{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,10,8]],"date-time":"2026-10-08T18:37:31Z","timestamp":1791484651693,"version":"4.3.4"},"reference-count":85,"publisher":"MIT Press","issue":"1","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Neural Computation"],"published-print":{"date-parts":[[2014,1]]},"abstract":"<jats:p>Information-maximization clustering learns a probabilistic classifier in an unsupervised manner so that mutual information between feature vectors and cluster assignments is maximized. A notable advantage of this approach is that it involves only continuous optimization of model parameters, which is substantially simpler than discrete optimization of cluster assignments. However, existing methods still involve nonconvex optimization problems, and therefore finding a good local optimal solution is not straightforward in practice. In this letter, we propose an alternative information-maximization clustering method based on a squared-loss variant of mutual information. This novel approach gives a clustering solution analytically in a computationally efficient way via kernel eigenvalue decomposition. Furthermore, we provide a practical model selection procedure that allows us to objectively optimize tuning parameters included in the kernel function. Through experiments, we demonstrate the usefulness of the proposed approach.<\/jats:p>","DOI":"10.1162\/neco_a_00534","type":"journal-article","created":{"date-parts":[[2013,10,8]],"date-time":"2013-10-08T15:42:59Z","timestamp":1381246979000},"page":"84-131","source":"Crossref","is-referenced-by-count":27,"title":["Information-Maximization Clustering Based on Squared-Loss Mutual Information"],"prefix":"10.1162","volume":"26","author":[{"given":"Masashi","family":"Sugiyama","sequence":"first","affiliation":[{"name":"Tokyo Institute of Technology, Merugo-ku, Tokyo 152-8552, Japan"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Gang","family":"Niu","sequence":"additional","affiliation":[{"name":"Tokyo Institute of Technology, Merugo-ku, Tokyo 152-8552, Japan"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Makoto","family":"Yamada","sequence":"additional","affiliation":[{"name":"Yahoo Labs, Sunnyvale, CA 94089, U.S.A."}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Manabu","family":"Kimura","sequence":"additional","affiliation":[{"name":"Tokyo Institute of Technology, Merugo-ku, Tokyo 152-8552, Japan"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Hirotaka","family":"Hachiya","sequence":"additional","affiliation":[{"name":"Tokyo Institute of Technology, Merugo-ku, Tokyo 152-8552, Japan"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"281","reference":[{"key":"B1","first-page":"17","volume-title":"Advances in neural information processing systems","volume":"18","author":"Agakov F.","year":"2006"},{"key":"B2","doi-asserted-by":"crossref","first-page":"131","DOI":"10.1111\/j.2517-6161.1966.tb00626.x","volume":"28","author":"Ali S. M.","year":"1966","journal-title":"Journal of the Royal Statistical Society, Series B"},{"key":"B3","doi-asserted-by":"publisher","DOI":"10.1007\/s10994-009-5103-0"},{"key":"B4","doi-asserted-by":"publisher","DOI":"10.1109\/PGEC.1967.264666"},{"key":"B5","doi-asserted-by":"publisher","DOI":"10.1023\/A:1020281327116"},{"key":"B6","doi-asserted-by":"publisher","DOI":"10.1214\/aos\/1176342871"},{"key":"B7","doi-asserted-by":"publisher","DOI":"10.1090\/S0002-9947-1950-0051437-7"},{"key":"B8","first-page":"209","volume-title":"Advances in neural information processing systems","volume":"12","author":"Attias H.","year":"2000"},{"key":"B9","first-page":"49","volume-title":"Advances in Neural information processing systems","volume":"20","author":"Bach F.","year":"2008"},{"key":"B10","first-page":"1963","volume":"7","author":"Bach F.","year":"2006","journal-title":"Journal of Machine Learning Research"},{"key":"B11","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-540-24646-6_1"},{"key":"B12","first-page":"79","volume-title":"Proceedings of International Forun on Applied Wearable Computing","author":"Bharatula