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From "Nathan Halko (JIRA)" <j...@apache.org>
Subject [jira] [Commented] (MAHOUT-796) Modified power iterations in existing SSVD code
Date Fri, 26 Aug 2011 02:48:29 GMT

    [ https://issues.apache.org/jira/browse/MAHOUT-796?page=com.atlassian.jira.plugin.system.issuetabpanels:comment-tabpanel&focusedCommentId=13091533#comment-13091533
] 

Nathan Halko commented on MAHOUT-796:
-------------------------------------

We did some work with facial recognition, computing 'eigenfaces' and reported in the paper.
 In this case there is only 2 orders of magnitude between the signal and the 'noise'.  It
shows a dramatic difference between the accuracy of one pass versus just one power iteration.
 Note that after one power iteration, there is now 6 orders of magnitude separating signal
and noise.  

But this is only looking at approximation error ||A-UU*A||.  It could very well be the case
in recommendation applications that this measure is not appropriate, I don't know.  But it
is a very valuable option to have at one's disposal just in case.

> 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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