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  Approximation Algorithms for Bregman Clustering Co-clustering and Tensor Clustering

Sra, S., Jegelka, S., & Banerjee, A.(2008). Approximation Algorithms for Bregman Clustering Co-clustering and Tensor Clustering (177). Tübingen, Germany: Max Planck Institute for Biological Cybernetics.

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MPIK-TR-177.pdf (Publisher version), 343KB
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Sra, S1, 2, Author              
Jegelka, S1, 2, Author              
Banerjee, A, Author
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1Department Empirical Inference, Max Planck Institute for Biological Cybernetics, Max Planck Society, ou_1497795              
2biological cy, ou_persistent22              

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 Abstract: The Euclidean K-means problem is fundamental to clustering and over the years it has been intensely investigated. More recently, generalizations such as Bregman k-means [8], co-clustering [10], and tensor (multi-way) clustering [40] have also gained prominence. A well-known computational difficulty encountered by these clustering problems is the NP-Hardness of the associated optimization task, and commonly used methods guarantee at most local optimality. Consequently, approximation algorithms of varying degrees of sophistication have been developed, though largely for the basic Euclidean K-means (or `1-norm K-median) problem. In this paper we present approximation algorithms for several Bregman clustering problems by building upon the recent paper of Arthur and Vassilvitskii [5]. Our algorithms obtain objective values within a factor O(logK) for Bregman k-means, Bregman co-clustering, Bregman tensor clustering, and weighted kernel k-means. To our knowledge, except for some special cases, approximation algorithms have not been considered for these general clustering problems. There are several important implications of our work: (i) under the same assumptions as Ackermann et al. [1] it yields a much faster algorithm (non-exponential in K, unlike [1]) for information-theoretic clustering, (ii) it answers several open problems posed by [4], including generalizations to Bregman co-clustering, and tensor clustering, (iii) it provides practical and easy to implement methods—in contrast to several other common approximation approaches.

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 Dates: 2008-09
 Publication Status: Published in print
 Pages: 21
 Publishing info: Tübingen, Germany : Max Planck Institute for Biological Cybernetics
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 Rev. Type: -
 Identifiers: Report Nr.: 177
BibTex Citekey: 5557
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Title: Technical Report of the Max Planck Institute for Biological Cybernetics
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Pages: - Volume / Issue: 177 Sequence Number: - Start / End Page: - Identifier: -