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.
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Hoser, B., Schröder, J. (2007). Automatic Determination of Clusters. In: Waldmann, KH., Stocker, U.M. (eds) Operations Research Proceedings 2006. Operations Research Proceedings, vol 2006. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-69995-8_70
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DOI: https://doi.org/10.1007/978-3-540-69995-8_70
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-69994-1
Online ISBN: 978-3-540-69995-8
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