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https://issues.apache.org/jira/browse/MAHOUT-1214?page=com.atlassian.jira.plugin.system.issuetabpanels:comment-tabpanel&focusedCommentId=13675707#comment-13675707
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Yiqun Hu commented on MAHOUT-1214:
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yes, implementing orthogonality check in EigenVerificationJob does affect the
verification job in general. So if we want applying it in spectral kmeans only,
maybe we have to implement a separate verification job. However, orthogonality
of the returned eigen vectors should always be ensured, because I can't think
of any situation in which orthogonality is not required. Correct me if I'm
wrong.
> 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
> Fix For: Backlog
>
>
> 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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