On the Equivalence of Nonnegative Matrix Factorization and K-means- Spectral Clustering

Conference · Sun Dec 04 00:00:00 EST 2005

OSTI ID:932676

Ding, Chris; He, Xiaofeng; Simon, Horst D; Jin, Rong

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.

• Research Organization: Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States)
• Sponsoring Organization: USDOE Director, Office of Science. Office of AdvancedScientific Computing Research
• DOE Contract Number: DE-AC02-05CH11231
• OSTI ID: 932676
• Report Number(s): LBNL-59622; R&D Project: KC6734; BnR: YN0100000; TRN: US200813%%458
• Resource Relation: Conference: SIAM Internation Conference on Data Mining,Newport Beach, CA, 04/21-23/2005
• Country of Publication: United States
• Language: English

Related Subjects

99
FACTORIZATION
KERNELS
MINING