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From Dmitriy Lyubimov <dlie...@gmail.com>
Subject Re: SSVD compute U * Sigma
Date Fri, 07 Sep 2012 20:19:52 GMT
On Fri, Sep 7, 2012 at 1:11 PM, Pat Ferrel <pat.ferrel@gmail.com> wrote:
> OK, U * Sigma seems to be working in the patch of SSVDSolver.
>
> However I still have no doc ids in U. Has anyone seen a case where they are preserved?

That should not be the case. Ids in rows of U are inherited from rows
of A. (should be at least).

>
> For
>     BtJob.run(conf,
>                 inputPath,
>                 qPath,
>                 pcaMeanPath,
>                 btPath,
>                 minSplitSize,
>                 k,
>                 p,
>                 outerBlockHeight,
>                 q <= 0 ? Math.min(1000, reduceTasks) : reduceTasks,
>                 broadcast,
>                 labelType,
>                 q <= 0);
>
> inputPath here contains a distributedRowMatrix with text doc ids.
>
> Bt-job/part-r-00000 has no ids after the BtJob. Not sure where else to look for them
and BtJob is the only place the input matrix is used, the rest are intermediates afaict and
anyway don't have ids either.
>
> Is something in BtJob stripping them? It looks like ids are ignored in the MR code but
maybe its hidden…
>
> Are the Keys of U guaranteed  to be the same as A? If so I could construct an index for
A and use it on U but it would be nice to get them out of the solver.

Yes, that's the idea.

B^t matrix will not have the ideas, not sure why you are looking
there. you need U matrix. Which is solved by another job.

>
> On Sep 7, 2012, at 9:18 AM, Dmitriy Lyubimov <dlieu.7@gmail.com> wrote:
>
> Yes you got it, thats what i was proposing before. A very easy patch.
> On Sep 7, 2012 9:11 AM, "Pat Ferrel" <pat.ferrel@gmail.com> 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,
>>                        qRow.dot(uHat.viewColumn(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 <dlieu.7@gmail.com> 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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