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https://issues.apache.org/jira/browse/MAHOUT-796?page=com.atlassian.jira.plugin.system.issuetabpanels:comment-tabpanel&focusedCommentId=13092179#comment-13092179
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Nathan Halko commented on MAHOUT-796:
-------------------------------------
The reorthogonalizations aren't essential and if its a barrier to power
iterations we should forego them at the moment. 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. This could be
extremely naive but I've been getting some good results with it. The accuracy
typically falls about half way between single pass and full power iterations so
it could be useful (although it could be dangerous as well).
sig_51 <- optimal
60.6531
full power iters 1
81.2668
full power iters 4
67.5545
row-wise power iters 1
89.4983
row-wise power iters 4
82.2247
single pass
92.8736
norm A
100.0000
The 'row-wise power iters' being (A_iA_i')^qA_i\Omega.
> 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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