Automatic Determination of Clusters

Bettina Hoser () and Jan Schröder ()
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Bettina Hoser: Universität Karlsruhe(TH)
Jan Schröder: Universität Karlsruhe(TH)

A chapter in Operations Research Proceedings 2006, 2007, pp 439-444 from Springer

Abstract: Abstract In this paper we propose an automatic method for spectral clustering of weighted directed graphs. It is based on the eigensystem of a complex Hermitian adjacency matrix H n×n . The number of relevant clusters is determined automatically. Nodes are assigned to clusters using the inner product matrix S n×n calculated from a matrix R n×l of the l eigenvectors as column vectors which correspond to the positve eigenvalues of H. It can be shown that by assigning the vertices of the network to clusters such that a node i belongs to cluster p c if Re $$ {\text{(}}S_{i,p_c } {\text{)}} $$ = max j Re(S i,j) an good partitioning can be found. Simulation results are presented.

Keywords: Cluster Center; Spectral Cluster; Hermitian Matrix; Automatic Determination; Eigenvector Centrality (search for similar items in EconPapers)
Date: 2007
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Persistent link: https://EconPapers.repec.org/RePEc:spr:oprchp:978-3-540-69995-8_70

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DOI: 10.1007/978-3-540-69995-8_70

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