Spectral clustering based on the graph p-Laplacian

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 pLaplacian. The experiments show that the clustering found by p-spectral clustering is at least as good as normal spectral clustering, but often leads to significantly better results.

• Type: Conference
• Year: 2009
• Where: ICML
• Authors: Matthias Hein, Thomas Bühler
• Keywords: Graph P-Laplacian Converges, ICML 2009, Machine Learning, Normal Spectral Clustering, Standard Graph Laplacian