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https://issues.apache.org/jira/browse/MAHOUT-796?page=com.atlassian.jira.plugin.system.issuetabpanels:comment-tabpanel&focusedCommentId=13092386#comment-13092386
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Dmitriy Lyubimov edited comment on MAHOUT-796 at 8/28/11 12:52 AM:
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And finally, i can't see a reason why we can't incorporate "Cholesky trick"
either by substituting Y_1..Y_q = AB' instead of A\Omega to compute B_i.
In other words, MR operationally aside, if we assert that we have some function
such that currently provides B_0=g(Y_0) where Y_0=A\Omega, then there's no
reason to assume we can't use the same function g to compute B_i=g(Y_i) for as
long as Y_i=AB'_{i-1}. also see my scratchpad for the same.
was (Author: dlyubimov):
And finally, i can't see a reason why we can't incorporate "Cholesky trick"
either by substituting Y_1..Y_q = AB' instead of A\Omega to compute B_i.
In other words, if we assert that we have some function such that currently
provides B_0=g(Y_0) where Y_0=A\Omega, then there's no reason to assume we
can't use the same function g to compute B_i=g(Y_i) for as long as
Y_i=AB'_{i-1}. also see my scratchpad for the same.
> 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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