On the Equivalence of Nonnegative Matrix Factorization and Spectral Clustering

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