Heuristic Search for Cluster Centroids: An Ant-Based Approach for FCM Initialization
Identifieur interne : 001729 ( Istex/Corpus ); précédent : 001728; suivant : 001730Heuristic Search for Cluster Centroids: An Ant-Based Approach for FCM Initialization
Auteurs : Zhiding Yu ; Ruobing Zou ; Simin YuSource :
- Lecture Notes in Computer Science [ 0302-9743 ] ; 2009.
Abstract
Abstract: An ant-based approach to heuristic centroid searching is introduced. The proposed algorithm consists of three major stages: path construction, evaluation and pheromone updating. In the first stage, data pieces are deemed ants which probabilistically choose cluster centroids according to the heuristic and pheromone information of clusters. In the second stage, cluster centers are updated and cluster validity is evaluated using Bezdek’s partition coefficient. In the third stage, pheromone concentration on clusters is updated. When an ant goes to a cluster, it leaves on this centroid pheromone information, the amount of which is determined by evaluation result obtained in the second stage. Initial cluster number is intentionally chosen to be large and cluster merging is performed once the following two conditions are satisfied: 1. Size of the smallest cluster is smaller than a threshold size proportional to the average cluster size; 2. Distance between the smallest cluster and its nearest one is less than a threshold distance. This merging mechanism is shown to enable auto determination of cluster number. The above stages are iteratively performed for a certain number of iterations. The found centroids are used to initialize FCM clustering algorithm. Results on test data sets show that the partitions found using the ant initialization are better optimized than those obtained from random initializations.
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DOI: 10.1007/978-3-642-01510-6_91
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<record><TEI wicri:istexFullTextTei="biblStruct"><teiHeader><fileDesc><titleStmt><title xml:lang="en">Heuristic Search for Cluster Centroids: An Ant-Based Approach for FCM Initialization</title><author><name sortKey="Yu, Zhiding" sort="Yu, Zhiding" uniqKey="Yu Z" first="Zhiding" last="Yu">Zhiding Yu</name><affiliation><mods:affiliation>Department of Electronic & Computer Engineering, the Hong Kong University of Science & Technology, Clear Water Bay, Kowloon, Hong Kong</mods:affiliation></affiliation><affiliation><mods:affiliation>E-mail: hsfzchrisding@hotmail.com</mods:affiliation></affiliation></author><author><name sortKey="Zou, Ruobing" sort="Zou, Ruobing" uniqKey="Zou R" first="Ruobing" last="Zou">Ruobing Zou</name><affiliation><mods:affiliation>School of Electronic and Information Engineering, South China University of Technology, 510641, Guangzhou, China</mods:affiliation></affiliation></author><author><name sortKey="Yu, Simin" sort="Yu, Simin" uniqKey="Yu S" first="Simin" last="Yu">Simin Yu</name><affiliation><mods:affiliation>School of Automation, Guangdong University of Technology, 510006, Guangzhou, China</mods:affiliation></affiliation></author></titleStmt><publicationStmt><idno type="wicri:source">ISTEX</idno><idno type="RBID">ISTEX:F8EE1796927B3CCDAA9339D1FE14A936E9CDC1EF</idno><date when="2009" year="2009">2009</date><idno type="doi">10.1007/978-3-642-01510-6_91</idno><idno type="url">https://api.istex.fr/document/F8EE1796927B3CCDAA9339D1FE14A936E9CDC1EF/fulltext/pdf</idno><idno type="wicri:Area/Istex/Corpus">001729</idno></publicationStmt><sourceDesc><biblStruct><analytic><title level="a" type="main" xml:lang="en">Heuristic Search for Cluster Centroids: An Ant-Based Approach for FCM Initialization</title><author><name sortKey="Yu, Zhiding" sort="Yu, Zhiding" uniqKey="Yu Z" first="Zhiding" last="Yu">Zhiding Yu</name><affiliation><mods:affiliation>Department of Electronic & Computer Engineering, the Hong Kong University of Science & Technology, Clear Water Bay, Kowloon, Hong Kong</mods:affiliation></affiliation><affiliation><mods:affiliation>E-mail: hsfzchrisding@hotmail.com</mods:affiliation></affiliation></author><author><name sortKey="Zou, Ruobing" sort="Zou, Ruobing" uniqKey="Zou R" first="Ruobing" last="Zou">Ruobing Zou</name><affiliation><mods:affiliation>School of Electronic and Information Engineering, South China University of Technology, 510641, Guangzhou, China</mods:affiliation></affiliation></author><author><name sortKey="Yu, Simin" sort="Yu, Simin" uniqKey="Yu S" first="Simin" last="Yu">Simin Yu</name><affiliation><mods:affiliation>School of Automation, Guangdong University of Technology, 510006, Guangzhou, China</mods:affiliation></affiliation></author></analytic><monogr></monogr><series><title level="s">Lecture Notes in Computer Science</title><imprint><date>2009</date></imprint><idno type="ISSN">0302-9743</idno><idno type="eISSN">1611-3349</idno><idno type="ISSN">0302-9743</idno></series><idno type="istex">F8EE1796927B3CCDAA9339D1FE14A936E9CDC1EF</idno><idno type="DOI">10.1007/978-3-642-01510-6_91</idno><idno type="ChapterID">Chap91</idno><idno type="ChapterID">91</idno></biblStruct></sourceDesc><seriesStmt><idno type="ISSN">0302-9743</idno></seriesStmt></fileDesc><profileDesc><textClass></textClass><langUsage><language ident="en">en</language></langUsage></profileDesc></teiHeader><front><div type="abstract" xml:lang="en">Abstract: An ant-based approach to heuristic centroid searching is introduced. The proposed algorithm consists of three major stages: path construction, evaluation and pheromone updating. In the first stage, data pieces are deemed ants which probabilistically choose cluster centroids according to the heuristic and pheromone information of clusters. In the second stage, cluster centers are updated and cluster validity is evaluated using Bezdek’s partition coefficient. In the third stage, pheromone concentration on clusters is updated. When an ant goes to a cluster, it leaves on this centroid pheromone information, the amount of which is determined by evaluation result obtained in the second stage. Initial cluster number is intentionally chosen to be large and cluster merging is performed once the following two conditions are satisfied: 1. Size of the smallest cluster is smaller than a threshold size proportional to the average cluster size; 2. Distance between the smallest cluster and its nearest one is less than a threshold distance. This merging mechanism is shown to enable auto determination of cluster number. The above stages are iteratively performed for a certain number of iterations. The found centroids are used to initialize FCM clustering algorithm. Results on test data sets show that the partitions found using the ant initialization are better optimized than those obtained from random initializations.</div></front></TEI><istex><corpusName>springer</corpusName><author><json:item><name>Zhiding Yu</name><affiliations><json:string>Department of Electronic & Computer Engineering, the Hong Kong University of Science & Technology, Clear Water Bay, Kowloon, Hong Kong,</json:string><json:string>E-mail: hsfzchrisding@hotmail.com</json:string></affiliations></json:item><json:item><name>Ruobing Zou</name><affiliations><json:string>School of Electronic and Information Engineering, South China University of Technology, 510641, Guangzhou, China</json:string></affiliations></json:item><json:item><name>Simin Yu</name><affiliations><json:string>School of Automation, Guangdong University of Technology, 510006, Guangzhou, China</json:string></affiliations></json:item></author><language><json:string>eng</json:string></language><abstract>Abstract: An ant-based approach to heuristic centroid searching is introduced. The proposed algorithm consists of three major stages: path construction, evaluation and pheromone updating. In the first stage, data pieces