一、混淆矩阵
对于二分类的模型，预测结果与实际结果分别可以取0和1。我们用N和P代替0和1，T和F表示预测正确和错误。将他们两两组合，就形成了下图所示的混淆矩阵（注意：组合结果都是针对预测结果而言的）。
由于1和0是数字，阅读性不好，所以我们分别用P和N表示1和0两种结果。变换之后为PP，PN，NP，NN，阅读性也很差，我并不能轻易地看出来预测的正确性与否。因此，为了能够更清楚地分辨各种预测情况是否正确，我们将其中一个符号修改为T和F，以便于分辨出结果。
- P（Positive）：代表 1
- N（Negative）：代表 0
- T（True）：代表预测正确
- F（False）：代表预测错误
二、准确率、精确率、召回率、F1-Measure
- 准确率(Accuracy)：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。
- 精确率(Precision)**：精指分类正确的正样本个数（TP）占分类器判定为正样本的样本个数（TP+FP）的比例。
- 召回率(Recall)：召回率是指分类正确的正样本个数（TP）占真正的正样本个数（TP+FN）的比例。
- F1-Measure值：就是精确率和召回率的调和平均值。
每个评估指标都有其价值，但如果只从单一的评估指标出发去评估模型，往往会得出片面甚至错误的结论；只有通过一组互补的指标去评估模型，才能更好地发现并解决模型存在的问题，从而更好地解决实际业务场景中遇到的问题。
三、多分类评价指标-案例
假设有如下的数据
| 预测 | 真实 |
|---|---|
| A | A |
| A | A |
| B | A |
| C | A |
| B | B |
| B | B |
| C | B |
| B | C |
| C | C |
可以看出，上表为一份样本量为9，类别数为3的含标注结果的三分类预测样本。TN对于准召的计算而言是不需要的，因此下面的表格中未统计该值。
1、按照定义计算Precision、Recall
1.1 对于类别A
| TP = 2 | FP = 0 |
| FN = 2 | TN = ~ |
1.2 对于类别B
| TP = 2 | FP = 2 |
| FN = 1 | TN = ~ |
1.3 对于类别C
| TP = 1 | FP = 2 |
| FN = 1 | TN = ~ |
2、调用sklearn的api进行验证
from sklearn.metrics import classification_report
from sklearn.metrics import precision_score, recall_score, f1_score
true_lable = [0, 0, 0, 0, 1, 1, 1, 2, 2]
prediction = [0, 0, 1, 2, 1, 1, 2, 1, 2]
measure_result = classification_report(true_lable, prediction)
print('measure_result = \n', measure_result)
打印结果：
measure_result =
precision recall f1-score support
0 1.00 0.50 0.67 4
1 0.50 0.67 0.57 3
2 0.33 0.50 0.40 2
accuracy 0.56 9
macro avg 0.61 0.56 0.55 9
weighted avg 0.69 0.56 0.58 9
四、Micro-F1、Macro-F1、weighted-F1
总的来说，微观F1(micro-F1)和宏观F1(macro-F1)都是F1合并后的结果，这两个F1都是用在多分类任务中的评价指标，是两种不一样的求F1均值的方式；micro-F1和macro-F1的计算方法有差异，得出来的结果也略有差异；
1、Micro-F1
Micro-F1 不需要区分类别，直接使用总体样本的准召计算f1 score。
-
计算方法：先计算所有类别的总的Precision和Recall，然后计算出来的F1值即为micro-F1；
-
使用场景：在计算公式中考虑到了每个类别的数量，所以适用于数据分布不平衡的情况；但同时因为考虑到数据的数量，所以在数据极度不平衡的情况下，数量较多数量的类会较大的影响到F1的值；
该样本的混淆矩阵如下：
| TP = 5 | FP = 4 |
| FN = 2 | TN = ~ |
2、Macro-F1
不同于micro f1，macro f1需要先计算出每一个类别的准召及其f1 score，然后通过求均值得到在整个样本上的f1 score。
- 计算方法：将所有类别的Precision和Recall求平均，然后计算F1值作为macro-F1；
- 使用场景：没有考虑到数据的数量，所以会平等的看待每一类（因为每一类的precision和recall都在0-1之间），会相对受高precision和高recall类的影响较大；
类别A的：
类别B的：
类别C的：
Macro-F1为上面三者的平均值：
3、weighted-F1
除了micro-F1和macro-F1，还有weighted-F1，是一个将F1-score乘以该类的比例之后相加的结果，也可以看做是macro-F1的变体吧。
weighted-F1和macro-F1的区别在于：macro-F1对每一类都赋予了相同的权重，而weighted-F1则根据每一类的比例分别赋予不同的权重。
五、指标的选择问题
“我们看到，对于 Macro 来说， 小类别相当程度上拉高了 Precision 的值，而实际上， 并没有那么多样本被正确分类，考虑到实际的环境中，真实样本分布和训练样本分布相同的情况下，这种指标明显是有问题的， 小类别起到的作用太大，以至于大样本的分类情况不佳。 而对于 Micro 来说，其考虑到了这种样本不均衡的问题， 因此在这种情况下相对较佳。