N. B.","year":"2005"},{"key":"B13","doi-asserted-by":"publisher","DOI":"10.1007\/978-0-387-45528-0"},{"key":"B14","doi-asserted-by":"publisher","DOI":"10.1214\/06-BA104"},{"key":"B15","doi-asserted-by":"publisher","DOI":"10.1145\/1143844.1143864"},{"key":"B16","doi-asserted-by":"publisher","DOI":"10.1109\/TPAMI.2007.1057"},{"key":"B17","doi-asserted-by":"publisher","DOI":"10.1109\/34.400568"},{"key":"B18","volume-title":"Spectral graph theory","author":"Chung F. R. K.","year":"1997"},{"key":"B20","volume-title":"Elements of information theory","author":"Cover T. M.","year":"2006"},{"key":"B21","first-page":"229","volume":"2","author":"Csisz\u00e1r I.","year":"1967","journal-title":"Studia Scientiarum Mathematicarum Hungarica"},{"key":"B22","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1111\/j.2517-6161.1977.tb01600.x","volume":"39","author":"Dempster A. P.","year":"1977","journal-title":"Journal of the Royal Statistical Society, series B"},{"key":"B23","doi-asserted-by":"crossref","first-page":"551","DOI":"10.1145\/1014052.1014118","volume-title":"Proceedings of the Tenth ACM SIGKDD International Conference on Knowledge Discovery and Data Mining","author":"Dhillon I. S.","year":"2004"},{"key":"B24","doi-asserted-by":"publisher","DOI":"10.1145\/1015330.1015408"},{"key":"B25","volume-title":"Pattern classification","author":"Duda R. O.","year":"2001"},{"key":"B26","first-page":"625","volume-title":"Advances in neural information processing systems","volume":"14","author":"Duffy N.","year":"2002"},{"key":"B27","first-page":"351","volume-title":"Proceedings of 27th International Conference on Machine Learning (ICML2010)","author":"Faivishevsky L.","year":"2010"},{"key":"B28","doi-asserted-by":"publisher","DOI":"10.1214\/aos\/1176342360"},{"key":"B29","doi-asserted-by":"publisher","DOI":"10.1109\/TIT.1975.1055330"},{"key":"B30","doi-asserted-by":"publisher","DOI":"10.1145\/959242.959248"},{"key":"B31","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-540-45167-9_11"},{"key":"B32","first-page":"449","volume-title":"Advances in neural information processing systems","volume":"12","author":"Ghahramani Z.","year":"2000"},{"key":"B33","doi-asserted-by":"publisher","DOI":"10.1109\/TNN.2002.1000150"},{"key":"B34","volume-title":"Matrix computations","author":"Golub G. H.","year":"1989"},{"key":"B35","first-page":"766","volume-title":"Advances in neural information processing systems","volume":"23","author":"Gomes R.","year":"2010"},{"key":"B36","doi-asserted-by":"publisher","DOI":"10.1007\/11564089_7"},{"key":"B37","doi-asserted-by":"publisher","DOI":"10.1016\/j.neucom.2011.09.016"},{"key":"B38","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-642-17146-8"},{"key":"B39","doi-asserted-by":"publisher","DOI":"10.1017\/CBO9780511810817"},{"key":"B40","doi-asserted-by":"publisher","DOI":"10.1007\/BF01908075"},{"key":"B41","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4615-0907-3"},{"key":"B42","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4757-1904-8"},{"key":"B43","first-page":"285","volume-title":"Proceedings of 1998 IEEE International Conference on Acoustics, Speech, and Signal Processing (ICASSP1998)","author":"Kain A.","year":"1988"},{"key":"B44","first-page":"291","volume-title":"Proceedings of the Nineteenth International Conference on Machine Learning","author":"Kashima H.","year":"2002"},{"key":"B45","first-page":"321","volume-title":"Proceedings of the Twentieth International Conference on Machine Learning","author":"Kashima H.","year":"2003"},{"key":"B46","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-0348-8829-5_11"},{"key":"B47","doi-asserted-by":"publisher","DOI":"10.2307\/3318636"},{"key":"B48","first-page":"315","volume-title":"Proceedings of the Nineteenth International Conference on Machine Learning","author":"Kondor R. I.","year":"2002"},{"key":"B49","first-page":"95","volume":"23","author":"Kozachenko L. F.","year":"1987","journal-title":"Problems of Information Transmission"},{"key":"B50","doi-asserted-by":"publisher","DOI":"10.1214\/aoms\/1177729694"},{"key":"B51","doi-asserted-by":"publisher","DOI":"10.1162\/neco.2008.12-06-421"},{"key":"B52","doi-asserted-by":"publisher","DOI":"10.3115\/1118693.1118699"},{"key":"B54","first-page":"1387","volume-title":"Advances in neural information processing systems","volume":"23","author":"Lin