On the equivalence of nonnegative matrix factorization and spectral clustering

Chris Ding; Xiaofeng He; Horst D. Simon

doi:10.1137/1.9781611972757.70

On the equivalence of nonnegative matrix factorization and spectral clustering

Chris Ding
, Xiaofeng He
, Horst D. Simon

Lawrence Berkeley National Laboratory

Research output: Contribution to conference › Paper › peer-review

953 Scopus citations

Abstract

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.

Original language	English
Pages	606-610
Number of pages	5
DOIs	https://doi.org/10.1137/1.9781611972757.70
State	Published - 2005
Externally published	Yes
Event	5th SIAM International Conference on Data Mining, SDM 2005 - Newport Beach, CA, United States Duration: 21 Apr 2005 → 23 Apr 2005

Conference

Conference	5th SIAM International Conference on Data Mining, SDM 2005
Country/Territory	United States
City	Newport Beach, CA
Period	21/04/05 → 23/04/05

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10.1137/1.9781611972757.70

Cite this

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abstract = "Current nonnegative matrix factorization (NMF) deals with X = FG T 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 K-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.",

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AU - He, Xiaofeng

AU - Simon, Horst D.

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AB - Current nonnegative matrix factorization (NMF) deals with X = FG T 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 K-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.

UR - https://www.scopus.com/pages/publications/33749255098

U2 - 10.1137/1.9781611972757.70

DO - 10.1137/1.9781611972757.70

M3 - 论文

AN - SCOPUS:33749255098

SP - 606

EP - 610

T2 - 5th SIAM International Conference on Data Mining, SDM 2005

Y2 - 21 April 2005 through 23 April 2005

ER -

On the equivalence of nonnegative matrix factorization and spectral clustering

Abstract

Conference

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