Learning Choquet-Integral-Based Metrics for Semisupervised Clustering
We consider an application of fuzzy measures to the problem of metric learning in semisupervised clustering. We investigate the necessary and sufficient conditions on the underlying fuzzy measure that make the discrete Choquet integral suitable for defining a metric. As a byproduct, we can obtain th...
Gespeichert in:
Veröffentlicht in: | IEEE transactions on fuzzy systems 2011-06, Vol.19 (3), p.562-574 |
---|---|
Hauptverfasser: | , , |
Format: | Artikel |
Sprache: | eng |
Schlagworte: | |
Online-Zugang: | Volltext bestellen |
Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
container_end_page | 574 |
---|---|
container_issue | 3 |
container_start_page | 562 |
container_title | IEEE transactions on fuzzy systems |
container_volume | 19 |
creator | Beliakov, G James, S Gang Li |
description | We consider an application of fuzzy measures to the problem of metric learning in semisupervised clustering. We investigate the necessary and sufficient conditions on the underlying fuzzy measure that make the discrete Choquet integral suitable for defining a metric. As a byproduct, we can obtain the analogous conditions for the ordered-weighted-averaging (OWA) operators, which constitute a special case. We then generalize these results for power-based Choquet and OWA operators. We show that this metric-learning problem can be formulated as a linear-programming problem and specify the required sets of linear constraints. We present the results of numerical experiments on artificial- and real-world datasets, which illustrate the potential, usefulness, and limitations of this construction. |
doi_str_mv | 10.1109/TFUZZ.2011.2123899 |
format | Article |
fullrecord | <record><control><sourceid>proquest_RIE</sourceid><recordid>TN_cdi_proquest_miscellaneous_889400009</recordid><sourceformat>XML</sourceformat><sourcesystem>PC</sourcesystem><ieee_id>5725180</ieee_id><sourcerecordid>2556616531</sourcerecordid><originalsourceid>FETCH-LOGICAL-c326t-b67def15c3e0ce9d692445c6b85c717a35aba0011b5f04607bf8595c3ba8a6b33</originalsourceid><addsrcrecordid>eNpdkL1OwzAURi0EEqXwArBELEwp_o89QtRCpSIG2qWL5bg3JVWaFDtB4u1xKGLAy7V0z3f16SB0TfCEEKzvl7PVej2hmJAJJZQprU_QiGhOUowZP41_LFkqMyzP0UUIO4wJF0SN0HQB1jdVs03y9_ajhy6dNx1sva3TRxtgk7xA5ysXkrL1yRvsq9AfwH9Wwyqv-9CBj-FLdFbaOsDV7xyj1Wy6zJ_TxevTPH9YpI5R2aWFzDZQEuEYYAd6IzXlXDhZKOEyklkmbGFjNVKIEnOJs6JUQke8sMrKgrExujvePfihbOhMLOSgrm0DbR-MUprj-HQkb_-Ru7b3TSxnNOGZpETRCNEj5HwbgofSHHy1t_7LEGwGr-bHqxm8ml-vMXRzDFUA8BcQGY0-MfsGR0Bz_g</addsrcrecordid><sourcetype>Aggregation Database</sourcetype><iscdi>true</iscdi><recordtype>article</recordtype><pqid>914762182</pqid></control><display><type>article</type><title>Learning Choquet-Integral-Based Metrics for Semisupervised Clustering</title><source>IEEE Electronic Library (IEL)</source><creator>Beliakov, G ; James, S ; Gang Li</creator><creatorcontrib>Beliakov, G ; James, S ; Gang Li</creatorcontrib><description>We consider an application of fuzzy measures to the problem of metric learning in semisupervised clustering. We investigate the necessary and sufficient conditions on the underlying fuzzy measure that make the discrete Choquet integral suitable for defining a metric. As a byproduct, we can obtain the analogous conditions for the ordered-weighted-averaging (OWA) operators, which constitute a special case. We then generalize these results for power-based Choquet and OWA operators. We show that this metric-learning problem can be formulated as a linear-programming problem and specify the required sets of linear constraints. We present the results of numerical experiments on artificial- and real-world datasets, which illustrate the potential, usefulness, and limitations of this construction.