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https://issues.apache.org/jira/browse/MAHOUT-796?page=com.atlassian.jira.plugin.system.issuetabpanels:comment-tabpanel&focusedCommentId=13092380#comment-13092380
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Dmitriy Lyubimov commented on MAHOUT-796:
-----------------------------------------
Hi,
I put together B_i pipeline
https://github.com/dlyubimov/ssvd-lsi/wiki/Power-iterations-scratchpad. It
seems it is a pretty straightforward enhancement that falls back on a lot of
existing stuff, with fundamental additions of AB' multiplication and QR
pushdown to reducer of the first job (instead of doing it in the mapper of the
first job)
bq. A quick and dirty trick to avoid even sweeping through A again is to
neglect the cross terms in the product (AA')^qA\Omega and just use
(A_iA_i')^qA_i\Omega.
I think that even if that's less flops, it is still more difficult to implement
than the full power iterations with reorthogonalization as you've initially
proposed.
After all, IMO there's no big reason to be afraid of more work for as long as
it brings more precision and we have a control over how much more work we want
to do.
I also can incorporate a Cholesky trick into B_0 pipeline at some point -- or
just have it as an alternative flow controlled by a job parameter.
> Modified power iterations in existing SSVD code
> -----------------------------------------------
>
> Key: MAHOUT-796
> URL: https://issues.apache.org/jira/browse/MAHOUT-796
> Project: Mahout
> Issue Type: Improvement
> Components: Math
> Affects Versions: 0.5
> Reporter: Dmitriy Lyubimov
> Assignee: Dmitriy Lyubimov
> Labels: SSVD
> Fix For: 0.6
>
>
> Nathan Halko contacted me and pointed out importance of availability of power
> iterations and their significant effect on accuracy of smaller eigenvalues
> and noise attenuation.
> Essentially, we would like to introduce yet another job parameter, q, that
> governs amount of optional power iterations. The suggestion how to modify the
> algorithm is outlined here :
> https://github.com/dlyubimov/ssvd-lsi/wiki/Power-iterations-scratchpad .
> Note that it is different from original power iterations formula in the paper
> in the sense that additional orthogonalization performed after each
> iteration. Nathan points out that that improves errors in smaller eigenvalues
> a lot (If i interpret it right).
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