are deemed ants which probabilistically choose cluster centroids according to the heuristic and pheromone information of clusters. In the second stage, cluster centers are updated and cluster validity is evaluated using Bezdek’s partition coefficient. In the third stage, pheromone concentration on clusters is updated. When an ant goes to a cluster, it leaves on this centroid pheromone information, the amount of which is determined by evaluation result obtained in the second stage. Initial cluster number is intentionally chosen to be large and cluster merging is performed once the following two conditions are satisfied: 1. Size of the smallest cluster is smaller than a threshold size proportional to the average cluster size; 2. Distance between the smallest cluster and its nearest one is less than a threshold distance. This merging mechanism is shown to enable auto determination of cluster number. The above stages are iteratively performed for a certain number of iterations. The found centroids are used to initialize FCM clustering algorithm. Results on test data sets show that the partitions found using the ant initialization are better optimized than those obtained from random initializations.</abstract><qualityIndicators><score>6.224</score><pdfVersion>1.3</pdfVersion><pdfPageSize>430 x 660 pts</pdfPageSize><refBibsNative>false</refBibsNative><keywordCount>0</keywordCount><abstractCharCount>1433</abstractCharCount><pdfWordCount>3656</pdfWordCount><pdfCharCount>21606</pdfCharCount><pdfPageCount>11</pdfPageCount><abstractWordCount>214</abstractWordCount></qualityIndicators><title>Heuristic Search for Cluster Centroids: An Ant-Based Approach for FCM Initialization</title><chapterId><json:string>Chap91</json:string><json:string>91</json:string></chapterId><genre><json:string>conference [research-article]</json:string></genre><serie><editor><json:item><name>David Hutchison</name><affiliations><json:string>Lancaster University, Lancaster, UK</json:string></affiliations></json:item><json:item><name>Takeo Kanade</name><affiliations><json:string>Carnegie Mellon University, Pittsburgh, PA, USA</json:string></affiliations></json:item><json:item><name>Josef Kittler</name><affiliations><json:string>University of Surrey, Guildford, UK</json:string></affiliations></json:item><json:item><name>Jon M. 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St. Joseph Street,, SD 57701,, Rapid City,, USA</json:string><json:string>E-mail: nian.zhang@sdsmt.edu</json:string></affiliations></json:item></editor><subject><json:item><value>Computer Science</value></json:item><json:item><value>Computer Science</value></json:item><json:item><value>Computation by Abstract Devices</value></json:item><json:item><value>Computer Communication Networks</value></json:item><json:item><value>Algorithm Analysis and Problem Complexity</value></json:item><json:item><value>Discrete Mathematics in Computer Science</value></json:item><json:item><value>Artificial Intelligence (incl. 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The proposed algorithm consists of three major stages: path construction, evaluation and pheromone updating. In the first stage, data pieces are deemed ants which probabilistically choose cluster centroids according to the heuristic and pheromone information of clusters. In the second stage, cluster centers are updated and cluster validity is evaluated using Bezdek’s partition coefficient. In the third stage, pheromone concentration on clusters is updated. When an ant goes to a cluster, it leaves on this centroid pheromone information, the amount of which is determined by evaluation result obtained in the second stage. Initial cluster number is intentionally chosen to be large and cluster merging is performed once the following two conditions are satisfied: 1. Size of the smallest cluster is smaller than a threshold size proportional to the average cluster size; 2. Distance between the smallest cluster and its nearest one is less than a threshold distance. This merging mechanism is shown to enable auto determination of cluster number. The above stages are iteratively performed for a certain number of iterations. The found centroids are used to initialize FCM clustering algorithm. Results on test data sets show that the partitions found using the ant initialization are better optimized than those obtained from random initializations.