Spectral Clustering Based on the Graph p-Laplacian

author: Thomas Bühler, Department of Computer Science, Saarland University
published: Aug. 26, 2009,   recorded: June 2009,   views: 6251


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We present a generalized version of spectral clustering using the graph p-Laplacian, a nonlinear generalization of the standard graph Laplacian. We show that the second eigenvector of the graph p-Laplacian interpolates between a relaxation of the normalized and the Cheeger cut. Moreover, we prove that in the limit as p ! 1 the cut found by thresholding the second eigenvector of the graph p-Laplacian converges to the optimal Cheeger cut. Furthermore, we provide an efficient numerical scheme to compute the second eigenvector of the graph p- Laplacian. The experiments show that the clustering found by p-spectral clustering is at least as good as normal spectral clustering, but often leads to signifi cantly better results.

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