Abstract
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.
Keywords
National laboratoryNon-negative matrix factorizationFactorizationBipartite graphCluster analysisMathematicsCombinatoricsComputer scienceLibrary scienceMatrix decompositionGraphAlgorithmArtificial intelligenceEigenvalues and eigenvectorsPhysicsEngineering physics
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Publication Info
- Year
- 2005
- Type
- article
- Citations
- 975
- Access
- Closed
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Cite This
Chris Ding,
Xiaofeng He,
Horst D. Simon
(2005).
On the Equivalence of Nonnegative Matrix Factorization and Spectral Clustering.
.
https://doi.org/10.1137/1.9781611972757.70
Identifiers
- DOI
- 10.1137/1.9781611972757.70