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https://issues.apache.org/jira/browse/MAHOUT-796?page=com.atlassian.jira.plugin.system.issuetabpanels:comment-tabpanel&focusedCommentId=13091545#comment-13091545
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Nathan Halko edited comment on MAHOUT-796 at 8/26/11 3:32 AM:
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I checked Dmitriy's scheme today and it makes sense. It accumulates Q' using
the machinery already in place, QJob and BtJob
QR = Y = A\Omega
B0 = Q'A
B1 = (AB0')'A = B0A'A = (Q'AA')A = (Q_new)'A
A'A should never be computed, only Z = A'AY where Y is dense and X=AY, Z=A'X
avoiding the problem of scarce overlap and fill in.
was (Author: nathanhalko):
I checked Dmitriy's scheme today and it makes sense. It accumulates Q*
using the machinery already in place, QJob and BtJob
QR = Y = A\Omega
B0 = Q*A
B1 = (AB0*)*A = B0A*A = (Q*AA*)A = (Q_new)*A
A'A should never be computed, only Z = A'AY where Y is dense and X=AY, Z=A'X
avoiding the problem of scarce overlap and fill in.
> 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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