</description><identifier>ISSN: 1063-6706</identifier><identifier>EISSN: 1941-0034</identifier><identifier>DOI: 10.1109/TFUZZ.2011.2123899</identifier><identifier>CODEN: IEFSEV</identifier><language>eng</language><publisher>New York: IEEE</publisher><subject>Additives ; Byproducts ; Choquet integral ; Clustering ; Context ; Fuzzy ; fuzzy c-means (FCM) ; Fuzzy logic ; fuzzy measure ; Fuzzy set theory ; Indexes ; Integrals ; Learning ; Linear programming ; Measurement ; metric learning ; Open wireless architecture ; Operators ; ordered-weighted averaging (OWA) ; Silicon</subject><ispartof>IEEE transactions on fuzzy systems, 2011-06, Vol.19 (3), p.562-574</ispartof><rights>Copyright The Institute of Electrical and Electronics Engineers, Inc. (IEEE) Jun 2011</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c326t-b67def15c3e0ce9d692445c6b85c717a35aba0011b5f04607bf8595c3ba8a6b33</citedby><cites>FETCH-LOGICAL-c326t-b67def15c3e0ce9d692445c6b85c717a35aba0011b5f04607bf8595c3ba8a6b33</cites></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktohtml>$$Uhttps://ieeexplore.ieee.org/document/5725180$$EHTML$$P50$$Gieee$$H</linktohtml><link.rule.ids>314,780,784,796,27924,27925,54758</link.rule.ids><linktorsrc>$$Uhttps://ieeexplore.ieee.org/document/5725180$$EView_record_in_IEEE$$FView_record_in_$$GIEEE</linktorsrc></links><search><creatorcontrib>Beliakov, G</creatorcontrib><creatorcontrib>James, S</creatorcontrib><creatorcontrib>Gang Li</creatorcontrib><title>Learning Choquet-Integral-Based Metrics for Semisupervised Clustering</title><title>IEEE transactions on fuzzy systems</title><addtitle>TFUZZ</addtitle><description>We consider an application of fuzzy measures to the problem of metric learning in semisupervised clustering. We investigate the necessary and sufficient conditions on the underlying fuzzy measure that make the discrete Choquet integral suitable for defining a metric. As a byproduct, we can obtain the analogous conditions for the ordered-weighted-averaging (OWA) operators, which constitute a special case. We then generalize these results for power-based Choquet and OWA operators. We show that this metric-learning problem can be formulated as a linear-programming problem and specify the required sets of linear constraints. We present the results of numerical experiments on artificial- and real-world datasets, which illustrate the potential, usefulness, and limitations of this construction.</description><subject>Additives</subject><subject>Byproducts</subject><subject>Choquet integral</subject><subject>Clustering</subject><subject>Context</subject><subject>Fuzzy</subject><subject>fuzzy c-means (FCM)</subject><subject>Fuzzy logic</subject><subject>fuzzy measure</subject><subject>Fuzzy set theory</subject><subject>Indexes</subject><subject>Integrals</subject><subject>Learning</subject><subject>Linear programming</subject><subject>Measurement</subject><subject>metric learning</subject><subject>Open wireless architecture</subject><subject>Operators</subject><subject>ordered-weighted averaging (OWA)</subject><subject>Silicon</subject><issn>1063-6706</issn><issn>1941-0034</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2011</creationdate><recordtype>article</recordtype><sourceid>RIE</sourceid><recordid>eNpdkL1OwzAURi0EEqXwArBELEwp_o89QtRCpSIG2qWL5bg3JVWaFDtB4u1xKGLAy7V0z3f16SB0TfCEEKzvl7PVej2hmJAJJZQprU_QiGhOUowZP41_LFkqMyzP0UUIO4wJF0SN0HQB1jdVs03y9_ajhy6dNx1sva3TRxtgk7xA5ysXkrL1yRvsq9AfwH9Wwyqv-9CBj-FLdFbaOsDV7xyj1Wy6zJ_TxevTPH9YpI5R2aWFzDZQEuEYYAd6IzXlXDhZKOEyklkmbGFjNVKIEnOJs6JUQke8sMrKgrExujvePfihbOhMLOSgrm0DbR-MUprj-HQkb_-Ru7b3TSxnNOGZpETRCNEj5HwbgofSHHy1t_7LEGwGr-bHqxm8ml-vMXRzDFUA8BcQGY0-MfsGR0Bz_g</recordid><startdate>201106</startdate><enddate>201106</enddate><creator>Beliakov, G</creator><creator>James, S</creator><creator>Gang Li</creator><general>IEEE</general><general>The Institute of Electrical and Electronics Engineers, Inc. (IEEE)</general><scope>97E</scope><scope>RIA</scope><scope>RIE</scope><scope>AAYXX</scope><scope>CITATION</scope><scope>7SC</scope><scope>8FD</scope><scope>JQ2</scope><scope>L7M</scope><scope>L~C</scope><scope>L~D</scope><scope>7SP</scope><scope>F28</scope><scope>FR3</scope></search><sort><creationdate>201106</creationdate><title>Learning Choquet-Integral-Based Metrics for Semisupervised Clustering</title><author>Beliakov, G ; James, S ; Gang Li</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c326t-b67def15c3e0ce9d692445c6b85c717a35aba0011b5f04607bf8595c3ba8a6b33</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2011</creationdate><topic>Additives</topic><topic>Byproducts</topic><topic>Choquet integral</topic><topic>Clustering</topic><topic>Context</topic><topic>Fuzzy</topic><topic>fuzzy c-means (FCM)</topic><topic>Fuzzy logic</topic><topic>fuzzy measure</topic><topic>Fuzzy set theory</topic><topic>Indexes</topic><topic>Integrals</topic><topic>Learning</topic><topic>Linear