Improved Perron Cluster Analysis

Please always quote using this URN: urn:nbn:de:0297-zib-7260
  • The problem of clustering data can often be transformed into the problem of finding a hidden block diagonal structure in a stochastic matrix. Deuflhard et al. have proposed an algorithm that state s the number $k$ of clusters and uses the sign structure of $k$ eigenvectors of the stochastic matrix to solve the cluster problem. Recently Weber and Galliat discovered that this system of eigenvectors can easily be transformed into a system of $k$ membership functions or soft characteristic functions describing the clusters. In this article we explain the corresponding cluster algorithm and point out the underlying theory. By means of numerical examples we explain how the grade of membership can be interpreted.

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Metadaten
Author:Marcus Weber
Document Type:ZIB-Report
Tag:almost invariant sets; cluster analysis; stochastic matrices
MSC-Classification:62-XX STATISTICS / 62Hxx Multivariate analysis [See also 60Exx] / 62H30 Classification and discrimination; cluster analysis [See also 68T10]
Date of first Publication:2003/03/06
Series (Serial Number):ZIB-Report (03-04)