{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2024,6,3]],"date-time":"2024-06-03T02:12:37Z","timestamp":1717380757179},"reference-count":45,"publisher":"MIT Press - Journals","issue":"9","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Neural Computation"],"published-print":{"date-parts":[[2014,9]]},"abstract":"<jats:p> Clustering is a representative of unsupervised learning and one of the important approaches in exploratory data analysis. By its very nature, clustering without strong assumption on data distribution is desirable. Information-theoretic clustering is a class of clustering methods that optimize information-theoretic quantities such as entropy and mutual information. These quantities can be estimated in a nonparametric manner, and information-theoretic clustering algorithms are capable of capturing various intrinsic data structures. It is also possible to estimate information-theoretic quantities using a data set with sampling weight for each datum. Assuming the data set is sampled from a certain cluster and assigning different sampling weights depending on the clusters, the cluster-conditional information-theoretic quantities are estimated. In this letter, a simple iterative clustering algorithm is proposed based on a nonparametric estimator of the log likelihood for weighted data sets. The clustering algorithm is also derived from the principle of conditional entropy minimization with maximum entropy regularization. The proposed algorithm does not contain a tuning parameter. The algorithm is experimentally shown to be comparable to or outperform conventional nonparametric clustering methods. <\/jats:p>","DOI":"10.1162\/neco_a_00628","type":"journal-article","created":{"date-parts":[[2014,6,12]],"date-time":"2014-06-12T22:58:23Z","timestamp":1402613903000},"page":"2074-2101","source":"Crossref","is-referenced-by-count":3,"title":["A Nonparametric Clustering Algorithm with a Quantile-Based Likelihood Estimator"],"prefix":"10.1162","volume":"26","author":[{"given":"Hideitsu","family":"Hino","sequence":"first","affiliation":[{"name":"Graduate School of Systems and Information Engineering, University of Tsukuba, Tsukuba, Ibaraki, Japan, 305-8573"}]},{"given":"Noboru","family":"Murata","sequence":"additional","affiliation":[{"name":"School of Science and Engineering, Waseda University, Shinjuku, Tokyo, Japan, 169-8555"}]}],"member":"281","reference":[{"key":"B1","first-page":"1027","volume-title":"SODA \u201907: Proceedings of the Eighteenth Annual ACM-SIAM Symposium on Discrete Algorithms","author":"Arthur D.","year":"2007"},{"key":"B2","doi-asserted-by":"publisher","DOI":"10.1007\/BF01246098"},{"key":"B3","doi-asserted-by":"publisher","DOI":"10.3724\/SP.J.1001.2010.03494"},{"key":"B4","volume-title":"Spectral graph theory","author":"Chung F.R.K.","year":"1997"},{"key":"B5","doi-asserted-by":"publisher","DOI":"10.1109\/34.1000236"},{"key":"B6","doi-asserted-by":"publisher","DOI":"10.1109\/TSP.2004.831130"},{"key":"B7","doi-asserted-by":"publisher","DOI":"10.1002\/0471200611"},{"key":"B8","doi-asserted-by":"publisher","DOI":"10.1145\/1014052.1014118"},{"key":"B9","first-page":"433","volume-title":"Advances in neural information processing systems, 21","author":"Faivishevsky L.","year":"2009"},{"key":"B10","first-page":"351","volume-title":"Proceedings of the 27th International Conference on Machine Learning","author":"Faivishevsky L.","year":"2010"},{"key":"B11","doi-asserted-by":"publisher","DOI":"10.1109\/34.982897"},{"key":"B12","first-page":"775","volume-title":"Advances in neural information processing systems, 23","author":"Gomes