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Clustering by using a simplex structure

Please always quote using this URN: urn:nbn:de:0297-zib-7782
  • In this paper we interpret clustering as a mapping of data into a simplex. If the data itself has simplicial struture this mapping becomes linear. Spectral analysis is an often used tool for clustering data. We will show that corresponding singular vectors or eigenvectors comprise simplicial structure. Therefore they lead to a cluster algorithm, which consists of a simple linear mapping. An example for this kind of algorithms is the Perron cluster analysis (PCCA). We have applied it in practice to identify metastable sets of molecular dynamical systems. In contrast to other algorithms, this kind of approach provides an a priori criterion to determine the number of clusters. In this paper we extend the ideas to more general problems like clustering of bipartite graphs.

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Author:Marcus Weber
Document Type:ZIB-Report
Tag:Perron cluster analysis; bipartite graphs; cluster algorithms; stochastic matrices
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
Date of first Publication:2003/12/19
Series (Serial Number):ZIB-Report (04-03)
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