Matches in SemOpenAlex for { <https://semopenalex.org/work/W1575173685> ?p ?o ?g. }
- W1575173685 abstract "On the Equivalence of Nonnegative Matrix Factorization and K-means — Spectral Clustering Chris Ding ∗ Xiaofeng He ∗ Horst D. Simon ∗ Rong Jin † December 4, 2005 Abstract We provide a systematic analysis of nonnegative matrix factorization (NMF) relating to data cluster- ing. We generalize the usual X = F G T decomposition to the symmetric W = HH T and W = HSH T decompositions. We show that (1) W = HH T is equivalent to Kernel K-means clustering and the Laplacian-based spectral clustering. (2) X = F G T is equivalent to simultaneous clustering of rows and columns of a bipartite graph. We emphasizes the importance of orthogonality in NMF and soft clustering nature of NMF. These results are verified with experiments on face images and newsgroups. Introduction Standard factorization of a data matrix uses singular value decomposition (SVD) as widely used in principal component analysis (PCA). However, for many dataset such as images and text, the original data matrices are nonnegative. A factorization such as SVD contains negative entries and is difficult to interpret for some applications. In contrast, nonnegative matrix factorization (NMF) [18, 19] restricts the entries in matrix factors to be nonnegative. NMF has been shown recently to be useful for many applications in environment [25], chemometrics [29], pattern recognition [20], multimedia [6], text mining [31, 26] and DNA gene expressions [3]. This is also extended to classification [27]. A number of stuides focus on further developing NMF computational methodologies [15, 22, 26, 5, 21]. Let X = (x 1 , . . . , x n ) ∈ R p×n be the data matrix of nonnegative elements. In image processing, each column x i is a 2D array of pixels gray level. In text processing, each column is a document. The NMF factorizes X into two nonnegative matrices, X ≈ F G T , n×k where F = (f 1 , · · · , f k ) ∈ R p×k and G = (g 1 , · · · , g k ) ∈ R + . k is a pre-specified parameter. NMF can be traced back to 1970s (communication from Gene Golub) and has been studied by Paatero [25, 29]. The work of Lee and Seung [18, 19] brought much attention to NMF in machine learning and data mining communities. There appears to have some confusions, however. Lee and Seung emphasizes[18] that NMF factors f k contain coherent parts of the original data (images), for example a nose or an eye. Later experiments [16, 20] do not support the parts-of-whole interpretation of NMF. In fact, Hoyer[16] and Li, et al[20] specifically propose sparsification schemes to achieve the parts-of-whole pictures. ∗ Lawrence † Department Berkeley National Laboratory, University of California, Berkeley, CA 94720. of Computer Science and Engineering, Michigan State University, East Lansing, MI 48824." @default.
- W1575173685 created "2016-06-24" @default.
- W1575173685 creator A5005503474 @default.
- W1575173685 creator A5018733173 @default.
- W1575173685 creator A5066426676 @default.
- W1575173685 creator A5069394608 @default.
- W1575173685 date "2005-12-04" @default.
- W1575173685 modified "2023-09-24" @default.
- W1575173685 title "On the Equivalence of Nonnegative Matrix Factorization and K-means - Spectral Clustering" @default.
- W1575173685 cites W1550273947 @default.
- W1575173685 cites W1790954942 @default.
- W1575173685 cites W1902027874 @default.
- W1575173685 cites W1986007546 @default.
- W1575173685 cites W200434350 @default.
- W1575173685 cites W2013029404 @default.
- W1575173685 cites W2052819443 @default.
- W1575173685 cites W2059745395 @default.
- W1575173685 cites W2066808305 @default.
- W1575173685 cites W206759535 @default.
- W1575173685 cites W2085148302 @default.
- W1575173685 cites W2100689281 @default.
- W1575173685 cites W2113076747 @default.
- W1575173685 cites W2116216716 @default.
- W1575173685 cites W2118718620 @default.
- W1575173685 cites W2121947440 @default.
- W1575173685 cites W2125531986 @default.
- W1575173685 cites W2134737843 @default.
- W1575173685 cites W2136171036 @default.
- W1575173685 cites W2136787567 @default.
- W1575173685 cites W2138103367 @default.
