{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,3,27]],"date-time":"2025-03-27T14:48:13Z","timestamp":1743086893594,"version":"3.40.3"},"publisher-location":"Berlin, Heidelberg","reference-count":17,"publisher":"Springer Berlin Heidelberg","isbn-type":[{"type":"print","value":"9783642285509"},{"type":"electronic","value":"9783642285516"}],"license":[{"start":{"date-parts":[[2012,1,1]],"date-time":"2012-01-01T00:00:00Z","timestamp":1325376000000},"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":[[2012]]},"DOI":"10.1007\/978-3-642-28551-6_33","type":"book-chapter","created":{"date-parts":[[2012,2,8]],"date-time":"2012-02-08T17:52:46Z","timestamp":1328723566000},"page":"263-271","source":"Crossref","is-referenced-by-count":0,"title":["Nonnegative Matrix Factorization via Generalized Product Rule and Its Application for Classification"],"prefix":"10.1007","author":[{"given":"Yu","family":"Fujimoto","sequence":"first","affiliation":[]},{"given":"Noboru","family":"Murata","sequence":"additional","affiliation":[]}],"member":"297","reference":[{"key":"33_CR1","doi-asserted-by":"crossref","unstructured":"Agresti, A.: Categorical Data Analysis. Wiley Inc. (2002)","DOI":"10.1002\/0471249688"},{"key":"33_CR2","doi-asserted-by":"crossref","unstructured":"Benetos, E., Kotropoulos, C., Lidy, T., Rauber, A.: Testing supervised classifiers based on non-negative matrix factorization to musical instrument classification. In: 2006 IEEE International Conference on Multimedia and Expo. (2006)","DOI":"10.1109\/ICME.2006.262650"},{"key":"33_CR3","unstructured":"Bottou, L.: Stochastic gradient learning in neural networks. In: Proc. Neuro-N\u00edmes 1991 (1991)"},{"key":"33_CR4","doi-asserted-by":"crossref","unstructured":"Cichocki, A., Zdunek, R., Phan, A.H., Amari, S.: Nonnegative Matrix and Tensor Factorizations -Applications to Exploratory Multi-way Data Analysis and Blind Source Separation. Wiley (2009)","DOI":"10.1002\/9780470747278"},{"key":"33_CR5","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"153","DOI":"10.1007\/978-3-642-15381-5_19","volume-title":"Intelligent Data Engineering and Automated Learning \u2013 IDEAL 2010","author":"Y. Fujimoto","year":"2010","unstructured":"Fujimoto, Y., Murata, N.: A Generalization of Independence in Naive Bayes Model. In: Fyfe, C., Tino, P., Charles, D., Garcia-Osorio, C., Yin, H. (eds.) IDEAL 2010. LNCS, vol.\u00a06283, pp. 153\u2013161. Springer, Heidelberg (2010)"},{"issue":"3","key":"33_CR6","doi-asserted-by":"publisher","first-page":"549","DOI":"10.1093\/biomet\/74.3.549","volume":"74","author":"C. Genest","year":"1987","unstructured":"Genest, C.: Frank\u2019s family of bivariate distributions. Biometrika\u00a074(3), 549\u2013555 (1987)","journal-title":"Biometrika"},{"key":"33_CR7","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1006\/inco.1996.2612","volume":"132","author":"J. Kivinen","year":"1997","unstructured":"Kivinen, J., Warmuth, M.K.: Exponentiated gradient versus gradient descent for linear predictors. Information and Computation\u00a0132, 1\u201363 (1997)","journal-title":"Information and Computation"},{"key":"33_CR8","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 nonnegative matrix factorization. Nature\u00a0401, 788\u2013791 (1999)","journal-title":"Nature"},{"key":"33_CR9","unstructured":"Lee, D.D., Seung, H.S.: Algorithms for non-negative matrix factorization. In: Advances in Neural Information Processing Systems, vol.\u00a013, pp. 556\u2013562 (2001)"},{"issue":"10","key":"33_CR10","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(10), 2756\u20132779 (2007)","journal-title":"Neural Computation"},{"key":"33_CR11","first-page":"97","volume":"1","author":"N. Murata","year":"2009","unstructured":"Murata, N., Fujimoto, Y.: Bregman divergence and density integration. Journal of Math-for-Industry\u00a01, 97\u2013104 (2009)","journal-title":"Journal of Math-for-Industry"},{"key":"33_CR12","volume-title":"An Introduction to Copulas","author":"R.B. Nelsen","year":"2006","unstructured":"Nelsen, R.B.: An Introduction to Copulas. Springer, Heidelberg (2006)"},{"key":"33_CR13","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 nonnegative factor model with optimal utilization of error estimates of data values. Environmetrics\u00a05, 111\u2013126 (1994)","journal-title":"Environmetrics"},{"issue":"2","key":"33_CR14","doi-asserted-by":"publisher","first-page":"373","DOI":"10.1016\/j.ipm.2004.11.005","volume":"42","author":"F. Shahnaz","year":"2006","unstructured":"Shahnaz, F., Berry, M.W., Pauca, V.P., Plemmons, R.J.: Document clustering using nonnegative matrix factorization. Information Processing and Management\u00a042(2), 373\u2013386 (2006)","journal-title":"Information Processing and Management"},{"key":"33_CR15","unstructured":"Smaragdis, P., Brown, J.C.: Non-negative matrix factorization for polyphonic music transcription. In: Proc. IEEE Workshop on Application of Signal Processing to Audio and Acoustics (2003)"},{"key":"33_CR16","unstructured":"Watanabe, S., Pakvasa, N.: Subspace method in pattern recognition. In: Proc. 1st International Joint Conference on Pattern Recognition, pp. 25\u201332 (1973)"},{"key":"33_CR17","doi-asserted-by":"crossref","unstructured":"Zhang, D., Zhou, Z.-H., Chen, S.: Non-negative matrix factorization on kernels. In: The 9th Pacific Rim International Conference on Artificial Intelligence, pp. 404\u2013412 (2006)","DOI":"10.1007\/978-3-540-36668-3_44"}],"container-title":["Lecture Notes in Computer Science","Latent Variable Analysis and Signal Separation"],"original-title":[],"link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/978-3-642-28551-6_33","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,4,27]],"date-time":"2019-04-27T06:24:02Z","timestamp":1556346242000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/978-3-642-28551-6_33"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2012]]},"ISBN":["9783642285509","9783642285516"],"references-count":17,"URL":"https:\/\/doi.org\/10.1007\/978-3-642-28551-6_33","relation":{},"ISSN":["0302-9743","1611-3349"],"issn-type":[{"type":"print","value":"0302-9743"},{"type":"electronic","value":"1611-3349"}],"subject":[],"published":{"date-parts":[[2012]]}}}