{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,27]],"date-time":"2025-10-27T20:34:43Z","timestamp":1761597283136,"version":"3.40.3"},"publisher-location":"Berlin, Heidelberg","reference-count":15,"publisher":"Springer Berlin Heidelberg","isbn-type":[{"type":"print","value":"9783642217340"},{"type":"electronic","value":"9783642217357"}],"license":[{"start":{"date-parts":[[2011,1,1]],"date-time":"2011-01-01T00:00:00Z","timestamp":1293840000000},"content-version":"unspecified","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2011]]},"DOI":"10.1007\/978-3-642-21735-7_31","type":"book-chapter","created":{"date-parts":[[2011,6,12]],"date-time":"2011-06-12T12:10:52Z","timestamp":1307880652000},"page":"250-257","source":"Crossref","is-referenced-by-count":24,"title":["Kullback-Leibler Divergence for Nonnegative Matrix Factorization"],"prefix":"10.1007","author":[{"given":"Zhirong","family":"Yang","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"He","family":"Zhang","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Zhijian","family":"Yuan","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Erkki","family":"Oja","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","reference":[{"key":"31_CR1","doi-asserted-by":"publisher","first-page":"111","DOI":"10.1002\/env.3170050203","volume":"5","author":"P. Paatero","year":"1994","unstructured":"Paatero, P., Tapper, U.: Positive matrix factorization: A non-negative factor model with optimal utilization of error estimates of data values. Environmetrics\u00a05, 111\u2013126 (1994)","journal-title":"Environmetrics"},{"key":"31_CR2","doi-asserted-by":"publisher","first-page":"788","DOI":"10.1038\/44565","volume":"401","author":"D.D. Lee","year":"1999","unstructured":"Lee, D.D., Seung, H.S.: Learning the parts of objects by non-negative matrix factorization. Nature\u00a0401, 788\u2013791 (1999)","journal-title":"Nature"},{"key":"31_CR3","doi-asserted-by":"publisher","DOI":"10.1002\/9780470747278","volume-title":"Nonnegative Matrix and Tensor Factorizations: Applications to Exploratory Multi-way Data Analysis","author":"A. Cichocki","year":"2009","unstructured":"Cichocki, A., Zdunek, R., Phan, A.-H., Amari, S.: Nonnegative Matrix and Tensor Factorizations: Applications to Exploratory Multi-way Data Analysis. John Wiley, Chichester (2009)"},{"key":"31_CR4","first-page":"283","volume":"18","author":"I.S. Dhillon","year":"2006","unstructured":"Dhillon, I.S., Sra, S.: Generalized nonnegative matrix approximations with bregman divergences. Advances in Neural Information Processing Systems\u00a018, 283\u2013290 (2006)","journal-title":"Advances in Neural Information Processing Systems"},{"issue":"3","key":"31_CR5","doi-asserted-by":"publisher","first-page":"793","DOI":"10.1162\/neco.2008.04-08-771","volume":"21","author":"C. F\u00e9votte","year":"2009","unstructured":"F\u00e9votte, C., Bertin, N., Durrieu, J. L.: Nonnegative matrix factorization with the Itakura-Saito divergence: With application to music analysis. Neural Computation\u00a021(3), 793\u2013830 (2009)","journal-title":"Neural Computation"},{"key":"31_CR6","volume-title":"Mathematics: From the Birth of Numbers","author":"J. Gullberg","year":"1997","unstructured":"Gullberg, J.: Mathematics: From the Birth of Numbers. W. W. Norton & Company, New York (1997)"},{"key":"31_CR7","first-page":"2579","volume":"9","author":"L. Maaten van der","year":"2008","unstructured":"van der Maaten, L., Hinton, G.: Visualizing data using t-SNE. Journal of Machine Learning Research\u00a09, 2579\u20132605 (2008)","journal-title":"Journal of Machine Learning Research"},{"issue":"5-6","key":"31_CR8","doi-asserted-by":"publisher","first-page":"1020","DOI":"10.1016\/j.laa.2007.02.026","volume":"429","author":"N.