</p></abstract><textClass><keywords scheme="Book Subject Collection"><list><label>SUCO11645</label><item><term>Computer Science</term></item></list></keywords></textClass><textClass><keywords scheme="Book Subject Group"><list><label>I</label><label>I16013</label><label>I13022</label><label>I16021</label><label>I17028</label><label>I21017</label><label>I2203X</label><item><term>Computer Science</term></item><item><term>Computation by Abstract Devices</term></item><item><term>Computer Communication Networks</term></item><item><term>Algorithm Analysis and Problem Complexity</term></item><item><term>Discrete Mathematics in Computer Science</term></item><item><term>Artificial Intelligence (incl. 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University</OrgName><OrgAddress><City>Pittsburgh</City><State>PA</State><Country>USA</Country></OrgAddress></Affiliation><Affiliation ID="Aff3"><OrgName>University of Surrey</OrgName><OrgAddress><City>Guildford</City><Country>UK</Country></OrgAddress></Affiliation><Affiliation ID="Aff4"><OrgName>Cornell University</OrgName><OrgAddress><City>Ithaca</City><State>NY</State><Country>USA</Country></OrgAddress></Affiliation><Affiliation ID="Aff5"><OrgName>ETH Zurich</OrgName><OrgAddress><City>Zurich</City><Country>Switzerland</Country></OrgAddress></Affiliation><Affiliation ID="Aff6"><OrgName>Stanford University</OrgName><OrgAddress><City>Stanford</City><State>CA</State><Country>USA</Country></OrgAddress></Affiliation><Affiliation ID="Aff7"><OrgName>Weizmann Institute of Science</OrgName><OrgAddress><City>Rehovot</City><Country>Israel</Country></OrgAddress></Affiliation><Affiliation ID="Aff8"><OrgName>University of Bern</OrgName><OrgAddress><City>Bern</City><Country>Switzerland</Country></OrgAddress></Affiliation><Affiliation ID="Aff9"><OrgName>Indian Institute of Technology</OrgName><OrgAddress><City>Madras</City><Country>India</Country></OrgAddress></Affiliation><Affiliation ID="Aff10"><OrgName>University of Dortmund</OrgName><OrgAddress><City>Dortmund</City><Country>Germany</Country></OrgAddress></Affiliation><Affiliation ID="Aff11"><OrgName>Massachusetts Institute of Technology</OrgName><OrgAddress><State>MA</State><Country>USA</Country></OrgAddress></Affiliation><Affiliation ID="Aff12"><OrgName>University of California</OrgName><OrgAddress><City>Los Angeles</City><State>CA</State><Country>USA</Country></OrgAddress></Affiliation><Affiliation ID="Aff13"><OrgName>University of California</OrgName><OrgAddress><City>Berkeley</City><State>CA</State><Country>USA</Country></OrgAddress></Affiliation><Affiliation ID="Aff14"><OrgName>Rice University</OrgName><OrgAddress><City>Houston</City><State>TX</State><Country>USA</Country></OrgAddress></Affiliation><Affiliation ID="Aff15"><OrgName>Max-Planck Institute of Computer Science</OrgName><OrgAddress><City>Saarbrücken</City><Country>Germany</Country></OrgAddress></Affiliation></EditorGroup></SeriesHeader><Book Language="En"><BookInfo BookProductType="Proceedings" ContainsESM="No" Language="En" MediaType="eBook" NumberingStyle="Unnumbered" OutputMedium="All" TocLevels="0"><BookID>978-3-642-01510-6</BookID><BookTitle>Advances in Neural Networks – ISNN 2009</BookTitle><BookSubTitle>6th International Symposium on Neural Networks, ISNN 2009 Wuhan, China, May 26-29, 2009 Proceedings, Part