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Perron Cluster Analysis and Its Connection to Graph Partitioning for Noisy Data

Please always quote using this URN: urn:nbn:de:0297-zib-8140
  • The problem of clustering data can be formulated as a graph partitioning problem. Spectral methods for obtaining optimal solutions have reveceived a lot of attention recently. We describe Perron Cluster Cluster Analysis (PCCA) and, for the first time, establish a connection to spectral graph partitioning. We show that in our approach a clustering can be efficiently computed using a simple linear map of the eigenvector data. To deal with the prevalent problem of noisy and possibly overlapping data we introduce the min Chi indicator which helps in selecting the number of clusters and confirming the existence of a partition of the data. This gives a non-probabilistic alternative to statistical mixture-models. We close with showing favorable results on the analysis of gene expressi on data for two different cancer types.

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Author:Marcus Weber, Wasinee Rungsarityotin, Alexander Schliep
Document Type:ZIB-Report
Tag:Perron cluster analysis; clustering; gene expression; spectral graph theory
MSC-Classification:62-XX STATISTICS / 62Hxx Multivariate analysis [See also 60Exx] / 62H30 Classification and discrimination; cluster analysis [See also 68T10]
65-XX NUMERICAL ANALYSIS / 65Fxx Numerical linear algebra / 65F15 Eigenvalues, eigenvectors
92-XX BIOLOGY AND OTHER NATURAL SCIENCES / 92-08 Computational methods
Date of first Publication:2004/09/29
Series (Serial Number):ZIB-Report (04-39)
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