programming</topic><topic>Measurement</topic><topic>metric learning</topic><topic>Open wireless architecture</topic><topic>Operators</topic><topic>ordered-weighted averaging (OWA)</topic><topic>Silicon</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Beliakov, G</creatorcontrib><creatorcontrib>James, S</creatorcontrib><creatorcontrib>Gang Li</creatorcontrib><collection>IEEE All-Society Periodicals Package (ASPP) 2005-present</collection><collection>IEEE All-Society Periodicals Package (ASPP) 1998-Present</collection><collection>IEEE Electronic Library (IEL)</collection><collection>CrossRef</collection><collection>Computer and Information Systems Abstracts</collection><collection>Technology Research Database</collection><collection>ProQuest Computer Science Collection</collection><collection>Advanced Technologies Database with Aerospace</collection><collection>Computer and Information Systems Abstracts Academic</collection><collection>Computer and Information Systems Abstracts Professional</collection><collection>Electronics & Communications Abstracts</collection><collection>ANTE: Abstracts in New Technology & Engineering</collection><collection>Engineering Research Database</collection><jtitle>IEEE transactions on fuzzy systems</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext_linktorsrc</fulltext></delivery><addata><au>Beliakov, G</au><au>James, S</au><au>Gang Li</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Learning Choquet-Integral-Based Metrics for Semisupervised Clustering</atitle><jtitle>IEEE transactions on fuzzy systems</jtitle><stitle>TFUZZ</stitle><date>2011-06</date><risdate>2011</risdate><volume>19</volume><issue>3</issue><spage>562</spage><epage>574</epage><pages>562-574</pages><issn>1063-6706</issn><eissn>1941-0034</eissn><coden>IEFSEV</coden><abstract>We consider an application of fuzzy measures to the problem of metric learning in semisupervised clustering. We investigate the necessary and sufficient conditions on the underlying fuzzy measure that make the discrete Choquet integral suitable for defining a metric. As a byproduct, we can obtain the analogous conditions for the ordered-weighted-averaging (OWA) operators, which constitute a special case. We then generalize these results for power-based Choquet and OWA operators. We show that this metric-learning problem can be formulated as a linear-programming problem and specify the required sets of linear constraints. We present the results of numerical experiments on artificial- and real-world datasets, which illustrate the potential, usefulness, and limitations of this construction.</abstract><cop>New York</cop><pub>IEEE</pub><doi>10.1109/TFUZZ.2011.2123899</doi><tpages>13</tpages></addata></record> |
fulltext | fulltext_linktorsrc |
identifier | ISSN: 1063-6706 |
ispartof | IEEE transactions on fuzzy systems, 2011-06, Vol.19 (3), p.562-574 |
issn | 1063-6706 1941-0034 |
language | eng |
recordid | cdi_proquest_miscellaneous_889400009 |
source | IEEE Electronic Library (IEL) |
subjects | Additives Byproducts Choquet integral Clustering Context Fuzzy fuzzy c-means (FCM) Fuzzy logic fuzzy measure Fuzzy set theory Indexes Integrals Learning Linear programming Measurement metric learning Open wireless architecture Operators ordered-weighted averaging (OWA) Silicon |
title | Learning Choquet-Integral-Based Metrics for Semisupervised Clustering |
url | https://sfx.bib-bvb.de/sfx_tum?ctx_ver=Z39.88-2004&ctx_enc=info:ofi/enc:UTF-8&ctx_tim=2024-12-25T00%3A16%3A03IST&url_ver=Z39.88-2004&url_ctx_fmt=infofi/fmt:kev:mtx:ctx&rfr_id=info:sid/primo.exlibrisgroup.com:primo3-Article-proquest_RIE&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.genre=article&rft.atitle=Learning%20Choquet-Integral-Based%20Metrics%20for%20Semisupervised%20Clustering&rft.jtitle=IEEE%20transactions%20on%20fuzzy%20systems&rft.au=Beliakov,%20G&rft.date=2011-06&rft.volume=19&rft.issue=3&rft.spage=562&rft.epage=574&rft.pages=562-574&rft.issn=1063-6706&rft.eissn=1941-0034&rft.coden=IEFSEV&rft_id=info:doi/10.1109/TFUZZ.2011.2123899&rft_dat=%3Cproquest_RIE%3E2556616531%3C/proquest_RIE%3E%3Curl%3E%3C/url%3E&disable_directlink=true&sfx.directlink=off&sfx.report_link=0&rft_id=info:oai/&rft_pqid=914762182&rft_id=info:pmid/&rft_ieee_id=5725180&rfr_iscdi=true |