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https://issues.apache.org/jira/browse/MAHOUT-796?page=com.atlassian.jira.plugin.system.issuetabpanels:comment-tabpanel&focusedCommentId=13091601#comment-13091601
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Ted Dunning commented on MAHOUT-796:
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One problem here is that the Q's are large and potentially dense. Thus,
accumulating them is not a great idea. That can be worked around in the single
iteration because we can keep R in memory and can reconstruct chunks of Y given
chunks of A.
That trick becomes a bit more involved if we want to keep all of the Q's in
such an implicit form. Computing (AA')^q A\Omega is relatively simple as you
point out if A' is available as a linear operator, but I thought I understood
that reorthogonalizing was a good idea. What I don't see is how to
re-orthogonalize without keeping very large matrices in memory or doing a
dangerously dense operation. Yet.
> 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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