Non-negative matrix factorization: Difference between revisions

Revision as of 04:29, 27 January 2007

Revision as of 04:35, 27 January 2007

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<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, andmatrix factor '''W''' contains cluster centroids and '''H''' contains the cluster indicatormembership indicators; therefore NMF provides a new framework for data clustering. It is also known

<ref>

Chris Ding and Xiaofeng He, " Nonnegative Matrix Factorization and Probabilistic Latent Semantic Indexing: Equivalence, Chi-square Statistic, and a Hybrid Method", Proc. AAAI National Conf. on Artificial Intelligence (AAAI-06), July 2006.</ref>

that NMF is identical to [[probabilistic latent semantic analysis]] using the [[Kullback–Leibler divergence]] objective function, which can be simplified to the Chi-square functionstatistic at first order approximation.

== Uniqueness ==