On weighting clustering
Recent papers and patents in iterative unsupervised learning have emphasized a new trend in clustering. It basically consists of penalizing solutions via weights on the instance points, somehow making clustering move toward the hardest points to cluster. The motivations come principally from an anal...
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| Vydáno v: | IEEE transactions on pattern analysis and machine intelligence Ročník 28; číslo 8; s. 1223 - 1235 |
|---|---|
| Hlavní autoři: | , |
| Médium: | Journal Article |
| Jazyk: | angličtina |
| Vydáno: |
Los Alamitos, CA
IEEE
01.08.2006
IEEE Computer Society The Institute of Electrical and Electronics Engineers, Inc. (IEEE) |
| Témata: | |
| ISSN: | 0162-8828, 2160-9292, 1939-3539 |
| On-line přístup: | Získat plný text |
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| Abstract | Recent papers and patents in iterative unsupervised learning have emphasized a new trend in clustering. It basically consists of penalizing solutions via weights on the instance points, somehow making clustering move toward the hardest points to cluster. The motivations come principally from an analogy with powerful supervised classification methods known as boosting algorithms. However, interest in this analogy has so far been mainly borne out from experimental studies only. This paper is, to the best of our knowledge, the first attempt at its formalization. More precisely, we handle clustering as a constrained minimization of a Bregman divergence. Weight modifications rely on the local variations of the expected complete log-likelihoods. Theoretical results show benefits resembling those of boosting algorithms and bring modified (weighted) versions of clustering algorithms such as k-means, fuzzy c-means, expectation maximization (EM), and k-harmonic means. Experiments are provided for all these algorithms, with a readily available code. They display the advantages that subtle data reweighting may bring to clustering |
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| AbstractList | Recent papers and patents in iterative unsupervised learning have emphasized a new trend in clustering. It basically consists of penalizing solutions via weights on the instance points, somehow making clustering move toward the hardest points to cluster. The motivations come principally from an analogy with powerful supervised classification methods known as boosting algorithms. However, interest in this analogy has so far been mainly borne out from experimental studies only. This paper is, to the best of our knowledge, the first attempt at its formalization. More precisely, we handle clustering as a constrained minimization of a Bregman divergence. Weight modifications rely on the local variations of the expected complete log-likelihoods. Theoretical results show benefits resembling those of boosting algorithms and bring modified (weighted) versions of clustering algorithms such as k-means, fuzzy c-means, expectation maximization (EM), and k-harmonic means. Experiments are provided for all these algorithms, with a readily available code. They display the advantages that subtle data reweighting may bring to clustering Recent papers and patents in iterative unsupervised learning have emphasized a new trend in clustering. It basically consists of penalizing solutions via weights on the instance points, somehow making clustering move toward the hardest points to cluster. The motivations come principally from an analogy with powerful supervised classification methods known as boosting algorithms. However, interest in this analogy has so far been mainly borne out from experimental studies only. This paper is, to the best of our knowledge, the first attempt at its formalization. More precisely, we handle clustering as a constrained minimization of a Bregman divergence. Weight modifications rely on the local variations of the expected complete log-likelihoods. Theoretical results show benefits resembling those of boosting algorithms and bring modified (weighted) versions of clustering algorithms such as k-means, fuzzy c-means, Expectation Maximization (EM), and k-harmonic means. Experiments are provided for all these algorithms, with a readily available code. They display the advantages that subtle data reweighting may bring to clustering.Recent papers and patents in iterative unsupervised learning have emphasized a new trend in clustering. It basically consists of penalizing solutions via weights on the instance points, somehow making clustering move toward the hardest points to cluster. The motivations come principally from an analogy with powerful supervised classification methods known as boosting algorithms. However, interest in this analogy has so far been mainly borne out from experimental studies only. This paper is, to the best of our knowledge, the first attempt at its formalization. More precisely, we handle clustering as a constrained minimization of a Bregman divergence. Weight modifications rely on the local variations of the expected complete log-likelihoods. Theoretical results show benefits resembling those of boosting algorithms and bring modified (weighted) versions of clustering algorithms such as k-means, fuzzy c-means, Expectation Maximization (EM), and k-harmonic means. Experiments are provided for all these algorithms, with a readily available code. They display the advantages that subtle data reweighting may bring to clustering. Recent papers and patents in iterative unsupervised learning have emphasized a new trend in clustering. It basically consists of penalizing solutions via weights on the instance points, somehow making clustering move toward the hardest points to cluster. The motivations come principally from an analogy with powerful supervised classification methods known as boosting algorithms. However, interest in this analogy has so far been mainly borne out from experimental studies only. This paper is, to the best of our knowledge, the first attempt at its formalization. More precisely, we handle clustering as a constrained minimization of a Bregman divergence. Weight modifications rely on the local variations of the expected complete log-likelihoods. Theoretical results show benefits resembling those of boosting algorithms and bring modified (weighted) versions of clustering algorithms such as k-means, fuzzy c-means, Expectation Maximization (EM), and k-harmonic means. Experiments are provided for all these algorithms, with a readily available code. They display the advantages that subtle data reweighting may bring to clustering. Recent papers and patents in iterative unsupervised learning have emphasized a new trend in clustering. It basically consists of penalizing solutions via weights on the instance points, somehow making clustering move toward the hardest points to cluster. The motivations come principally from an analogy with powerful supervised classification methods known as boosting algorithms. However, interest in this analogy has so far been mainly borne out from experimental studies only. This paper is, to the best of our knowledge, the first attempt at its formalization. More precisely, we handle clustering as a constrained minimization of a Bregman divergence. Weight modifications rely on the local variations of the expected complete log-likelihoods. Theoretical results show benefits resembling those of boosting algorithms and bring modified (weighted) versions of clustering algorithms such as k{-}rm means, fuzzy c{-}rm means, Expectation Maximization (EM), and k{-}rm harmonic means. Experiments are provided for all these algorithms, with a readily available code. They display the advantages that subtle data reweighting may bring to clustering. [...] we handle clustering as a constrained minimization of a Bregman divergence. |
| Author | Nock, R. Nielsen, F. |
| Author_xml | – sequence: 1 givenname: R. surname: Nock fullname: Nock, R. organization: Departement Sci. Inter-facultaire, Univ. Antilles-Guyane, Martinique – sequence: 2 givenname: F. surname: Nielsen fullname: Nielsen, F. |
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| Cites_doi | 10.1007/978-1-4757-0450-1 10.2307/2984875 10.1137/1.9781611972740.22 10.1145/307400.307424 10.1006/jcss.1997.1504 10.1007/978-1-4612-0711-5 10.1145/584792.584890 10.1093/oso/9780198526155.003.0025 10.1145/279943.279960 10.1109/ICPR.2004.1334105 |
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| Keywords | Fuzzy logic fuzzy k-means Bregman divergences harmonic means clustering k-means K means algorithm expectation maximization Clustering EM algorithm Pattern analysis Unsupervised learning Constrained optimization |
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| References | ref15 ref14 ref20 Kearns (ref5) 1988 ref10 ref2 Kearns (ref16) Attias (ref19) 1999 ref8 ref7 Budimir (ref17) 2000; 3 ref4 ref3 ref6 Gentile (ref1) Zhang (ref12) 2000 McQueen (ref13) Zhang (ref11) 2000 Devroye (ref18) 1996 Zhang (ref9) 2000 |
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| Title | On weighting clustering |
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