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https://issues.apache.org/jira/browse/MAHOUT-797?page=com.atlassian.jira.plugin.system.issuetabpanels:comment-tabpanel&focusedCommentId=13167379#comment-13167379
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Ted Dunning commented on MAHOUT-797:
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The problem you are having is that a rank deficient matrix doesn't have an
inverse because some of the singular values are zero.
In the Cholesky decomposition of a rank deficient matrix, each step proceeds by
dividing by the next remaining diagonal element. If that element is zero, then
things cannot proceed. If you are lucky, you already have the basis formed and
could just quit. Otherwise, there is more work to do, but that work depends on
doing the step with the zero diagonal. With pivoting, you work on the
columns/rows of the remaining matrix out of order so that you guarantee to
complete the basis.
In general, you should never compute the inverse of any matrix. Instead, you
should use some sort of solver. In the case of a triangular matrix, the solver
is a back-substitution.
> MapReduce SSVD: provide alternative B-pipeline per B=R' ^{-1} Y'A
> -----------------------------------------------------------------
>
> Key: MAHOUT-797
> URL: https://issues.apache.org/jira/browse/MAHOUT-797
> Project: Mahout
> Issue Type: Improvement
> Affects Versions: 0.5, 0.6
> Reporter: Dmitriy Lyubimov
> Assignee: Dmitriy Lyubimov
> Fix For: Backlog
>
> Attachments: MAHOUT-797.pdf
>
> Original Estimate: 48h
> Remaining Estimate: 48h
>
> Since alternative flow using Cholesky decomposition is extremely easy to add
> to existing computations of BB', I am thinking of just adding an option that
> chooses between B-pipeline with QR step and B-pipeline with Y'Y-Cholesky
> step.
> Ongoing work and some initial code (Y'Y step) is here
> https://github.com/dlyubimov/mahout-commits/tree/MAHOUT-797.
> I also want to fix what's left unfixed in MAHOUT-638.
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