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https://issues.apache.org/jira/browse/MAHOUT-796?page=com.atlassian.jira.plugin.system.issuetabpanels:comment-tabpanel&focusedCommentId=13092000#comment-13092000
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Ted Dunning commented on MAHOUT-796:
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To clarify a bit about my worries, the issue that I see is that we could
compute A\Omega in a single pass of A because we could effectively store all of
\Omega in memory (i.e. just keep the seed and hash function). This is nice
because row-wise decomposition of A makes everything work nicely.
In computing (AB') A out-of-core, however, we have a product of A by a tall
skinny matrix B that requires roughly as much storage as A. Each row-wise
patch of A will have to be combined with each row-wise chunk of B' (i.e. each
column-wise chunk of B). This means that we have to read B many times which
leads to quadratic time.
> 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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