Pearson–Matthews correlation coefficients for binary and multinary classification

• Published in: Signal processing Vol. 222; p. 109511
• Main Authors: Stoica, Petre, Babu, Prabhu
• Format: Journal Article
• Language: English
• Published: Elsevier B.V 01.09.2024
• Subjects: Matthews correlation coefficient (MCC); Multinary classification; Multivariate Pearson correlation (MPC); Multivariate Pearson correlation (MPC); Matthews correlation coefficient (MCC); Multinary classification
• ISSN: 0165-1684; 1872-7557; 1872-7557
• DOI: 10.1016/j.sigpro.2024.109511

The Pearson–Matthews correlation coefficient (usually abbreviated MCC) is considered to be one of the most useful metrics for the performance of a binary classification. For multinary classification tasks (with more than two classes) the existing extension of MCC, commonly called the RK metric, has also been successfully used in many applications. The present paper begins with an introductory discussion on certain aspects of MCC. Then we go on to discuss the topic of multinary classification that is the main focus of this paper and which, despite its practical and theoretical importance, appears to be less developed than the topic of binary classification. Our discussion of the RK is followed by the introduction of two other metrics for multinary classification derived from the multivariate Pearson correlation (MPC) coefficients. We show that both RK and the MPC metrics suffer from the problem of not decisively indicating poor classification results when they should, and introduce three new enhanced metrics that do not suffer from this problem. We also present an additional new metric for multinary classification which can be viewed as a direct extension of MCC.