{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,13]],"date-time":"2026-02-13T18:10:02Z","timestamp":1771006202271,"version":"3.50.1"},"publisher-location":"Cham","reference-count":13,"publisher":"Springer International Publishing","isbn-type":[{"value":"9783319686110","type":"print"},{"value":"9783319686127","type":"electronic"}],"license":[{"start":{"date-parts":[[2017,1,1]],"date-time":"2017-01-01T00:00:00Z","timestamp":1483228800000},"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":[[2017]]},"DOI":"10.1007\/978-3-319-68612-7_17","type":"book-chapter","created":{"date-parts":[[2017,10,24]],"date-time":"2017-10-24T07:31:17Z","timestamp":1508830277000},"page":"146-154","source":"Crossref","is-referenced-by-count":2,"title":["Phase Transition Structure of Variational Bayesian Nonnegative Matrix Factorization"],"prefix":"10.1007","author":[{"given":"Masahiro","family":"Kohjima","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Sumio","family":"Watanabe","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2017,10,25]]},"reference":[{"key":"17_CR1","unstructured":"Lee, D.D., Seung, H.S.: Algorithms for non-negative matrix factorization. In: Advances in Neural Information Processing Systems, pp. 556\u2013562 (2001)"},{"issue":"6755","key":"17_CR2","doi-asserted-by":"crossref","first-page":"788","DOI":"10.1038\/44565","volume":"401","author":"DD Lee","year":"1999","unstructured":"Lee, D.D., Seung, H.S.: Learning the parts of objects by non-negative matrix factorization. Nature 401(6755), 788\u2013791 (1999)","journal-title":"Nature"},{"key":"17_CR3","doi-asserted-by":"crossref","DOI":"10.1002\/9780470747278","volume-title":"Nonnegative Matrix and Tensor Factorizations: Applications to Exploratory Multi-way Data Analysis and Blind Source Separation","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 and Blind Source Separation. Wiley, Chichester (2009)"},{"key":"17_CR4","doi-asserted-by":"publisher","first-page":"17","DOI":"10.1155\/2009\/785152","volume":"2009","author":"AT Cemgil","year":"2009","unstructured":"Cemgil, A.T.: Bayesian inference for nonnegative matrix factorisation models. Comput. Intell. Neurosc. 2009, 17 (2009). doi:\n10.1155\/2009\/785152\n\n. Article ID: 785152","journal-title":"Comput. Intell. Neurosc."},{"key":"17_CR5","doi-asserted-by":"crossref","unstructured":"Kohjima, M., Matsubayashi, T., Sawada, H.: Probabilistic non-negative inconsistent-resolution matrices factorization. In: Proceedings of the 24th ACM International Conference on Information and Knowledge Management, pp. 1855\u20131858 (2015)","DOI":"10.1145\/2806416.2806636"},{"key":"17_CR6","doi-asserted-by":"crossref","unstructured":"Deng, D., Shahabi, C., Demiryurek, U., Zhu, L., Yu, R., Liu, Y.: Latent space model for road networks to predict time-varying traffic. In: Proceedings of the 22nd ACM SIGKDD International Conference on Knowledge Discovery and Data Mining, pp. 1525\u20131534 (2016)","DOI":"10.1145\/2939672.2939860"},{"key":"17_CR7","first-page":"625","volume":"7","author":"K Watanabe","year":"2006","unstructured":"Watanabe, K., Watanabe, S.: Stochastic complexities of Gaussian mixtures in variational Bayesian approximation. J. Mach. Learn. Res. 7, 625\u2013644 (2006)","journal-title":"J. Mach. Learn. Res."},{"issue":"2","key":"17_CR8","doi-asserted-by":"crossref","first-page":"199","DOI":"10.1007\/s10994-008-5099-x","volume":"75","author":"K Watanabe","year":"2009","unstructured":"Watanabe, K., Shiga, M., Watanabe, S.: Upper bound for variational free energy of bayesian networks. Mach. Learn. 75(2), 199\u2013215 (2009)","journal-title":"Mach. Learn."},{"key":"17_CR9","unstructured":"Nakajima, S., Sato, I., Sugiyama, M., Watanabe, K., Kobayashi, H.: Analysis of variational Bayesian latent dirichlet allocation: weaker sparsity than map. In: Advances in Neural Information Processing Systems, pp. 1224\u20131232 (2014)"},{"key":"17_CR10","doi-asserted-by":"crossref","first-page":"149","DOI":"10.1016\/0024-3795(93)90224-C","volume":"190","author":"JE Cohen","year":"1993","unstructured":"Cohen, J.E., Rothblum, U.G.: Nonnegative ranks, decompositions, and factorizations of nonnegative matrices. Linear Algebra Appl. 190, 149\u2013168 (1993)","journal-title":"Linear Algebra Appl."},{"issue":"3","key":"17_CR11","doi-asserted-by":"crossref","first-page":"1364","DOI":"10.1137\/070709967","volume":"20","author":"SA Vavasis","year":"2009","unstructured":"Vavasis, S.A.: On the complexity of nonnegative matrix factorization. SIAM J. Optim. 20(3), 1364\u20131377 (2009)","journal-title":"SIAM J. Optim."},{"key":"17_CR12","volume-title":"Asymptotic Statistics","author":"AW Van der Vaart","year":"2000","unstructured":"Van der Vaart, A.W.: Asymptotic Statistics, vol. 3. Cambridge University Press, Cambridge (2000)"},{"issue":"217","key":"17_CR13","doi-asserted-by":"crossref","first-page":"373","DOI":"10.1090\/S0025-5718-97-00807-7","volume":"66","author":"H Alzer","year":"1997","unstructured":"Alzer, H.: On some inequalities for the gamma and psi functions. Math. Comput. Am. Math. Soc. 66(217), 373\u2013389 (1997)","journal-title":"Math. Comput. Am. Math. Soc."}],"container-title":["Lecture Notes in Computer Science","Artificial Neural Networks and Machine Learning \u2013 ICANN 2017"],"original-title":[],"link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/978-3-319-68612-7_17","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2017,10,24]],"date-time":"2017-10-24T07:35:24Z","timestamp":1508830524000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/978-3-319-68612-7_17"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2017]]},"ISBN":["9783319686110","9783319686127"],"references-count":13,"URL":"https:\/\/doi.org\/10.1007\/978-3-319-68612-7_17","relation":{},"ISSN":["0302-9743","1611-3349"],"issn-type":[{"value":"0302-9743","type":"print"},{"value":"1611-3349","type":"electronic"}],"subject":[],"published":{"date-parts":[[2017]]}}}