D.","year":"2010"},{"key":"B55","doi-asserted-by":"publisher","DOI":"10.1162\/153244302760200687"},{"key":"B56","volume-title":"Information theory, inference, and learning algorithms","author":"MacKay D. J. C.","year":"2003"},{"key":"B57","first-page":"281","volume-title":"Proceedings of the 5th Berkeley Symposium on Mathematical Statistics and Probability","author":"MacQueen J. B.","year":"1967"},{"key":"B58","first-page":"873","volume-title":"Advances in neural information processing systems","volume":"13","author":"Meila M.","year":"2001"},{"key":"B59","doi-asserted-by":"crossref","first-page":"249","DOI":"10.1080\/10618600.2000.10474879","volume":"9","author":"Neal R. M.","year":"2000","journal-title":"Journal of Computational and Graphical Statistics"},{"key":"B60","first-page":"849","volume-title":"Advances in neural information processing systems","volume":"14","author":"Ng A. Y.","year":"2002"},{"key":"B62","doi-asserted-by":"publisher","DOI":"10.3115\/1220575.1220689"},{"key":"B63","doi-asserted-by":"publisher","DOI":"10.1080\/14786440009463897"},{"key":"B64","doi-asserted-by":"publisher","DOI":"10.1080\/14786440109462720"},{"key":"B65","doi-asserted-by":"publisher","DOI":"10.1080\/01621459.1971.10482356"},{"key":"B66","doi-asserted-by":"publisher","DOI":"10.1198\/016214508000000553"},{"key":"B67","volume-title":"Learning with kernels","author":"Sch\u00f6lkopf B.","year":"2002"},{"key":"B68","doi-asserted-by":"publisher","DOI":"10.1109\/ICCV.2003.1238633"},{"key":"B69","doi-asserted-by":"publisher","DOI":"10.1109\/34.868688"},{"key":"B70","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4899-3324-9"},{"key":"B71","doi-asserted-by":"publisher","DOI":"10.1145\/1273496.1273599"},{"key":"B72","first-page":"1027","volume":"8","author":"Sugiyama M.","year":"2007","journal-title":"Journal of Machine Learning Research"},{"key":"B73","doi-asserted-by":"publisher","DOI":"10.3390\/e15010080"},{"key":"B74","doi-asserted-by":"publisher","DOI":"10.1017\/CBO9781139035613"},{"key":"B75","doi-asserted-by":"publisher","DOI":"10.1007\/s10463-008-0197-x"},{"key":"B76","first-page":"65","volume-title":"Proceedings of 28th International Conference on Machine Learning (ICML2011)","author":"Sugiyama M.","year":"2011"},{"key":"B77","doi-asserted-by":"publisher","DOI":"10.1186\/1471-2105-10-S1-S52"},{"key":"B79","doi-asserted-by":"publisher","DOI":"10.1198\/016214506000000302"},{"key":"B80","doi-asserted-by":"publisher","DOI":"10.1162\/089976600300015088"},{"key":"B81","first-page":"1417","volume-title":"Advances in neural information processing systems","volume":"19","author":"Valizadegan H.","year":"2007"},{"key":"B82","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4757-2440-0"},{"key":"B84","doi-asserted-by":"publisher","DOI":"10.1109\/TNN.2009.2036998"},{"key":"B85","first-page":"1537","volume-title":"Advances in neural information processing systems","volume":"17","author":"Xu L.","year":"2005"},{"key":"B86","doi-asserted-by":"publisher","DOI":"10.1137\/1.9781611972801.10"},{"key":"B87","first-page":"1601","volume-title":"Advances in neural information processing systems","volume":"17","author":"Zelnik-Manor L.","year":"2005"},{"key":"B88","first-page":"1057","volume-title":"Advances in neural information processing systems","volume":"14","author":"Zha H.","year":"2002"},{"key":"B89","doi-asserted-by":"publisher","DOI":"10.1109\/TNN.2008.2010620"},{"key":"B90","doi-asserted-by":"publisher","DOI":"10.1137\/1.9781611972788.68"}],"container-title":["Neural Computation"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mitpressjournals.org\/doi\/pdf\/10.1162\/NECO_a_00534","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,5,18]],"date-time":"2024-05-18T13:58:36Z","timestamp":1716040716000},"score":1,"resource":{"primary":{"URL":"https:\/\/direct.mit.edu\/neco\/article\/26\/1\/84-131\/7943"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2014,1]]},"references-count":85,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2014,1]]}},"alternative-id":["10.1162\/NECO_a_00534"],"URL":"https:\/\/doi.org\/10.1162\/neco_a_00534","relation":{},"ISSN":["0899-7667","1530-888X"],"issn-type":[{"value":"0899-7667","type":"print"},{"value":"1530-888X","type":"electronic"}],"subject":[],"published":{"date-parts":[[2014,1]]}}}