- W1575173685 cites W2139850885 @default.
- W1575173685 cites W2141465109 @default.
- W1575173685 cites W2155754954 @default.
- W1575173685 cites W2165874743 @default.
- W1575173685 cites W2171583777 @default.
- W1575173685 cites W2571268788 @default.
- W1575173685 cites W37308083 @default.
- W1575173685 cites W72893484 @default.
- W1575173685 hasPublicationYear "2005" @default.
- W1575173685 type Work @default.
- W1575173685 sameAs 1575173685 @default.
- W1575173685 citedByCount "40" @default.
- W1575173685 countsByYear W15751736852012 @default.
- W1575173685 countsByYear W15751736852014 @default.
- W1575173685 countsByYear W15751736852015 @default.
- W1575173685 countsByYear W15751736852016 @default.
- W1575173685 countsByYear W15751736852017 @default.
- W1575173685 countsByYear W15751736852018 @default.
- W1575173685 countsByYear W15751736852019 @default.
- W1575173685 countsByYear W15751736852020 @default.
- W1575173685 countsByYear W15751736852021 @default.
- W1575173685 crossrefType "journal-article" @default.
- W1575173685 hasAuthorship W1575173685A5005503474 @default.
- W1575173685 hasAuthorship W1575173685A5018733173 @default.
- W1575173685 hasAuthorship W1575173685A5066426676 @default.
- W1575173685 hasAuthorship W1575173685A5069394608 @default.
- W1575173685 hasConcept C105611402 @default.
- W1575173685 hasConcept C105795698 @default.
- W1575173685 hasConcept C11413529 @default.
- W1575173685 hasConcept C114614502 @default.
- W1575173685 hasConcept C121332964 @default.
- W1575173685 hasConcept C132525143 @default.
- W1575173685 hasConcept C139018669 @default.
- W1575173685 hasConcept C152671427 @default.
- W1575173685 hasConcept C153180895 @default.
- W1575173685 hasConcept C154945302 @default.
- W1575173685 hasConcept C158693339 @default.
- W1575173685 hasConcept C187834632 @default.
- W1575173685 hasConcept C197657726 @default.
- W1575173685 hasConcept C22789450 @default.
- W1575173685 hasConcept C33923547 @default.
- W1575173685 hasConcept C41008148 @default.
- W1575173685 hasConcept C42355184 @default.
- W1575173685 hasConcept C54848796 @default.
- W1575173685 hasConcept C62520636 @default.
- W1575173685 hasConcept C73555534 @default.
- W1575173685 hasConcept C74193536 @default.
- W1575173685 hasConceptScore W1575173685C105611402 @default.
- W1575173685 hasConceptScore W1575173685C105795698 @default.
- W1575173685 hasConceptScore W1575173685C11413529 @default.
- W1575173685 hasConceptScore W1575173685C114614502 @default.
- W1575173685 hasConceptScore W1575173685C121332964 @default.
- W1575173685 hasConceptScore W1575173685C132525143 @default.
- W1575173685 hasConceptScore W1575173685C139018669 @default.
- W1575173685 hasConceptScore W1575173685C152671427 @default.
- W1575173685 hasConceptScore W1575173685C153180895 @default.
- W1575173685 hasConceptScore W1575173685C154945302 @default.
- W1575173685 hasConceptScore W1575173685C158693339 @default.
- W1575173685 hasConceptScore W1575173685C187834632 @default.
- W1575173685 hasConceptScore W1575173685C197657726 @default.
- W1575173685 hasConceptScore W1575173685C22789450 @default.
- W1575173685 hasConceptScore W1575173685C33923547 @default.
- W1575173685 hasConceptScore W1575173685C41008148 @default.
- W1575173685 hasConceptScore W1575173685C42355184 @default.
- W1575173685 hasConceptScore W1575173685C54848796 @default.
- W1575173685 hasConceptScore W1575173685C62520636 @default.
- W1575173685 hasConceptScore W1575173685C73555534 @default.
- W1575173685 hasConceptScore W1575173685C74193536 @default.
- W1575173685 hasLocation W15751736851 @default.
- W1575173685 hasOpenAccess W1575173685 @default.