On the eigenvectors of p-Laplacian

Spectral analysis approaches have been actively studied in machine learning and data mining areas, due to their generality, efficiency, and rich theoretical foundations. As a natural non-linear generalization of Graph Laplacian, p-Laplacian has recently been proposed, which interpolates between a relaxation of normalized cut and the Cheeger cut. However, the relaxation can only be applied to two-class cases. In this paper, we propose full eigenvector analysis of p-Laplacian and obtain a natural global embedding for multi-class clustering problems, instead of using greedy search strategy implemented by previous researchers. An efficient gradient descend optimization approach is introduced to obtain the p-Laplacian embedding space, which is guaranteed to converge to feasible local solutions. Empirical results suggest that the greedy search method often fails in many real-world applications with non-trivial data structures, but our approach consistently gets robust clustering results. Vis...

• Type: Journal
• Year: 2010
• Where: ML
• Authors: Dijun Luo, Heng Huang, Chris H. Q. Ding, Feiping Nie
• Keywords: Embedding Space, Greedy Search, Machine Learning, ML 2010, Natural Non-linear Generalization