R.","year":"2010"},{"key":"B13","doi-asserted-by":"publisher","DOI":"10.1080\/104852504200026815"},{"key":"B14","doi-asserted-by":"publisher","DOI":"10.1007\/978-0-387-84858-7"},{"key":"B15","doi-asserted-by":"publisher","DOI":"10.1162\/NECO_a_00008"},{"key":"B16","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-642-21738-8_39"},{"key":"B17","doi-asserted-by":"publisher","DOI":"10.1016\/j.neunet.2013.06.005"},{"key":"B18","doi-asserted-by":"publisher","DOI":"10.1007\/BF01908075"},{"key":"B19","doi-asserted-by":"publisher","DOI":"10.1145\/331499.331504"},{"key":"B20","doi-asserted-by":"publisher","DOI":"10.1109\/TPAMI.2009.100"},{"key":"B21","doi-asserted-by":"publisher","DOI":"10.1016\/j.patcog.2006.06.028"},{"key":"B22","volume-title":"Principal component analysis","author":"Jolliffe I.","year":"2002"},{"key":"B23","first-page":"2402","volume-title":"Advances in neural information processing systems","volume":"25","author":"Kalogeratos A.","year":"2012"},{"key":"B24","first-page":"95","volume":"23","author":"Kozachenko L. F.","year":"1987","journal-title":"Problems of Information Transmission"},{"key":"B25","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevE.69.066138"},{"key":"B27","volume-title":"Proc. of the Fifth Berkeley Symposium on Mathematical Statistics and Probability","author":"MacQueen J. B.","year":"1967"},{"key":"B28","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-642-14980-1_32"},{"key":"B29","volume-title":"Mixture models: Inference and applications to clustering","author":"McLachlan G. J.","year":"1988"},{"key":"B30","doi-asserted-by":"publisher","DOI":"10.1207\/s15327906mbr2104_5"},{"key":"B31","doi-asserted-by":"publisher","DOI":"10.1016\/0165-1684(89)90132-1"},{"key":"B32","volume-title":"UCI Repository of machine learning databases","author":"Murphy P. M.","year":"1994"},{"key":"B33","first-page":"849","volume-title":"Advances in neural information processing systems, 14","author":"Ng A. Y.","year":"2001"},{"key":"B34","first-page":"727","volume-title":"Proceedings of the 17th International Conference on Machine Learning","author":"Pelleg D.","year":"2000"},{"key":"B35","doi-asserted-by":"publisher","DOI":"10.1109\/MLSP.2007.4414325"},{"key":"B36","volume-title":"The design and analysis of spatial data structures","author":"Samet H.","year":"1990"},{"key":"B37","doi-asserted-by":"publisher","DOI":"10.1162\/089976698300017467"},{"key":"B38","doi-asserted-by":"publisher","DOI":"10.1017\/CBO9780511809682"},{"key":"B39","doi-asserted-by":"publisher","DOI":"10.1073\/pnas.0507432102"},{"key":"B40","volume-title":"Advances in neural information processing systems","volume":"16","author":"Still S.","year":"2004"},{"key":"B41","first-page":"65","volume-title":"Proceedings of the 27th Conference on Machine Learning","author":"Sugiyama M.","year":"2011"},{"key":"B42","doi-asserted-by":"publisher","DOI":"10.1111\/1467-9868.00293"},{"key":"B44","doi-asserted-by":"publisher","DOI":"10.1109\/MLSP.2013.6661968"},{"key":"B45","doi-asserted-by":"publisher","DOI":"10.1201\/b14876"},{"key":"B46","first-page":"761","volume":"15","author":"Wang M.","year":"2011","journal-title":"Journal of Machine Learning Research\u2014Proceedings Track"},{"key":"B47","first-page":"1601","volume-title":"Advances in neural information processing systems, 17","author":"Zelnik-Manor L.","year":"2005"}],"container-title":["Neural Computation"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mitpressjournals.org\/doi\/pdf\/10.1162\/NECO_a_00628","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2021,3,12]],"date-time":"2021-03-12T21:40:25Z","timestamp":1615585225000},"score":1,"resource":{"primary":{"URL":"https:\/\/direct.mit.edu\/neco\/article\/26\/9\/2074-2101\/8009"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2014,9]]},"references-count":45,"journal-issue":{"issue":"9","published-print":{"date-parts":[[2014,9]]}},"alternative-id":["10.1162\/NECO_a_00628"],"URL":"https:\/\/doi.org\/10.1162\/neco_a_00628","relation":{},"ISSN":["0899-7667","1530-888X"],"issn-type":[{"value":"0899-7667","type":"print"},{"value":"1530-888X","type":"electronic"}],"subject":[],"published":{"date-parts":[[2014,9]]}}}