-D. Ho","year":"2008","unstructured":"Ho, N. D., Dooren, P.V.: Non-negative matrix factorization with fixed row and column sums. Linear Algebra and its Applications\u00a0429(5-6), 1020\u20131025 (2008)","journal-title":"Linear Algebra and its Applications"},{"issue":"8","key":"31_CR9","doi-asserted-by":"publisher","first-page":"3913","DOI":"10.1016\/j.csda.2008.01.011","volume":"52","author":"C. Ding","year":"2008","unstructured":"Ding, C., Li, T., Peng, W.: On the equivalence between non-negative matrix factorization and probabilistic laten semantic indexing. Computational Statistics and Data Analysis\u00a052(8), 3913\u20133927 (2008)","journal-title":"Computational Statistics and Data Analysis"},{"key":"31_CR10","first-page":"556","volume":"13","author":"D.D. Lee","year":"2001","unstructured":"Lee, D.D., Seung, H.S.: Algorithms for non-negative matrix factorization. Advances in Neural Information Processing Systems\u00a013, 556\u2013562 (2001)","journal-title":"Advances in Neural Information Processing Systems"},{"key":"31_CR11","unstructured":"Gonzales, E.F., Zhang, Y.: Accelerating the lee-seung algorithm for non-negative matrix factorization. Technical report, Dept. of Computational and Applied Mathematics. Rice University (2005)"},{"issue":"6","key":"31_CR12","doi-asserted-by":"publisher","first-page":"1589","DOI":"10.1109\/TNN.2007.895831","volume":"18","author":"C.-J. Lin","year":"2007","unstructured":"Lin, C. J.: On the convergence of multiplicative update algorithms for nonnegative matrix factorization. IEEE Transactions on Neural Networks\u00a018(6), 1589\u20131596 (2007)","journal-title":"IEEE Transactions on Neural Networks"},{"key":"31_CR13","doi-asserted-by":"publisher","first-page":"2756","DOI":"10.1162\/neco.2007.19.10.2756","volume":"19","author":"C.J. Lin","year":"2007","unstructured":"Lin, C.J.: Projected gradient methods for non-negative matrix factorization. Neural Computation\u00a019, 2756\u20132779 (2007)","journal-title":"Neural Computation"},{"issue":"1","key":"31_CR14","doi-asserted-by":"publisher","first-page":"38","DOI":"10.1002\/sam.104","volume":"1","author":"D. Kim","year":"2008","unstructured":"Kim, D., Sra, S., Dhillon, I.S.: Fast projection-based methods for the least squares nonnegative matrix approximation problem. Statistical Analysis and Data Mining\u00a01(1), 38\u201351 (2008)","journal-title":"Statistical Analysis and Data Mining"},{"issue":"2","key":"31_CR15","doi-asserted-by":"publisher","first-page":"713","DOI":"10.1137\/07069239X","volume":"30","author":"H. Kim","year":"2008","unstructured":"Kim, H., Park, H.: Nonnegative matrix factorization based on alternating non-negativity-constrained least squares and the active set method. SIAM Journal on Matrix Analysis and Applications\u00a030(2), 713\u2013730 (2008)","journal-title":"SIAM Journal on Matrix Analysis and Applications"}],"container-title":["Lecture Notes in Computer Science","Artificial Neural Networks and Machine Learning \u2013 ICANN 2011"],"original-title":[],"link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/978-3-642-21735-7_31","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,3,28]],"date-time":"2019-03-28T14:22:24Z","timestamp":1553782944000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/978-3-642-21735-7_31"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2011]]},"ISBN":["9783642217340","9783642217357"],"references-count":15,"URL":"https:\/\/doi.org\/10.1007\/978-3-642-21735-7_31","relation":{},"ISSN":["0302-9743","1611-3349"],"issn-type":[{"type":"print","value":"0302-9743"},{"type":"electronic","value":"1611-3349"}],"subject":[],"published":{"date-parts":[[2011]]}}}