arXiv:2611.08799v1 Announce Type: new
Abstract: Fifty years after its introduction, the Matthews Correlation Coefficient (MCC) remains central -and debated- in binary classification. This survey offers a comprehensive retrospective and an in-depth analysis of MCC, covering its historical development, mathematical foundations, and implications for practice. We clarify long-standing misconceptions, formalize its equivalences (to Pearson's correlation and to Chi2 in 2×2 tables), and examine its behavior under class imbalance. Beyond MCC, we develop analytical (derivatives) and graphical (contour plots) frameworks that generalize to any confusion-matrix-based metric. These frameworks expose structural properties -bias, robustness, sensitivity- that scalar summaries conceal, and they provide actionable guidance for selecting and interpreting performance measures in applications where reliability and fairness matter. Together, our results position MCC within a broader toolkit while clarifying when it is informative -and when alternatives may be preferable.
Abstract: Fifty years after its introduction, the Matthews Correlation Coefficient (MCC) remains central -and debated- in binary classification. This survey offers a comprehensive retrospective and an in-depth analysis of MCC, covering its historical development, mathematical foundations, and implications for practice. We clarify long-standing misconceptions, formalize its equivalences (to Pearson's correlation and to Chi2 in 2×2 tables), and examine its behavior under class imbalance. Beyond MCC, we develop analytical (derivatives) and graphical (contour plots) frameworks that generalize to any confusion-matrix-based metric. These frameworks expose structural properties -bias, robustness, sensitivity- that scalar summaries conceal, and they provide actionable guidance for selecting and interpreting performance measures in applications where reliability and fairness matter. Together, our results position MCC within a broader toolkit while clarifying when it is informative -and when alternatives may be preferable.
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