On the Equivalence of Nonnegative Matrix Factorization and Spectral Clustering

摘要

Current nonnegative matrix factorization (NMF) deals with X = FG~T type. We provide a systematic analysis and extensions of NMF to the symmetric W = HH~T, and the weighted W = HSH~T. We show that (1) W = HH~T is equivalent to Kernel K-means clustering and the Laplacian-based spectral clustering. (2) X = FG~T is equivalent to simultaneous clustering of rows and columns of a bipartite graph. Algorithms are given for computing these symmetric NMFs.