ROC曲线以及评估指标F1-Score, recall, precision-整理版

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最近一直在看ROC曲线，查阅了一些资料，并进行了整理，文章结尾有原资料链接。希望能自己和各位节约时间来找资料，花更多的时间来学习。

ROC（Receiver Operating Characteristic）曲线和AUC常被用来评价一个二值分类器（binary classifier）的优劣。ROC曲线怎么来的呢，我们来看经典的混淆矩阵：

ROC曲线一般的横轴是FPR，纵轴是FPR。AUC为曲线下面的面积，作为评估指标，AUC值越大，说明模型越好。如下图：

当然还有其他的一些评估指标，常见的有：ROC、AUC、precision、recall、F1-score。下面是指标详细：

Terminology and derivations
from a confusion matrix

sensitivity or true positive rate (TPR): eqv. with hit rate, recall; $\mathit{TPR} = \frac {\mathit{TP}} {P} = \frac {\mathit{TP}} {\mathit{TP}+\mathit{FN}}$
specificity (SPC) or true negative rate (TNR): $\mathit{SPC} = \frac {\mathit{TN}} {N} = \frac {\mathit{TN}} {\mathit{FP} + \mathit{TN}}$
precision or positive predictive value (PPV): $\mathit{PPV} = \frac {\mathit{TP}} {\mathit{TP} + \mathit{FP}}$
negative predictive value (NPV): $\mathit{NPV} = \frac {\mathit{TN}} {\mathit{TN} + \mathit{FN}}$
fall-out or false positive rate (FPR): $\mathit{FPR} = \frac {\mathit{FP}} {N} = \frac {\mathit{FP}} {\mathit{FP} + \mathit{TN}} = 1 - \mathit{SPC}$
false discovery rate (FDR): $\mathit{FDR} = \frac {\mathit{FP}} {\mathit{FP} + \mathit{TP}} = 1 - \mathit{PPV}$
miss rate or false negative rate (FNR): $\mathit{FNR} = \frac {\mathit{FN}} {P} = \frac {\mathit{FN}} {\mathit{FN} + \mathit{TP}}$

accuracy (ACC): $\mathit{ACC} = \frac {\mathit{TP} + \mathit{TN}} {P + N}$
F1 score: is the harmonic mean of precision and sensitivity; $\mathit{F1} = \frac {2 \mathit{TP}} {2 \mathit{TP} + \mathit{FP} + \mathit{FN}}$
Matthews correlation coefficient (MCC): $\frac{ TP \times TN - FP \times FN } {\sqrt{ (TP+FP) ( TP + FN ) ( TN + FP ) ( TN + FN ) } }$

$Informedness = Sensitivity + Specificity - 1$
$Markedness = Precision + NPV - 1$

以下是指标的介绍：感觉原博主讲的很好，我就不作修改了，复制粘贴排版会乱，就直接截图了。

参考来源：

http://www.w2bc.com/Article/88963

https://en.wikipedia.org/wiki/Receiver_operating_characteristic

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