Local clustering of large graphs by approximate fiedler vectors

Authors:
Pekka Orponen;Satu Elisa Schaeffer
Affiliations:
Laboratory for Theoretical Computer Science, TKK Helsinki University of Technology, Finland;Laboratory for Theoretical Computer Science, TKK Helsinki University of Technology, Finland
Venue:
WEA'05 Proceedings of the 4th international conference on Experimental and Efficient Algorithms
Year:
2005

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Abstract

We address the problem of determining the natural neighbourhood of a given node i in a large nonunifom network G in a way that uses only local computations, i.e. without recourse to the full adjacency matrix of G. We view the problem as that of computing potential values in a diffusive system, where node i is fixed at zero potential, and the potentials at the other nodes are then induced by the adjacency relation of G. This point of view leads to a constrained spectral clustering approach. We observe that a gradient method for computing the respective Fiedler vector values at each node can be implemented in a local manner, leading to our eventual algorithm. The algorithm is evaluated experimentally using three types of nonuniform networks: randomised “caveman graphs”, a scientific collaboration network, and a small social interaction network.