A validity measure for hard and fuzzy clustering derived from Fisher's linear discriminant
Autor(a) principal: | |
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Data de Publicação: | 2002 |
Outros Autores: | , |
Tipo de documento: | Relatório |
Idioma: | eng |
Título da fonte: | Repositório Institucional da UFRJ |
Texto Completo: | http://hdl.handle.net/11422/1894 |
Resumo: | Cluster analysis has a growing importance in many research areas, especially those involving problems of pattern recognition. Generally, in real world problems, the number of classes is unknown in advance, being necessary to have criterions to Identify the best choice of clusters. Here we propose an extension to Fisher Linear Discriminant, the EFLD that does not impose limits on the minimum number of samples, can be applied to fuzzy and crisp partitions and can be calculated more efficiently. We also propose a nem fast and efficient validity method based in the EFLD that measures the compactness and separation of partitions produced by any fuzzy or crisp clustering algorithm. The simulations performed indicate that it's a efficient and fast measure even when the overlapping between clusters is high. Finally, we propose an algorithm that applies the new validity measure to the problem of finding the patterns for the fuzzy K-NN classifier. This algorithm is applied to the problem of cursive digits recognition. |
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Franco, Cláudia Rita deVidal, Leonardo SilvaCruz, Adriano Joaquim de Oliveira2017-05-08T15:07:01Z2023-11-30T03:00:27Z2002-12-30FRANCO, C. R. de.; VIDAL, L. S.; CRUZ, A. J. DE O. A validity measure for hard and fuzzy clustering derived from Fischer's linear discriminant. Rio de Janeiro: NCE/UFRJ, 2002. 6 p. (Relatório Técnico, 02/02)http://hdl.handle.net/11422/1894Cluster analysis has a growing importance in many research areas, especially those involving problems of pattern recognition. Generally, in real world problems, the number of classes is unknown in advance, being necessary to have criterions to Identify the best choice of clusters. Here we propose an extension to Fisher Linear Discriminant, the EFLD that does not impose limits on the minimum number of samples, can be applied to fuzzy and crisp partitions and can be calculated more efficiently. We also propose a nem fast and efficient validity method based in the EFLD that measures the compactness and separation of partitions produced by any fuzzy or crisp clustering algorithm. The simulations performed indicate that it's a efficient and fast measure even when the overlapping between clusters is high. Finally, we propose an algorithm that applies the new validity measure to the problem of finding the patterns for the fuzzy K-NN classifier. This algorithm is applied to the problem of cursive digits recognition.Submitted by Raquel Porto (raquel@nce.ufrj.br) on 2017-05-08T15:07:01Z No. of bitstreams: 1 02_02_000613368.pdf: 1015902 bytes, checksum: 