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Techniques to Deal with Off-Diagonal Elements in Confusion Matrices

Author

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  • Inmaculada Barranco-Chamorro

    (Departamento de Estadística e Investigación Operativa, Facultad de Matemáticas, Universidad de Sevilla, 41012 Sevilla, Spain
    These authors contributed equally to this work.)

  • Rosa M. Carrillo-García

    (Departamento de Estadística e Investigación Operativa, Facultad de Matemáticas, Universidad de Sevilla, 41012 Sevilla, Spain
    These authors contributed equally to this work.)

Abstract

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.

Suggested Citation

  • Inmaculada Barranco-Chamorro & Rosa M. Carrillo-García, 2021. "Techniques to Deal with Off-Diagonal Elements in Confusion Matrices," Mathematics, MDPI, vol. 9(24), pages 1-22, December.
    • Handle: RePEc:gam:jmathe:v:9:y:2021:i:24:p:3233-:d:702073
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    References listed on IDEAS

    as
    1. Allen Edwards, 1948. "Note on the “correction for continuity” in testing the significance of the difference between correlated proportions," Psychometrika, Springer;The Psychometric Society, vol. 13(3), pages 185-187, September.
    2. Quinn McNemar, 1947. "Note on the sampling error of the difference between correlated proportions or percentages," Psychometrika, Springer;The Psychometric Society, vol. 12(2), pages 153-157, June.
    3. Barranco-Chamorro, I. & Luque-Calvo, P.L. & Jiménez-Gamero, M.D. & Alba-Fernández, M.V., 2017. "A study of risks of Bayes estimators in the generalized half-logistic distribution for progressively type-II censored samples," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 137(C), pages 130-147.
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