二分类模型评估指标的计算方法与代码实现
一、定义
在研究评估指标之前，先给出分类结果混淆矩阵（confusion matrix）。
|
预测
真实
|
正例 | 反例 |
| 正例 | TP | FN |
| 反例 | FP | TN |
1.准确率--accuracy
- 定义：对于给定的测试数据集，分类器正确分类的样本数与总样本数之比。
- 计算方法：
2.精确率--precision（P）
- 定义：被判定为正例（反例）的样本中，真正的正例样本（反例样本）的比例。
- 计算方法：
3.召回率--recall（R）
- 定义：被正确分类的正例（反例）样本，占所有正例（反例）样本的比例。
- 计算方法：
4.F1_score
- 定义：基于精确率和召回率的调和平均。
- 计算方法：
5.macro 度量
- 定义：对于n个二分类混淆矩阵，在各混淆矩阵上分别计算精确率和召回率，记（P1,R1），（P2,R2）...（Pn，Rn），再计算平均值，得到宏精确率（macro-P）、宏召回率（macro-R），继而得到宏F1（macro-F1）。
6.micro度量
- 定义：对于n个二分类混淆矩阵，先对TP、FN、FP、TN求平均值，再用均值计算得到微精确率（micro-P）、微召回率（micro-P），继而得到微F1（micro-F1）。
二、python代码实现
# -*-coding: utf-8 -*-
import numpy
#true = [真实组1，真实组2...真实组N]，predict = [预测组1，预测组2...预测组N]
def evaluation(true,predict):
num = len(true)#确定有几组
(TP, FP, FN, TN) = ([0] * num for i in range(4))#赋初值
for m in range(0,len(true)):
if(len(true[m]) != len(predict[m])):#样本数都不等，显然是有错误的
print "真实结果与预测结果样本数不一致。"
else:
for i in range(0,len(true[m])):#对每一组数据分别计数
if (predict[m][i] == 1) and ((true[m][i] == 1)): TP[m] += 1.0
elif (predict[m][i] == 1) and ((true[m][i] == 0)): FP[m] += 1.0
elif (predict[m][i] == 0) and ((true[m][i] == 1)): FN[m] += 1.0
elif (predict[m][i] == 0) and ((true[m][i] == 0)): TN[m] += 1.0
# macro度量，先求每一组的评价指标，再求均值
(accuracy_macro, \
precision1_macro, precision0_macro, \
recall1_macro, recall0_macro, \
F1_score1_macro,F1_score0_macro) = \
([0] * num for i in range(7))
for m in range(0,num):
accuracy_macro[m] = (TP[m] + TN[m]) / (TP[m] + FP[m] + FN[m] +TN[m])
if (TP[m] + FP[m] == 0) : precision1_macro[m] = 0#预防一些分母为0的情况
else :precision1_macro[m] = TP[m] / (TP[m] + FP[m])
if (TN[m] + FN[m] == 0) : precision0_macro[m] = 0
else :precision0_macro[m] = TN[m] / (TN[m] + FN[m])
if (TP[m] + FN[m] == 0) : recall1_macro[m] = 0
else :recall1_macro[m] = TP[m] / (TP[m] + FN[m])
if (TN[m] + FP[m] == 0) : recall0_macro[m] = 0
recall0_macro[m] = TN[m] / (TN[m] + FP[m])
macro_accuracy = numpy.mean(accuracy_macro)
macro_precision1 = numpy.mean(precision1_macro)
macro_precision0 = numpy.mean(precision0_macro)
macro_recall1 = numpy.mean(recall1_macro)
macro_recall0 = numpy.mean(recall0_macro)
#F1_score还是按这个公式来算，用macro-P和macro-R
if (macro_precision1 + macro_recall1 == 0): macro_F1_score1 = 0
else: macro_F1_score1 = 2 * macro_precision1 * macro_recall1 / (macro_precision1 + macro_recall1)
if (macro_precision0 + macro_recall0 == 0): macro_F1_score0 = 0
else: macro_F1_score0 = 2 * macro_precision0 * macro_recall0 / (macro_precision0 + macro_recall0)
#micro度量，是用TP、TN、FP、FN的均值来计算评价指标
TPM = numpy.mean(TP)
TNM = numpy.mean(TN)
FPM = numpy.mean(FP)
FNM = numpy.mean(FN)
micro_accuracy = (TPM + TNM) / (TPM + FPM + FNM + TNM)
if(TPM + FPM ==0): micro_precision1 = 0#预防一些分母为0的情况
else: micro_precision1 = TPM / (TPM + FPM)
if(TNM + FNM ==0): micro_precision0 = 0
else: micro_precision0 = TNM / (TNM + FNM)
if (TPM + FNM == 0):micro_recall1 = 0
else: micro_recall1 = TPM / (TPM + FNM)
if (TNM + FPM == 0):micro_recall0 = 0
else: micro_recall0 = TNM / (TNM + FPM)
# F1_score仍然按这个公式来算，用micro-P和micro-R
if (micro_precision1 + micro_recall1 == 0): micro_F1_score1 = 0
else :micro_F1_score1 = 2 * micro_precision1 * micro_recall1 / (micro_precision1 + micro_recall1)
if (micro_precision0 + micro_recall0 == 0): micro_F1_score0 = 0
else :micro_F1_score0 = 2 * micro_precision0 * micro_recall0 / (micro_precision0 + micro_recall0)
print "*****************************macro*****************************"
print "accuracy",":%.3f" % macro_accuracy
print "%20s"%'precision',"%12s"%'recall',"%12s"%'F1_score'
print "%5s" % "0", "%14.3f" % macro_precision0, "%12.3f" % macro_recall0, "%12.3f" %macro_F1_score0
print "%5s" % "1", "%14.3f" % macro_precision1, "%12.3f" % macro_recall1, "%12.3f" %macro_F1_score1
print "%5s" % "avg","%14.3f" % ((macro_precision0+macro_precision1)/2), \
"%12.3f" % ((macro_recall0+macro_recall1)/2), "%12.3f" %((macro_F1_score1+macro_F1_score0)/2)
print "*****************************micro*****************************"
print "accuracy",":%.3f" % micro_accuracy
print "%20s"%'precision',"%12s"%'recall',"%12s"%'F1_score'
print "%5s" % "0", "%14.3f" % micro_precision0, "%12.3f" % micro_recall0, "%12.3f" %micro_F1_score0
print "%5s" % "1", "%14.3f" % micro_precision1, "%12.3f" % micro_recall1, "%12.3f" %micro_F1_score1
print "%5s" % "avg", "%14.3f" % ((micro_precision0 + micro_precision1) / 2), \
"%12.3f" % ((micro_recall0 + micro_recall1) / 2), "%12.3f" % ((micro_F1_score0 + micro_F1_score1) / 2)
if __name__ == "__main__":
#简单举例
true = [[0, 1, 0, 1, 0], [0, 1, 1, 0]]
predict = [[0, 1, 1, 1, 0], [0, 1, 0, 1]]
evaluation(true,predict)
三、运行结果
*****************************macro*****************************
accuracy :0.650
precision recall F1_score
0 0.750 0.583 0.656
1 0.583 0.750 0.656
avg 0.667 0.667 0.656
*****************************micro*****************************
accuracy :0.667
precision recall F1_score
0 0.750 0.600 0.667
1 0.600 0.750 0.667
avg 0.675 0.675 0.667
可以看到，结果相当直观了。
当未采用交叉验证方法时，显然true和predict都只有一组，macro和micro会输出一样的值。