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== Relation to Data Clustering ==
In the initial paper by Lee & Seung, NMF is proposed mainly for parts-of-whole decomposition
Chris Ding, Xiaofeng He, and Horst D. Simon. "[http://crd.lbl.gov/~cding/papers/nmfSIAM1.pdf On the Equivalence of Nonnegative Matrix Factorization and Spectral Clustering]". Proc. SIAM Int'l Conf. Data Mining, 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.
It is also known that NMF is an instance of so-called "multinomial PCA".<ref>Wray Buntine, "[http://cosco.hiit.fi/Articles/ecml02.pdf Extensions to EM and Multinomial PCA]", Proc. European Conference on Machine Learning (ECML-02), LNAI 2430, pp. 23-34, 2002. </ref>
When NMF is obtained by minimizing the [[Kullback–Leibler divergence]], it is also equivalent <REF>
Chris Ding, Tao Li, Wei Peng, "[http://crd.lbl.gov/~cding/papers/nmfpLSI.pdf Nonnegative Matrix Factorization and Probabilistic Latent Semantic Indexing: Equivalence, Chi-square Statistic, and a Hybrid Method]", Proc. of AAAI National Conf. on Artificial Intelligence (AAAI-06), July 2006.</REF> to another instance of multinomial PCA, [[probabilistic latent semantic analysis]],<ref>Eric Gaussier and Cyril Goutte, "[http://eprints.pascal-network.org/archive/00000971/01/39-gaussier.pdf Relation between PLSA and NMF and Implications]", Proc. 28th international ACM SIGIR conference on Research and development in information retrieval (SIGIR-05), pp. 601-602, 2005. </ref> which has long been used for analyzing and clustering textual data. == Uniqueness ==
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