Non-negative matrix factorization: Difference between revisions

Revision as of 04:24, 27 January 2007

Revision as of 04:29, 27 January 2007

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The different types arise from using different [[cost function]]s (divergence functions) and/or by [[regularization (mathematics)|regularization]] of the '''W''' and/or '''H''' matrices<ref>[[Inderjit S. Dhillon]], [[Suvrit Sra]], "[http://books.nips.cc/papers/files/nips18/NIPS2005_0203.pdf Generalized Nonnegative Matrix Approximations with Bregman Divergences]", [[NIPS]], 2005.</ref>.

== Relatioing to Data Clustering ==

Although initially NMF is considered to be different from vector quantization ([[K-means clustering]]), 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 athe relaxed [[K-means clustering]] using the Frobenius norm objective function whereand '''W''' iscontains the cluster centroids and '''H''' iscontains the cluster indicator; 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>