mahout-user mailing list archives

Site index · List index
Message view « Date » · « Thread »
Top « Date » · « Thread »
From Pat Ferrel <...@occamsmachete.com>
Subject Re: PCA doc question for devs:
Date Thu, 06 Sep 2012 00:20:35 GMT
Trying to do dimensionality reduction with SSVD then running the new doc matrix through kmeans.


The Lanczos + ClusterDump test of SVD + kmeans uses A-hat = A^t V^t. Unfortunately this results
in anonymous vectors in clusteredPoints after A-hat is run through kmeans. The doc ids are
lost due to the transpose I assume?

In any case Dmitriy pointed out that this might have been done because Lanczos does not produce
U. 

So I need to do US^-1? This would avoid the transpose and should preserve doc/row ids for
kmeans? And doing the PCA in SSVD will weight things properly so I don't need the --halfSigma?

Please correct me if I'm wrong.


On Sep 5, 2012, at 4:59 PM, Dmitriy Lyubimov <dlieu.7@gmail.com> wrote:

Yes i have an option to output U * Sigma^0.5 already.

But strictly speaking the way PCA space is defined would require just
U*Sigma output. Or it is not worth it?


On Wed, Sep 5, 2012 at 4:56 PM, Ted Dunning <ted.dunning@gmail.com> wrote:
> Yes.  (A-M)V is U \Sigma.  You may actually want something like U \sqrt
> \Sigma instead, though.
> 
> 
> On Wed, Sep 5, 2012 at 4:10 PM, Dmitriy Lyubimov <dlieu.7@gmail.com> wrote:
> 
>> Hello,
>> 
>> I have a question w.r.t what to advise people in the SSVD manual for PCA.
>> 
>> So we have
>> 
>> (A-M) \approx U \Sigma V^t
>> 
>> and strictly speaking since svd is reduced rank, we need to re-project
>> original data points as
>> 
>> Y= (A-M)V
>> 
>> However we can assume (A-M)V \approx U \Sigma, can't we? I.e. instead of
>> recomputing tough job of (A-M)V we can just advise to use U\Sigma or just U
>> in some cases, can't we?
>> 
>> Thanks.
>> -d
>> 


Mime
View raw message