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Automatic Determination of Clusters

In: Operations Research Proceedings 2006

Author

Listed:
  • Bettina Hoser

    (Universität Karlsruhe(TH))

  • Jan Schröder

    (Universität Karlsruhe(TH))

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.

Suggested Citation

  • Bettina Hoser & Jan Schröder, 2007. "Automatic Determination of Clusters," Operations Research Proceedings, in: Karl-Heinz Waldmann & Ulrike M. Stocker (ed.), Operations Research Proceedings 2006, pages 439-444, Springer.
    • Handle: RePEc:spr:oprchp:978-3-540-69995-8_70
    DOI: 10.1007/978-3-540-69995-8_70
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