9f4949ef5731d2bad998a46d743a3da3 (MD5)Made available in DSpace on 2017-05-08T15:07:01Z (GMT). No. of bitstreams: 1 02_02_000613368.pdf: 1015902 bytes, checksum: 9f4949ef5731d2bad998a46d743a3da3 (MD5) Previous issue date: 2002-12-30engRelatório Técnico NCECNPQ::CIENCIAS EXATAS E DA TERRA::CIENCIA DA COMPUTACAOAgrupamento difusoSistemas de reconhecimento de padrõesCluster validityFuzzy clusteringPattern recognitionCursive digits recognitionFisher's linear discriminantA validity measure for hard and fuzzy clustering derived from Fisher's linear discriminantinfo:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/report0202abertoBrasilInstituto Tércio Pacitti de Aplicações e Pesquisas Computacionaisinfo:eu-repo/semantics/openAccessreponame:Repositório Institucional da UFRJinstname:Universidade Federal do Rio de Janeiro (UFRJ)instacron:UFRJORIGINAL02_02_000613368.pdf02_02_000613368.pdfapplication/pdf545682http://pantheon.ufrj.br:80/bitstream/11422/1894/3/02_02_000613368.pdf425dc12bf18a3cfa048665cd812a46c4MD53LICENSElicense.txtlicense.txttext/plain; charset=utf-81853http://pantheon.ufrj.br:80/bitstream/11422/1894/2/license.txtdd32849f2bfb22da963c3aac6e26e255MD52TEXT02_02_000613368.pdf.txt02_02_000613368.pdf.txtExtracted texttext/plain24024http://pantheon.ufrj.br:80/bitstream/11422/1894/4/02_02_000613368.pdf.txtfdf3895799cc08d82a351adbd3902d38MD5411422/18942023-11-30 00:00:27.558oai:pantheon.ufrj.br:11422/1894TElDRU7Dh0EgTsODTy1FWENMVVNJVkEgREUgRElTVFJJQlVJw4fDg08KCkFvIGFzc2luYXIgZSBlbnRyZWdhciBlc3RhIGxpY2Vuw6dhLCB2b2PDqihzKSBvKHMpIGF1dG9yKGVzKSBvdSBwcm9wcmlldMOhcmlvKHMpIGRvcyBkaXJlaXRvcyBhdXRvcmFpcyBjb25jZWRlKG0pIGFvIFJlcG9zaXTDs3JpbyBQYW50aGVvbiBkYSBVbml2ZXJzaWRhZGUgRmVkZXJhbCBkbyBSaW8gZGUgSmFuZWlybyAoVUZSSikgbyBkaXJlaXRvIG7Do28gLSBleGNsdXNpdm8gZGUgcmVwcm9kdXppciwgY29udmVydGVyIChjb21vIGRlZmluaWRvIGFiYWl4byksIGUvb3UgZGlzdHJpYnVpciBvIGRvY3VtZW50byBlbnRyZWd1ZSAoaW5jbHVpbmRvIG8gcmVzdW1vKSBlbSB0b2RvIG8gbXVuZG8sIGVtIGZvcm1hdG8gZWxldHLDtG5pY28gZSBlbSBxdWFscXVlciBtZWlvLCBpbmNsdWluZG8sIG1hcyBuw6NvIGxpbWl0YWRvIGEgw6F1ZGlvIGUvb3UgdsOtZGVvLgoKVm9jw6ogY29uY29yZGEgcXVlIGEgVUZSSiBwb2RlLCBzZW0gYWx0ZXJhciBvIGNvbnRlw7pkbywgdHJhZHV6aXIgYSBhcHJlc2VudGHDp8OjbyBkZSBxdWFscXVlciBtZWlvIG91IGZvcm1hdG8gY29tIGEgZmluYWxpZGFkZSBkZSBwcmVzZXJ2YcOnw6NvLgoKVm9jw6ogdGFtYsOpbSBjb25jb3JkYSBxdWUgYSBVRlJKIHBvZGUgbWFudGVyIG1haXMgZGUgdW1hIGPDs3BpYSBkZXNzYSBzdWJtaXNzw6NvIHBhcmEgZmlucyBkZSBzZWd1cmFuw6dhLCBiYWNrLXVwIGUgcHJlc2VydmHDp8OjbyBkaWdpdGFsLgoKRGVjbGFyYSBxdWUgbyBkb2N1bWVudG8gZW50cmVndWUgw6kgc2V1IHRyYWJhbGhvIG9yaWdpbmFsLCBlIHF1ZSB2b2PDqiB0ZW0gbyBkaXJlaXRvIGRlIGNvbmNlZGVyIG9zIGRpcmVpdG9zIGNvbnRpZG9zIG5lc3RhIGxpY2Vuw6dhLiBWb2PDqiB0YW1iw6ltIGRlY2xhcmEgcXVlIGEgc3VhIGFwcmVzZW50YcOnw6NvLCBjb20gbyBtZWxob3IgZGUgc2V1cyBjb25oZWNpbWVudG9zLCBuw6NvIGluZnJpbmdpIGRpcmVpdG9zIGF1dG9yYWlzIGRlIHRlcmNlaXJvcy4KClNlIG8gZG9jdW1lbnRvIGVudHJlZ3VlIGNvbnTDqW0gbWF0ZXJpYWwgZG8gcXVhbCB2b2PDqiBuw6NvIHRlbSBkaXJlaXRvcyBkZSBhdXRvciwgZGVjbGFyYSBxdWUgb2J0ZXZlIGEgcGVybWlzc8OjbyBpcnJlc3RyaXRhIGRvIGRldGVudG9yIGRvcyBkaXJlaXRvcyBhdXRvcmFpcyBlIGNvbmNlZGUgYSBVRlJKIG9zIGRpcmVpdG9zIHJlcXVlcmlkb3MgcG9yIGVzdGEgbGljZW7Dp2EsIGUgcXVlIGVzc2UgbWF0ZXJpYWwgZGUgcHJvcHJpZWRhZGUgZGUgdGVyY2Vpcm9zIGVzdMOhIGNsYXJhbWVudGUgaWRlbnRpZmljYWRvIGUgcmVjb25oZWNpZG8gbm8gdGV4dG8gb3UgY29udGXDumRvIGRhIHN1Ym1pc3PDo28uCgpTZSBvIGRvY3VtZW50byBlbnRyZWd1ZSDDqSBiYXNlYWRvIGVtIHRyYWJhbGhvIHF1ZSBmb2ksIG91IHRlbSBzaWRvIHBhdHJvY2luYWRvIG91IGFwb2lhZG8gcG9yIHVtYSBhZ8OqbmNpYSBvdSBvdXRybyhzKSBvcmdhbmlzbW8ocykgcXVlIG7Do28gYSBVRlJKLCB2b2PDqiBkZWNsYXJhIHF1ZSBjdW1wcml1IHF1YWxxdWVyIGRpcmVpdG8gZGUgUkVWSVPDg08gb3UgZGUgb3V0cmFzIG9icmlnYcOnw7VlcyByZXF1ZXJpZGFzIHBvciBjb250cmF0byBvdSBhY29yZG8uCgpBIFVGUkogaXLDoSBpZGVudGlmaWNhciBjbGFyYW1lbnRlIG8ocykgc2V1KHMpIG5vbWUocykgY29tbyBhdXRvcihlcykgb3UgcHJvcHJpZXTDoXJpbyhzKSBkYSBzdWJtaXNzw6NvLCBlIG7Do28gZmFyw6EgcXVhbHF1ZXIgYWx0ZXJhw6fDo28sIHBhcmEgYWzDqW0gZGFzIHBlcm1pdGlkYXMgcG9yIGVzdGEgbGljZW7Dp2EsIG5vIGF0byBkZSBzdWJtaXNzw6NvLgo=Repositório de PublicaçõesPUBhttp://www.pantheon.ufrj.br/oai/requestopendoar:2023-11-30T03:00:27Repositório Institucional da UFRJ - Universidade Federal do Rio de Janeiro (UFRJ)false |
dc.title.pt_BR.fl_str_mv |
A validity measure for hard and fuzzy clustering derived from Fisher's linear discriminant |
title |
A validity measure for hard and fuzzy clustering derived from Fisher's linear discriminant |
spellingShingle |
A validity measure for hard and fuzzy clustering derived from Fisher's linear discriminant Franco, Cláudia Rita de CNPQ::CIENCIAS EXATAS E DA TERRA::CIENCIA DA COMPUTACAO Agrupamento difuso Sistemas de reconhecimento de padrões Cluster validity Fuzzy clustering Pattern recognition Cursive digits recognition Fisher's linear discriminant |
title_short |
A validity measure for hard and fuzzy clustering derived from Fisher's linear discriminant |
title_full |
A validity measure for hard and fuzzy clustering derived from Fisher's linear discriminant |
title_fullStr |
A validity measure for hard and fuzzy clustering derived from Fisher's linear discriminant |
title_full_unstemmed |
A validity measure for hard and fuzzy clustering derived from Fisher's linear discriminant |
title_sort |
A validity measure for hard and fuzzy clustering derived from Fisher's linear discriminant |
author |
Franco, Cláudia Rita de |
author_facet |
Franco, Cláudia Rita de Vidal, Leonardo Silva Cruz, Adriano Joaquim de Oliveira |
author_role |
author |
author2 |
Vidal, Leonardo Silva Cruz, Adriano Joaquim de Oliveira |
author2_role |
author author |
dc.contributor.author.fl_str_mv |
Franco, Cláudia Rita de Vidal, Leonardo Silva Cruz, Adriano Joaquim de Oliveira |
dc.subject.cnpq.fl_str_mv |
CNPQ::CIENCIAS EXATAS E DA TERRA::CIENCIA DA COMPUTACAO |
topic |
CNPQ::CIENCIAS EXATAS E DA TERRA::CIENCIA DA COMPUTACAO Agrupamento difuso Sistemas de reconhecimento de padrões Cluster validity Fuzzy clustering Pattern recognition Cursive digits recognition Fisher's linear discriminant |
dc.subject.por.fl_str_mv |
Agrupamento difuso Sistemas de reconhecimento de padrões |
dc.subject.eng.fl_str_mv |