II</BookSubTitle><BookVolumeNumber>5552</BookVolumeNumber><BookSequenceNumber>5552</BookSequenceNumber><BookDOI>10.1007/978-3-642-01510-6</BookDOI><BookTitleID>188228</BookTitleID><BookPrintISBN>978-3-642-01509-0</BookPrintISBN><BookElectronicISBN>978-3-642-01510-6</BookElectronicISBN><BookChapterCount>137</BookChapterCount><BookCopyright><CopyrightHolderName>Springer Berlin Heidelberg</CopyrightHolderName><CopyrightYear>2009</CopyrightYear></BookCopyright><BookSubjectGroup><BookSubject Code="I" Type="Primary">Computer Science</BookSubject><BookSubject Code="I16013" Priority="1" Type="Secondary">Computation by Abstract Devices</BookSubject><BookSubject Code="I13022" Priority="2" Type="Secondary">Computer Communication Networks</BookSubject><BookSubject Code="I16021" Priority="3" Type="Secondary">Algorithm Analysis and Problem Complexity</BookSubject><BookSubject Code="I17028" Priority="4" Type="Secondary">Discrete Mathematics in Computer Science</BookSubject><BookSubject Code="I21017" Priority="5" Type="Secondary">Artificial Intelligence (incl. Robotics)</BookSubject><BookSubject Code="I2203X" Priority="6" Type="Secondary">Pattern Recognition</BookSubject><SubjectCollection Code="SUCO11645">Computer Science</SubjectCollection></BookSubjectGroup><BookContext><SeriesID>558</SeriesID></BookContext></BookInfo><BookHeader><EditorGroup><Editor AffiliationIDS="Aff16"><EditorName DisplayOrder="Western"><GivenName>Wen</GivenName><FamilyName>Yu</FamilyName></EditorName><Contact><Email>yuw@ctrl.cinvestav.mx</Email></Contact></Editor><Editor AffiliationIDS="Aff17"><EditorName DisplayOrder="Western"><GivenName>Haibo</GivenName><FamilyName>He</FamilyName></EditorName><Contact><Email>hhe@stevens.edu</Email></Contact></Editor><Editor AffiliationIDS="Aff18"><EditorName DisplayOrder="Western"><GivenName>Nian</GivenName><FamilyName>Zhang</FamilyName></EditorName><Contact><Email>nian.zhang@sdsmt.edu</Email></Contact></Editor><Affiliation ID="Aff16"><OrgDivision>Departamento de Control Automático,</OrgDivision><OrgName>CINVESTAV-IPN,</OrgName><OrgAddress><Street>A.P. 14-740, Av.IPN 2508,</Street><Postcode>D.F., 07360,</Postcode><City>México</City><Country>México</Country></OrgAddress></Affiliation><Affiliation ID="Aff17"><OrgDivision>Deptartment of Electrical and Computer Engineering,</OrgDivision><OrgName>Stevens Institute of Technology,</OrgName><OrgAddress><Postcode>NJ 07030,</Postcode><City>Hoboken,</City><Country>USA</Country></OrgAddress></Affiliation><Affiliation ID="Aff18"><OrgDivision>Dept. of Electrical and Computer Engineering,</OrgDivision><OrgName>South Dakota School of Mines & Technology,</OrgName><OrgAddress><Street>501 E. St. Joseph Street,</Street><Postcode>SD 57701,</Postcode><City>Rapid City,</City><Country>USA</Country></OrgAddress></Affiliation></EditorGroup></BookHeader><Part ID="Part4"><PartInfo TocLevels="0"><PartID>4</PartID><PartSequenceNumber>4</PartSequenceNumber><PartTitle>Clustering and Classification</PartTitle><PartChapterCount>22</PartChapterCount><PartContext><SeriesID>558</SeriesID><BookTitle>Advances in Neural Networks – ISNN 2009</BookTitle></PartContext></PartInfo><Chapter ID="Chap91" Language="En"><ChapterInfo ChapterType="OriginalPaper" ContainsESM="No" NumberingStyle="Unnumbered" TocLevels="0"><ChapterID>91</ChapterID><ChapterDOI>10.1007/978-3-642-01510-6_91</ChapterDOI><ChapterSequenceNumber>91</ChapterSequenceNumber><ChapterTitle Language="En">Heuristic Search for Cluster Centroids: An Ant-Based Approach for FCM Initialization</ChapterTitle><ChapterFirstPage>810</ChapterFirstPage><ChapterLastPage>820</ChapterLastPage><ChapterCopyright><CopyrightHolderName>Springer-Verlag Berlin Heidelberg</CopyrightHolderName><CopyrightYear>2009</CopyrightYear></ChapterCopyright><ChapterGrants Type="Regular"><MetadataGrant Grant="OpenAccess"></MetadataGrant><AbstractGrant Grant="OpenAccess"></AbstractGrant><BodyPDFGrant Grant="Restricted"></BodyPDFGrant><BodyHTMLGrant Grant="Restricted"></BodyHTMLGrant><BibliographyGrant Grant="Restricted"></BibliographyGrant><ESMGrant