A cophenetic correlation coefficient for Tocher’s method
Autor(a) principal: | |
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Data de Publicação: | 2013 |
Outros Autores: | |
Tipo de documento: | Artigo |
Idioma: | eng |
Título da fonte: | Pesquisa Agropecuária Brasileira (Online) |
Texto Completo: | https://seer.sct.embrapa.br/index.php/pab/article/view/14764 |
Resumo: | The objective of this work was to propose a way of using the Tocher’s method of clustering to obtain a matrix similar to the cophenetic one obtained for hierarchical methods, which would allow the calculation of a cophenetic correlation. To illustrate the obtention of the proposed cophenetic matrix, we used two dissimilarity matrices – one obtained with the generalized quadratic Mahalanobis distance and the other with the Euclidean distance – between 17 garlic cultivars, based on six morphological characters. Basically, the proposal for obtaining the cophenetic matrix was to use the average distances within and between clusters, after performing the clustering. A function in R language was proposed to compute the cophenetic matrix for Tocher’s method. The empirical distribution of this correlation coefficient was briefly studied. For both dissimilarity measures, the values of cophenetic correlation obtained for the Tocher’s method were higher than those obtained with the hierarchical methods (Ward’s algorithm and average linkage – UPGMA). Comparisons between the clustering made with the agglomerative hierarchical methods and with the Tocher’s method can be performed using a criterion in common: the correlation between matrices of original and cophenetic distances. |
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A cophenetic correlation coefficient for Tocher’s methodUm coeficiente de correlação cofenética para o método de Tochercluster analysis; optimization methods; clustering consistencyering consistenceanálise de agrupamento; métodos de otimização; consistência do agrupamentoThe objective of this work was to propose a way of using the Tocher’s method of clustering to obtain a matrix similar to the cophenetic one obtained for hierarchical methods, which would allow the calculation of a cophenetic correlation. To illustrate the obtention of the proposed cophenetic matrix, we used two dissimilarity matrices – one obtained with the generalized quadratic Mahalanobis distance and the other with the Euclidean distance – between 17 garlic cultivars, based on six morphological characters. Basically, the proposal for obtaining the cophenetic matrix was to use the average distances within and between clusters, after performing the clustering. A function in R language was proposed to compute the cophenetic matrix for Tocher’s method. The empirical distribution of this correlation coefficient was briefly studied. For both dissimilarity measures, the values of cophenetic correlation obtained for the Tocher’s method were higher than those obtained with the hierarchical methods (Ward’s algorithm and average linkage – UPGMA). Comparisons between the clustering made with the agglomerative hierarchical methods and with the Tocher’s method can be performed using a criterion in common: the correlation between matrices of original and cophenetic distances.O objetivo deste trabalho foi propor uma forma de uso do método de Tocher para obtenção de uma matriz análoga à matriz cofenética obtida para métodos hierárquicos, o que permitiria o cálculo de uma correlação cofenética. Para ilustrar a obtenção da matriz cofenética proposta, foram utilizadas duas matrizes de dissimilaridade – uma obtida com a distância quadrada generalizada de Mahalanobis e outra com a distância euclidiana – entre dezessete cultivares de alho, com base em seis caracteres morfológicos. Basicamente, a proposta para obtenção da matriz cofenética foi a de usar, após a realização do agrupamento, as distâncias médias intra e intergrupos. Uma função em linguagem R foi proposta para computar a matriz cofenética para o método de Tocher. A distribuição empírica desse coeficiente de correlação foi estudada de forma sucinta. Para as duas medidas de dissimilaridade, os valores do coeficiente de correlação cofenética obtidos para o método de Tocher foram superiores aos obtidos com os métodos hierárquicos (algoritmo de Ward e ligação média – UPGMA). Comparações entre agrupamentos feitos com os métodos hierárquicos aglomerativos e com o método de Tocher podem ser realizadas com o uso de um critério em comum: o da correlação entre matrizes de distâncias cofenéticas e originais.Pesquisa Agropecuaria BrasileiraPesquisa Agropecuária BrasileiraSilva, Anderson Rodrigo daDias, Carlos Tadeu dos Santos2013-09-05info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionapplication/pdfhttps://seer.sct.embrapa.br/index.php/pab/article/view/14764Pesquisa Agropecuaria Brasileira; v.48, n.6, jun. 2013; 589-596Pesquisa Agropecuária Brasileira; v.48, n.6, jun. 2013; 589-5961678-39210100-104xreponame:Pesquisa Agropecuária Brasileira (Online)instname:Empresa Brasileira de Pesquisa Agropecuária (Embrapa)instacron:EMBRAPAenghttps://seer.sct.embrapa.br/index.php/pab/article/view/14764/12149https://seer.sct.embrapa.br/index.php/pab/article/downloadSuppFile/14764/9842info:eu-repo/semantics/openAccess2013-09-05T19:39:27Zoai:ojs.seer.sct.embrapa.br:article/14764Revistahttp://seer.sct.embrapa.br/index.php/pabPRIhttps://old.scielo.br/oai/scielo-oai.phppab@sct.embrapa.br || sct.pab@embrapa.br1678-39210100-204Xopendoar:2013-09-05T19:39:27Pesquisa Agropecuária Brasileira (Online) - Empresa Brasileira de Pesquisa Agropecuária (Embrapa)false |
