Techniques to Deal with Off-Diagonal Elements in Confusion Matrices

Confusion matrices are numerical structures that deal with the distribution of errors between different classes or categories in a classification process. From a quality perspective, it is of interest to know if the confusion between the true class A and the class labelled as B is not the same as th...

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Detalles Bibliográficos
Autores: Barranco Chamorro, Inmaculada, Carrillo García, Rosa María
Tipo de recurso: artículo
Estado:Versión publicada
Fecha de publicación:2021
País:España
Institución:Universidad de Sevilla (US)
Repositorio:idUS. Depósito de Investigación de la Universidad de Sevilla
OAI Identifier:oai:idus.us.es:11441/134917
Acceso en línea:https://hdl.handle.net/11441/134917
https://doi.org/10.3390/math9243233
Access Level:acceso abierto
Palabra clave:Bias of classification
Confusion matrix
Marginal homogeneity tests
Dirichlet distribution
Misclassification
Posterior density
Overprediction
Underprediction
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spelling Techniques to Deal with Off-Diagonal Elements in Confusion MatricesBarranco Chamorro, InmaculadaCarrillo García, Rosa MaríaBias of classificationConfusion matrixMarginal homogeneity testsDirichlet distributionMisclassificationPosterior densityOverpredictionUnderpredictionConfusion matrices are numerical structures that deal with the distribution of errors between different classes or categories in a classification process. From a quality perspective, it is of interest to know if the confusion between the true class A and the class labelled as B is not the same as the confusion between the true class B and the class labelled as A. Otherwise, a problem with the classifier, or of identifiability between classes, may exist. In this paper two statistical methods are considered to deal with this issue. Both of them focus on the study of the off-diagonal cells in confusion matrices. First, McNemar-type tests to test the marginal homogeneity are considered, which must be followed from a one versus all study for every pair of categories. Second, a Bayesian proposal based on the Dirichlet distribution is introduced. This allows us to assess the probabilities of misclassification in a confusion matrix. Three applications, including a set of omic data, have been carried out by using the software R.MDPIEstadística e Investigación Operativa2021info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionapplication/pdfapplication/pdfhttps://hdl.handle.net/11441/134917https://doi.org/10.3390/math9243233reponame:idUS. Depósito de Investigación de la Universidad de Sevillainstname:Universidad de Sevilla (US)InglésMathematics, 9, 2-22.https://doi.org/10.3390/math9243233info:eu-repo/semantics/openAccessoai:idus.us.es:11441/1349172026-06-17T12:51:07Z
dc.title.none.fl_str_mv Techniques to Deal with Off-Diagonal Elements in Confusion Matrices
title Techniques to Deal with Off-Diagonal Elements in Confusion Matrices
spellingShingle Techniques to Deal with Off-Diagonal Elements in Confusion Matrices
Barranco Chamorro, Inmaculada
Bias of classification
Confusion matrix
Marginal homogeneity tests
Dirichlet distribution
Misclassification
Posterior density
Overprediction
Underprediction
title_short Techniques to Deal with Off-Diagonal Elements in Confusion Matrices
title_full Techniques to Deal with Off-Diagonal Elements in Confusion Matrices
title_fullStr Techniques to Deal with Off-Diagonal Elements in Confusion Matrices
title_full_unstemmed Techniques to Deal with Off-Diagonal Elements in Confusion Matrices
title_sort Techniques to Deal with Off-Diagonal Elements in Confusion Matrices
dc.creator.none.fl_str_mv Barranco Chamorro, Inmaculada
Carrillo García, Rosa María
author Barranco Chamorro, Inmaculada
author_facet Barranco Chamorro, Inmaculada
Carrillo García, Rosa María
author_role author
author2 Carrillo García, Rosa María
author2_role author
dc.contributor.none.fl_str_mv Estadística e Investigación Operativa
dc.subject.none.fl_str_mv Bias of classification
Confusion matrix
Marginal homogeneity tests
Dirichlet distribution
Misclassification
Posterior density
Overprediction
Underprediction
topic Bias of classification
Confusion matrix
Marginal homogeneity tests
Dirichlet distribution
Misclassification
Posterior density
Overprediction
Underprediction
description Confusion matrices are numerical structures that deal with the distribution of errors between different classes or categories in a classification process. From a quality perspective, it is of interest to know if the confusion between the true class A and the class labelled as B is not the same as the confusion between the true class B and the class labelled as A. Otherwise, a problem with the classifier, or of identifiability between classes, may exist. In this paper two statistical methods are considered to deal with this issue. Both of them focus on the study of the off-diagonal cells in confusion matrices. First, McNemar-type tests to test the marginal homogeneity are considered, which must be followed from a one versus all study for every pair of categories. Second, a Bayesian proposal based on the Dirichlet distribution is introduced. This allows us to assess the probabilities of misclassification in a confusion matrix. Three applications, including a set of omic data, have been carried out by using the software R.
publishDate 2021
dc.date.none.fl_str_mv 2021
dc.type.none.fl_str_mv info:eu-repo/semantics/article
info:eu-repo/semantics/publishedVersion
format article
status_str publishedVersion
dc.identifier.none.fl_str_mv https://hdl.handle.net/11441/134917
https://doi.org/10.3390/math9243233
url https://hdl.handle.net/11441/134917
https://doi.org/10.3390/math9243233
dc.language.none.fl_str_mv Inglés
language_invalid_str_mv Inglés
dc.relation.none.fl_str_mv Mathematics, 9, 2-22.
https://doi.org/10.3390/math9243233
dc.rights.none.fl_str_mv info:eu-repo/semantics/openAccess
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv application/pdf
application/pdf
dc.publisher.none.fl_str_mv MDPI
publisher.none.fl_str_mv MDPI
dc.source.none.fl_str_mv reponame:idUS. Depósito de Investigación de la Universidad de Sevilla
instname:Universidad de Sevilla (US)
instname_str Universidad de Sevilla (US)
reponame_str idUS. Depósito de Investigación de la Universidad de Sevilla
collection idUS. Depósito de Investigación de la Universidad de Sevilla
repository.name.fl_str_mv
repository.mail.fl_str_mv
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