A Comparison of MCC and CEN Error Measures in Multi-Class Prediction

By Giuseppe Jurman, Samantha Riccadonna, Cesare Furlanello. PLoS ONE, 2010

381 citations recorded by the source corpus.

We show that the Confusion Entropy, a measure of performance in multiclass problems has a strong (monotone) relation with the multiclass generalization of a classical metric, the Matthews Correlation Coefficient. Analytical results are provided for the limit cases of general no-information (n-face dice rolling) of the binary classification. Computational evidence supports the claim in the general case.

Subfields: Artificial Intelligence, Computer Vision and Pattern Recognition

View Paper: https://www.semanticscholar.org/paper/ba938c65ab6a3c3cdf96e1adff88ba1fd1c5eb98

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Citations in the corpus

A fully integrated computer-aided diagnosis system for digital X-ray mammograms via deep learning detection, segmentation, and classification (2018, methodology): “MCC is used as a balanced measure of the quality of classi ﬁ cations even if the classes are in di ﬀ erent sizes, counting in true and false positives and negatives [67].”
The Matthews Correlation Coefficient (MCC) is More Informative Than Cohen’s Kappa and Brier Score in Binary Classification Assessment (2021, background): “The Matthews correlation coefﬁcient [1], in particular, is a rate that resulted being more informative than confusion entropy (CEN) [2], accuracy and F 1 score [3], balanced accuracy, bookmaker informedness, and markedness [4], and diagnostic odds ratio [5] in the past (Supplementary Information).”
Boosting methods for multi-class imbalanced data classification: an experimental review (2020, background): “However, it has been shown that the behavior of MCC remains consistent in multi-class settings [76].”
The Matthews correlation coefficient (MCC) should replace the ROC AUC as the standard metric for assessing binary classification (2023, background): “In some previous studies, we argued that the MCC is more informative than confusion entropy [15], F 1 score [6], accuracy [6], balanced accuracy [4], bookmaker informed-ness [4], markedness [4], diagnostic odds ratio [16], Cohen’s Kappa [17], and Brier score [17].”
Error Metrics and Performance Fitness Indicators for Artificial Intelligence and Machine Learning in Engineering and Sciences (2020, background): “15 Markedness (MK) Measures trustworthiness of positive and MK = PPV + NPV − 1 • Measures trustworthiness of positive and negative predictions by a model [103].”