Grant="Restricted"></ESMGrant></ChapterGrants><ChapterContext><SeriesID>558</SeriesID><PartID>4</PartID><BookID>978-3-642-01510-6</BookID><BookTitle>Advances in Neural Networks – ISNN 2009</BookTitle></ChapterContext></ChapterInfo><ChapterHeader><AuthorGroup><Author AffiliationIDS="Aff19"><AuthorName DisplayOrder="Western"><GivenName>Zhiding</GivenName><FamilyName>Yu</FamilyName></AuthorName><Contact><Email>hsfzchrisding@hotmail.com</Email></Contact></Author><Author AffiliationIDS="Aff20"><AuthorName DisplayOrder="Western"><GivenName>Ruobing</GivenName><FamilyName>Zou</FamilyName></AuthorName></Author><Author AffiliationIDS="Aff21"><AuthorName DisplayOrder="Western"><GivenName>Simin</GivenName><FamilyName>Yu</FamilyName></AuthorName></Author><Affiliation ID="Aff19"><OrgDivision>Department of Electronic & Computer Engineering</OrgDivision><OrgName>the Hong Kong University of Science & Technology, Clear Water Bay, Kowloon</OrgName><OrgAddress><City>Hong Kong</City><Country> </Country></OrgAddress></Affiliation><Affiliation ID="Aff20"><OrgDivision>School of Electronic and Information Engineering</OrgDivision><OrgName>South China University of Technology</OrgName><OrgAddress><City>Guangzhou</City><Postcode>510641</Postcode><Country>China</Country></OrgAddress></Affiliation><Affiliation ID="Aff21"><OrgDivision>School of Automation</OrgDivision><OrgName>Guangdong University of Technology</OrgName><OrgAddress><City>Guangzhou</City><Postcode>510006</Postcode><Country>China</Country></OrgAddress></Affiliation></AuthorGroup><Abstract ID="Abs1" Language="En"><Heading>Abstract</Heading><Para>An ant-based approach to heuristic centroid searching is introduced. The proposed algorithm consists of three major stages: path construction, evaluation and pheromone updating. In the first stage, data pieces are deemed ants which probabilistically choose cluster centroids according to the heuristic and pheromone information of clusters. In the second stage, cluster centers are updated and cluster validity is evaluated using Bezdek’s partition coefficient. In the third stage, pheromone concentration on clusters is updated. When an ant goes to a cluster, it leaves on this centroid pheromone information, the amount of which is determined by evaluation result obtained in the second stage. Initial cluster number is intentionally chosen to be large and cluster merging is performed once the following two conditions are satisfied: 1. Size of the smallest cluster is smaller than a threshold size proportional to the average cluster size; 2. Distance between the smallest cluster and its nearest one is less than a threshold distance. This merging mechanism is shown to enable auto determination of cluster number. The above stages are iteratively performed for a certain number of iterations. The found centroids are used to initialize FCM clustering algorithm. Results on test data sets show that the partitions found using the ant initialization are better optimized than those obtained from random initializations.</Para></Abstract><KeywordGroup Language="En"><Heading>Keywords</Heading><Keyword>Ant colony optimization</Keyword><Keyword>Fuzzy c-means</Keyword><Keyword>Clustering</Keyword></KeywordGroup></ChapterHeader><NoBody></NoBody></Chapter></Part></Book></Series></Publisher></istex:document></istex:metadataXml><mods version="3.6"><titleInfo lang="en"><title>Heuristic Search for Cluster Centroids: An Ant-Based Approach for FCM Initialization</title></titleInfo><titleInfo type="alternative" contentType="CDATA" lang="en"><title>Heuristic Search for Cluster Centroids: An Ant-Based Approach for FCM Initialization</title></titleInfo><name type="personal"><namePart type="given">Zhiding</namePart><namePart type="family">Yu</namePart><affiliation>Department of Electronic & Computer Engineering, the Hong Kong University of Science & Technology, Clear Water Bay, Kowloon, Hong Kong</affiliation><affiliation>E-mail: