Non-negative matrix factorization: Difference between revisions

Revision as of 12:41, 6 March 2007

Revision as of 23:37, 9 March 2007

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== Relation to Data Clustering ==

Although initially NMF is considered to be different from vector quantization ([[K-means clustering]]){{Fact|date=March 2007}}, it was later shown<ref>

Chris Ding, Xiaofeng He, and Horst D. Simon. "On the Equivalence of Nonnegative Matrix Factorization and Spectral Clustering". Proc. SIAM Int'l Conf. Data Mining (SDM'05), pp:606-610, April 2005.</ref>

that NMF is equivalent to the relaxed [[K-means clustering]] using the Frobenius norm objective function, matrix factor '''W''' contains cluster centroids and '''H''' contains cluster membership indicators; therefore NMF provides a framework for data clustering.