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.

本文研究二元分类器的表现，通过混淆矩阵描述该分类器的真阳性、真阴性、假阳性和假阴性，提出了 MCC，F1 和 FM 得分来总结混淆矩阵信息，其中 MCC 综合考虑整个混淆矩阵；作者证明了，在目标检测问题中有时候计算真阴性的数量太大，难以度量，因此提出仅考虑真阳性、假阳性和假阴性的 FM 和 F1 分数，同时证明 FM 和 MCC 实际上是等价的。