The performance of a binary classifier is described by a confusion matrix with four entries: the number of true positives (TP), true negatives (TN), false positives (FP), and false negatives (FN). The Matthew's Correlation Coefficient (MCC), F1, and Fowlkes--Mallows (FM) scores are scalars that summarize a confusion matrix. Both the F1 and FM scores are based on only three of the four entries in the confusion matrix (they ignore TN). In contrast, the MCC takes into account all four entries of the confusion matrix and thus can be seen as providing a more representative picture. However, in object detection problems, measuring the number of true negatives is so large it is often intractable. Thus we ask, what happens to the MCC as the number of true negatives approaches infinity? This paper provides insight into the relationship between the MCC and FM score by proving that the FM-measure is equal to the limit of the MCC as the number of true negatives approaches infinity.

翻译：二分类器的性能由包含四个条目的混淆矩阵描述：真正例数（TP）、真负例数（TN）、假正例数（FP）和假负例数（FN）。马修斯相关系数（MCC）、F1分数和Fowlkes–Mallows（FM）分数是总结混淆矩阵的标量。F1和FM分数仅基于混淆矩阵四个条目中的三个（忽略了TN）。相比之下，MCC利用了混淆矩阵的所有四个条目，因此可视为提供了更具代表性的图像。然而，在目标检测问题中，真负例的数目测量往往因过于庞大而难以处理。因此我们提出疑问：当真负例数量趋近无穷大时，MCC会如何变化？本文通过证明FM度量等于MCC在真负例数量趋于无穷时的极限，揭示了MCC与FM分数之间的关系。