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https://issues.apache.org/jira/browse/MAHOUT-180?page=com.atlassian.jira.plugin.system.issuetabpanels:comment-tabpanel&focusedCommentId=12832824#action_12832824
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Jake Mannix commented on MAHOUT-180:
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Yes. Multiplication of a matrix (or the square of a matrix) by a vector is the
primary operation of Lanczos, and that is done in a M/R iteration. If you want
the top-k singular vectors, you make k passes over the data.
Once stochastic decomposition is added later, it will be O(1) passes over the
data, but they will be slightly heavier duty passes.
> port Hadoop-ified Lanczos SVD implementation from decomposer
> ------------------------------------------------------------
>
> Key: MAHOUT-180
> URL: https://issues.apache.org/jira/browse/MAHOUT-180
> Project: Mahout
> Issue Type: New Feature
> Components: Math
> Affects Versions: 0.2
> Reporter: Jake Mannix
> Assignee: Jake Mannix
> Priority: Minor
> Fix For: 0.3
>
> Attachments: MAHOUT-180.patch, MAHOUT-180.patch, MAHOUT-180.patch,
> MAHOUT-180.patch
>
>
> I wrote up a hadoop version of the Lanczos algorithm for performing SVD on
> sparse matrices available at http://decomposer.googlecode.com/, which is
> Apache-licensed, and I'm willing to donate it. I'll have to port over the
> implementation to use Mahout vectors, or else add in these vectors as well.
> Current issues with the decomposer implementation include: if your matrix is
> really big, you need to re-normalize before decomposition: find the largest
> eigenvalue first, and divide all your rows by that value, then decompose, or
> else you'll blow over Double.MAX_VALUE once you've run too many iterations
> (the L^2 norm of intermediate vectors grows roughly as
> (largest-eigenvalue)^(num-eigenvalues-found-so-far), so losing precision on
> the lower end is better than blowing over MAX_VALUE). When this is ported to
> Mahout, we should add in the capability to do this automatically (run a
> couple iterations to find the largest eigenvalue, save that, then iterate
> while scaling vectors by 1/max_eigenvalue).
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