hsfzchrisding@hotmail.com</affiliation><role><roleTerm type="text">author</roleTerm></role></name><name type="personal"><namePart type="given">Ruobing</namePart><namePart type="family">Zou</namePart><affiliation>School of Electronic and Information Engineering, South China University of Technology, 510641, Guangzhou, China</affiliation><role><roleTerm type="text">author</roleTerm></role></name><name type="personal"><namePart type="given">Simin</namePart><namePart type="family">Yu</namePart><affiliation>School of Automation, Guangdong University of Technology, 510006, Guangzhou, China</affiliation><role><roleTerm type="text">author</roleTerm></role></name><typeOfResource>text</typeOfResource><genre type="conference [research-article]" displayLabel="OriginalPaper"></genre><originInfo><publisher>Springer Berlin Heidelberg</publisher><place><placeTerm type="text">Berlin, Heidelberg</placeTerm></place><dateIssued encoding="w3cdtf">2009</dateIssued><copyrightDate encoding="w3cdtf">2009</copyrightDate></originInfo><language><languageTerm type="code" authority="rfc3066">en</languageTerm><languageTerm type="code" authority="iso639-2b">eng</languageTerm></language><physicalDescription><internetMediaType>text/html</internetMediaType></physicalDescription><abstract lang="en">Abstract: An ant-based approach to heuristic centroid searching is introduced. The proposed algorithm consists of three major stages: path construction, evaluation and pheromone updating. In the first stage, data pieces are deemed ants which probabilistically choose cluster centroids according to the heuristic and pheromone information of clusters. In the second stage, cluster centers are updated and cluster validity is evaluated using Bezdek’s partition coefficient. In the third stage, pheromone concentration on clusters is updated. When an ant goes to a cluster, it leaves on this centroid pheromone information, the amount of which is determined by evaluation result obtained in the second stage. Initial cluster number is intentionally chosen to be large and cluster merging is performed once the following two conditions are satisfied: 1. Size of the smallest cluster is smaller than a threshold size proportional to the average cluster size; 2. Distance between the smallest cluster and its nearest one is less than a threshold distance. This merging mechanism is shown to enable auto determination of cluster number. The above stages are iteratively performed for a certain number of iterations. The found centroids are used to initialize FCM clustering algorithm. Results on test data sets show that the partitions found using the ant initialization are better optimized than those obtained from random initializations.</abstract><relatedItem type="host"><titleInfo><title>Advances in Neural Networks – ISNN 2009</title><subTitle>6th International Symposium on Neural Networks, ISNN 2009 Wuhan, China, May 26-29, 2009 Proceedings, Part II</subTitle></titleInfo><name type="personal"><namePart type="given">Wen</namePart><namePart type="family">Yu</namePart><affiliation>Departamento de Control Automático,, CINVESTAV-IPN,, A.P. 14-740, Av.IPN 2508,, D.F., 07360,, México, México</affiliation><affiliation>E-mail: yuw@ctrl.cinvestav.mx</affiliation><role><roleTerm type="text">editor</roleTerm></role></name><name type="personal"><namePart type="given">Haibo</namePart><namePart type="family">He</namePart><affiliation>Deptartment of Electrical and Computer Engineering,, Stevens Institute of Technology,, NJ 07030,, Hoboken,, USA</affiliation><affiliation>E-mail: hhe@stevens.edu</affiliation><role><roleTerm type="text">editor</roleTerm></role></name><name type="personal"><namePart type="given">Nian</namePart><namePart type="family">Zhang</namePart><affiliation>Dept. of Electrical and Computer Engineering,, South Dakota School of Mines & Technology,, 501 E. 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