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Date: Sun, 19 May 2013 18:01:16 +0000 (UTC)
From: "Ted Dunning (JIRA)" <jira@apache.org>
To: dev@mahout.apache.org
Message-ID: <JIRA.12647902.1368690849812.344690.1368986476293@arcas>
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References: <JIRA.12647902.1368690849812@arcas>
Subject: [jira] [Commented] (MAHOUT-1214) Improve the accuracy of the
 Spectral KMeans Method
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    [ https://issues.apache.org/jira/browse/MAHOUT-1214?page=com.atlassian.jira.plugin.system.issuetabpanels:comment-tabpanel&focusedCommentId=13661612#comment-13661612 ] 

Ted Dunning commented on MAHOUT-1214:
-------------------------------------

{quote}
You mean use SSVD exclusively in place of Lanczos?
{quote}

Yes.  Exactly.
                
> Improve the accuracy of the Spectral KMeans Method
> --------------------------------------------------
>
>                 Key: MAHOUT-1214
>                 URL: https://issues.apache.org/jira/browse/MAHOUT-1214
>             Project: Mahout
>          Issue Type: Improvement
>          Components: Clustering
>    Affects Versions: 0.7
>         Environment: Mahout 0.7
>            Reporter: Yiqun Hu
>              Labels: clustering, improvement
>
> The current implementation of the spectral KMeans algorithm (Andrew Ng. etc. NIPS 2002) in version 0.7 has two serious issues. These two incorrect implementations make it fail even for a very obvious trivial dataset. We have implemented a solution to resolve these two issues and hope to contribute back to the community.
> # Issue 1: 
> The EigenVerificationJob in version 0.7 does not check the orthogonality of eigenvectors, which is necessary to obtain the correct clustering results for the case of K>1; We have an idea and implementation to select based on cosAngle/orthogonality;
> # Issue 2:
> The random seed initialization of KMeans algorithm is not optimal and sometimes a bad initialization will generate wrong clustering result. In this case, the selected K eigenvector actually provides a better way to initalize cluster centroids because each selected eigenvector is a relaxed indicator of the memberships of one cluster. For every selected eigenvector, we use the data point whose eigen component achieves the maximum absolute value. 
> We have already verified our improvement on synthetic dataset and it shows that the improved version get the optimal clustering result while the current 0.7 version obtains the wrong result.

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