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https://issues.apache.org/jira/browse/MAHOUT-796?page=com.atlassian.jira.plugin.system.issuetabpanels:comment-tabpanel&focusedCommentId=13096264#comment-13096264
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Dmitriy Lyubimov edited comment on MAHOUT-796 at 9/2/11 8:18 PM:
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I am now convinced that all the inefficiency and cpu-bound behavior comes from
the multiplications Q'B, AB'. Indeed, I generate outer products which i then
output row by row and sum up in combiners and reducers. this creates tremendous
pressure in terms of keys for spill and reduce sorts. Although it seems
DRM.times(DRM) employs exactly the same problem.
I think tremendous improvements would result if we output outer products of B'
or AB' in vertical thin but long blocks.
This seem like a trivial idea but I was preoccupied by 'proof of concept'
issues whereas matrix multiplication has been seen as algorithmically trivial.
the command line i used:
bin/mahout ssvd --input /tmp/DRM/* --output /tmp/SSVD1 --tempDir /tmp/SSVD-tmp
-k 10 -p 3 -q 1 -r 10000 --reduceTasks 3 -Dmapred.child.java.opts='-Xmx500m'
For ABt job you need perhaps more than double the memory of the split in case
of dense input because ABtJob is catering to sparse inputs first and loads A
block column-wise using SequentialAccessSparseVectors. So for a split size of
64Mb standard -Xmx200m may not be enough, and it is definitely not enough for
128mb splits.
note also that I ran on CDH3u0 without any Mahout recompilation with CDH3
binaries and it seems to work out of the box.
was (Author: dlyubimov):
I am now convinced that all the inefficiency and cpu-bound behavior comes
from the multiplications Q'B, AB'. Indeed, I generate outer products which i
then output row by row and sum up in combiners and reducers. this creates
tremendous pressure in terms of keys for spill and reduce sorts.
I think tremendous improvements would result if we output outer products of B'
or AB' in vertical thin but long blocks. This seem like a trivial idea but I
was preoccupied by 'proof of concept' issues whereas matrix multiplication has
been seen as algorithmically trivial.
the command line i used:
bin/mahout ssvd --input /tmp/DRM/* --output /tmp/SSVD1 --tempDir /tmp/SSVD-tmp
-k 10 -p 3 -q 1 -r 10000 --reduceTasks 3 -Dmapred.child.java.opts='-Xmx500m'
note also that I ran on CDH3u0 without any Mahout recompilation with CDH3
binaries and it seems to work out of the box.
> 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
>
> Attachments: MAHOUT-796-2.patch, MAHOUT-796.patch
>
>
> 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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