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Spectral K-way ratio-cut partitioning and clustering

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3 Author(s)
P. K. Chan ; Dept. of Comput. Eng., California Univ., Santa Cruz, CA, USA ; M. D. F. Schlag ; J. Y. Zien

Recent research on partitioning has focused on the ratio-cut cost metric, which maintains a balance between the cost of the edges cut and the sizes of the partitions without fixing the size of the partitions a priori. Iterative approaches and spectral approaches to two-way ratio-cut partitioning have yielded higher quality partitioning results. In this paper, we develop a spectral approach to multi-way ratio-cut partitioning that provides a generalization of the ratio-cut cost metric to L-way partitioning and a lower bound on this cost metric. Our approach involves finding the k smallest eigenvalue/eigenvector pairs of the Laplacian of the graph. The eigenvectors provide an embedding of the graph's n vertices into a k-dimensional subspace. We devise a time and space efficient clustering heuristic to coerce the points in the embedding into k partitions. Advancement over the current work is evidenced by the results of experiments on the standard benchmarks

Published in:

IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems  (Volume:13 ,  Issue: 9 )