create a new flag, something like --uSigma (the CLI
> option looks like the hardest part actually). For the API there needs to be
> a new setter something like SSVDSolver#setComputeUSigma(true) then do an
> extra flag check in the setup for the UJob, something like the following
>       if (context.getConfiguration().get(PROP_U_SIGMA) != null) { //set
> from --uSigma option or SSVDSolver#setComputeUSigma(true)
>         sValues = SSVDHelper.loadVector(sigmaPath,
> context.getConfiguration());
>         // sValues.assign(Functions.SQRT);  // no need to take the sqrt
> for Sigma weighting
>       }
> sValues is already applied to U in the map, which would remain unchanged
> since the sigma weighted (instead of sqrt sigma) values will already be in
> sValues.
>       if (sValues != null) {
>         for (int i = 0; i < k; i++) {
>           uRow.setQuick(i,
>                *
> sValues.getQuick(i));
>         }
>       } else {
>         …
> I'll give this a try and if it seems reasonable submit a patch.
> On Sep 6, 2012, at 1:01 PM, Dmitriy Lyubimov <> wrote:
> >
> > When using PCA it's also preferable to use --uHalfSigma to create U with
> the SSVD solver. One difficulty is that to perform the multiplication you
> have to turn the singular values vector (diagonal values) into a
> distributed row matrix or write your own multiply function, correct?
> You could do that, but why? Sigma is a diagonal matrix (which
> additionally encoded as a very short vector of singular values of
> length k, say we denote it as 'sv'). Given that, there's absolutely 0
> reason to encode it as Distributed row matrix.
> Multiplication can be done on the fly as you load U, row by row:
> U*Sigma[i,j]=U[i,j]*sv[j]
> One inconvenience with that approach is that it assumes you can freely
> hack the code that loads U matrix for further processing.
> It is much easier to have SSVD to output U*Sigma directly using the
> same logic as above (requires a patch) or just have it output
> U*Sigma^0.5 (does not require a patch).
> You could even use U in some cases directly, but part of the problem
> is that data variances will be normalized in all directions compared
> to PCA space, which will affect actual distances between data points.
> If you want to retain proportions of the directional variances as in
> your original input, you need to use principal components with scaling
> applied, i.e. U*Sigma.

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