On the Equivalence of Nonnegative Matrix Factorization and K-means - Spectral Clustering
Chris H. Q. Ding, Xiaofeng He, Horst D. Simon, Rong Jin · University of North Texas Digital Library (University of North Texas) · 2005
We provide a systematic analysis of nonnegative matrix factorization (NMF) relating to data clustering. We generalize the usual X = FG{sup T} decomposition to the symmetric W = HH{sup T} and W = HSH{sup T} decompositions. We show that (1) W = HH{sup T} is equivalent to Kernel K-means clustering and the Laplacian-based spectral clustering. (2) X = FG{sup T} is equivalent to simultaneous clustering of rows and columns of a bipartite graph. We emphasizes the importance of orthogonality in NMF and soft clustering nature of NMF. These results are verified with experiments on face images and newsgroups.