dc.title.none.fl_str_mv |
A cophenetic correlation coefficient for Tocher’s method Um coeficiente de correlação cofenética para o método de Tocher |
title |
A cophenetic correlation coefficient for Tocher’s method |
spellingShingle |
A cophenetic correlation coefficient for Tocher’s method Silva, Anderson Rodrigo da cluster analysis; optimization methods; clustering consistencyering consistence análise de agrupamento; métodos de otimização; consistência do agrupamento |
title_short |
A cophenetic correlation coefficient for Tocher’s method |
title_full |
A cophenetic correlation coefficient for Tocher’s method |
title_fullStr |
A cophenetic correlation coefficient for Tocher’s method |
title_full_unstemmed |
A cophenetic correlation coefficient for Tocher’s method |
title_sort |
A cophenetic correlation coefficient for Tocher’s method |
author |
Silva, Anderson Rodrigo da |
author_facet |
Silva, Anderson Rodrigo da Dias, Carlos Tadeu dos Santos |
author_role |
author |
author2 |
Dias, Carlos Tadeu dos Santos |
author2_role |
author |
dc.contributor.none.fl_str_mv |
|
dc.contributor.author.fl_str_mv |
Silva, Anderson Rodrigo da Dias, Carlos Tadeu dos Santos |
dc.subject.por.fl_str_mv |
cluster analysis; optimization methods; clustering consistencyering consistence análise de agrupamento; métodos de otimização; consistência do agrupamento |
topic |
cluster analysis; optimization methods; clustering consistencyering consistence análise de agrupamento; métodos de otimização; consistência do agrupamento |
description |
The objective of this work was to propose a way of using the Tocher’s method of clustering to obtain a matrix similar to the cophenetic one obtained for hierarchical methods, which would allow the calculation of a cophenetic correlation. To illustrate the obtention of the proposed cophenetic matrix, we used two dissimilarity matrices – one obtained with the generalized quadratic Mahalanobis distance and the other with the Euclidean distance – between 17 garlic cultivars, based on six morphological characters. Basically, the proposal for obtaining the cophenetic matrix was to use the average distances within and between clusters, after performing the clustering. A function in R language was proposed to compute the cophenetic matrix for Tocher’s method. The empirical distribution of this correlation coefficient was briefly studied. For both dissimilarity measures, the values of cophenetic correlation obtained for the Tocher’s method were higher than those obtained with the hierarchical methods (Ward’s algorithm and average linkage – UPGMA). Comparisons between the clustering made with the agglomerative hierarchical methods and with the Tocher’s method can be performed using a criterion in common: the correlation between matrices of original and cophenetic distances. |
publishDate |
2013 |
dc.date.none.fl_str_mv |
2013-09-05 |
dc.type.none.fl_str_mv |
|
dc.type.driver.fl_str_mv |
info:eu-repo/semantics/article info:eu-repo/semantics/publishedVersion |
format |
article |
status_str |
publishedVersion |
dc.identifier.uri.fl_str_mv |
https://seer.sct.embrapa.br/index.php/pab/article/view/14764 |
url |
https://seer.sct.embrapa.br/index.php/pab/article/view/14764 |
dc.language.iso.fl_str_mv |
eng |
language |
eng |
dc.relation.none.fl_str_mv |
https://seer.sct.embrapa.br/index.php/pab/article/view/14764/12149 https://seer.sct.embrapa.br/index.php/pab/article/downloadSuppFile/14764/9842 |
dc.rights.driver.fl_str_mv |
info:eu-repo/semantics/openAccess |
eu_rights_str_mv |
openAccess |
dc.format.none.fl_str_mv |
application/pdf |
dc.publisher.none.fl_str_mv |
Pesquisa Agropecuaria Brasileira Pesquisa Agropecuária Brasileira |
publisher.none.fl_str_mv |
Pesquisa Agropecuaria Brasileira Pesquisa Agropecuária Brasileira |
dc.source.none.fl_str_mv |
Pesquisa Agropecuaria Brasileira; v.48, n.6, jun. 2013; 589-596 Pesquisa Agropecuária Brasileira; v.48, n.6, jun. 2013; 589-596 1678-3921 0100-104x reponame:Pesquisa Agropecuária Brasileira (Online) instname:Empresa Brasileira de Pesquisa Agropecuária (Embrapa) instacron:EMBRAPA |
instname_str |
Empresa Brasileira de Pesquisa Agropecuária (Embrapa) |
instacron_str |
EMBRAPA |
institution |
EMBRAPA |
reponame_str |
Pesquisa Agropecuária Brasileira (Online) |
collection |
Pesquisa Agropecuária Brasileira (Online) |
repository.name.fl_str_mv |
Pesquisa Agropecuária Brasileira (Online) - Empresa Brasileira de Pesquisa Agropecuária (Embrapa) |
repository.mail.fl_str_mv |
pab@sct.embrapa.br || sct.pab@embrapa.br |
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