Cluster validity Fuzzy clustering Pattern recognition Cursive digits recognition Fisher's linear discriminant |
description |
Cluster analysis has a growing importance in many research areas, especially those involving problems of pattern recognition. Generally, in real world problems, the number of classes is unknown in advance, being necessary to have criterions to Identify the best choice of clusters. Here we propose an extension to Fisher Linear Discriminant, the EFLD that does not impose limits on the minimum number of samples, can be applied to fuzzy and crisp partitions and can be calculated more efficiently. We also propose a nem fast and efficient validity method based in the EFLD that measures the compactness and separation of partitions produced by any fuzzy or crisp clustering algorithm. The simulations performed indicate that it's a efficient and fast measure even when the overlapping between clusters is high. Finally, we propose an algorithm that applies the new validity measure to the problem of finding the patterns for the fuzzy K-NN classifier. This algorithm is applied to the problem of cursive digits recognition. |
publishDate |
2002 |
dc.date.issued.fl_str_mv |
2002-12-30 |
dc.date.accessioned.fl_str_mv |
2017-05-08T15:07:01Z |
dc.date.available.fl_str_mv |
2023-11-30T03:00:27Z |
dc.type.status.fl_str_mv |
info:eu-repo/semantics/publishedVersion |
dc.type.driver.fl_str_mv |
info:eu-repo/semantics/report |
format |
report |
status_str |
publishedVersion |
dc.identifier.citation.fl_str_mv |
FRANCO, C. R. de.; VIDAL, L. S.; CRUZ, A. J. DE O. A validity measure for hard and fuzzy clustering derived from Fischer's linear discriminant. Rio de Janeiro: NCE/UFRJ, 2002. 6 p. (Relatório Técnico, 02/02) |
dc.identifier.uri.fl_str_mv |
http://hdl.handle.net/11422/1894 |
identifier_str_mv |
FRANCO, C. R. de.; VIDAL, L. S.; CRUZ, A. J. DE O. A validity measure for hard and fuzzy clustering derived from Fischer's linear discriminant. Rio de Janeiro: NCE/UFRJ, 2002. 6 p. (Relatório Técnico, 02/02) |
url |
http://hdl.handle.net/11422/1894 |
dc.language.iso.fl_str_mv |
eng |
language |
eng |
dc.relation.ispartof.pt_BR.fl_str_mv |
Relatório Técnico NCE |
dc.rights.driver.fl_str_mv |
info:eu-repo/semantics/openAccess |
eu_rights_str_mv |
openAccess |
dc.publisher.country.fl_str_mv |
Brasil |
dc.publisher.department.fl_str_mv |
Instituto Tércio Pacitti de Aplicações e Pesquisas Computacionais |
dc.source.none.fl_str_mv |
reponame:Repositório Institucional da UFRJ instname:Universidade Federal do Rio de Janeiro (UFRJ) instacron:UFRJ |
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Universidade Federal do Rio de Janeiro (UFRJ) |
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UFRJ |
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UFRJ |
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Repositório Institucional da UFRJ |
collection |
Repositório Institucional da UFRJ |
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