• 定義：對於給定的測試資料集，分類器正確分類的樣本數與總樣本數之比。
• 計算方法：

• 定義：被判定為正例（反例）的樣本中，真正的正例樣本（反例樣本）的比例。
• 計算方法：

• 定義：被正確分類的正例（反例）樣本，佔所有正例（反例）樣本的比例。
• 計算方法：

• 定義：基於精確率和召回率的調和平均。
• 計算方法：

• 定義：對於n個二分類混淆矩陣，在各混淆矩陣上分別計算精確率和召回率，記（P1,R1），（P2,R2）...（Pn，Rn），再計算平均值，得到巨集精確率（macro-P）、巨集召回率（macro-R），繼而得到巨集F1（macro-F1）。

• 定義：對於n個二分類混淆矩陣，先對TP、FN、FP、TN求平均值，再用均值計算得到微精確率（micro-P）、微召回率（micro-P），繼而得到微F1（micro-F1）。

二、python程式碼實現

# -*-coding: utf-8 -*-
import numpy

#true = [真實組1，真實組2...真實組N]，predict = [預測組1，預測組2...預測組N]
def evaluation(true,predict):

    num = len(true)#確定有幾組
    (TP, FP, FN, TN) = ([0] * num for i in range(4))#賦初值

    for m in range(0,len(true)):
        if(len(true[m]) != len(predict[m])):#樣本數都不等，顯然是有錯誤的
            print "真實結果與預測結果樣本數不一致。"
        else:
            for i in range(0,len(true[m])):#對每一組資料分別計數
                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，先求每一組的評價指標，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#預防一些分母為0的情況
        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還是按這個公式來算，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的均值來計算評價指標
    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#預防一些分母為0的情況
    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仍然按這個公式來算，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__":
    #簡單舉例
    true = [[0, 1, 0, 1, 0], [0, 1, 1, 0]]
    predict = [[0, 1, 1, 1, 0], [0, 1, 0, 1]]

    evaluation(true,predict)



 

三、執行結果

*****************************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，結果相當直觀了。

當未採用交叉驗證方法時，顯然true和predict都只有一組，macro和micro會輸出一樣的值。