总的来说， 如果你的类别比较均衡，则随便； 如果你认为大样本的类别应该占据更重要的位置， 使用Micro； 如果你认为小样本也应该占据重要的位置，则使用 Macro； 如果 Micro << Macro ， 则意味着在大样本类别中出现了严重的分类错误； 如果 Macro << Micro ， 则意味着小样本类别中出现了严重的分类错误。
为了解决 Macro 无法衡量样本均衡问题，一个很好的方法是求加权的 Macro， 因此 Weighed F1 出现了。”
六、代码
1、数据01
true_lable = [0, 0, 0, 0, 1, 1, 1, 2, 2]
prediction = [0, 0, 1, 2, 1, 1, 2, 1, 2]
from sklearn.metrics import classification_report
from sklearn.metrics import precision_score, recall_score, f1_score
true_lable = [0, 0, 0, 0, 1, 1, 1, 2, 2]
prediction = [0, 0, 1, 2, 1, 1, 2, 1, 2]
measure_result = classification_report(true_lable, prediction)
print('measure_result = \n', measure_result)
print("----------------------------- precision（精确率）-----------------------------")
precision_score_average_None = precision_score(true_lable, prediction, average=None)
precision_score_average_micro = precision_score(true_lable, prediction, average='micro')
precision_score_average_macro = precision_score(true_lable, prediction, average='macro')
precision_score_average_weighted = precision_score(true_lable, prediction, average='weighted')
print('precision_score_average_None = ', precision_score_average_None)
print('precision_score_average_micro = ', precision_score_average_micro)
print('precision_score_average_macro = ', precision_score_average_macro)
print('precision_score_average_weighted = ', precision_score_average_weighted)
print("\n\n----------------------------- recall（召回率）-----------------------------")
recall_score_average_None = recall_score(true_lable, prediction, average=None)
recall_score_average_micro = recall_score(true_lable, prediction, average='micro')
recall_score_average_macro = recall_score(true_lable, prediction, average='macro')
recall_score_average_weighted = recall_score(true_lable, prediction, average='weighted')
print('recall_score_average_None = ', recall_score_average_None)
print('recall_score_average_micro = ', recall_score_average_micro)
print('recall_score_average_macro = ', recall_score_average_macro)
print('recall_score_average_weighted = ', recall_score_average_weighted)
print("\n\n----------------------------- F1-value-----------------------------")
f1_score_average_None = f1_score(true_lable, prediction, average=None)
f1_score_average_micro = f1_score(true_lable, prediction, average='micro')
f1_score_average_macro = f1_score(true_lable, prediction, average='macro')
f1_score_average_weighted = f1_score(true_lable, prediction, average='weighted')
print('f1_score_average_None = ', f1_score_average_None)
print('f1_score_average_micro = ', f1_score_average_micro)
print('f1_score_average_macro = ', f1_score_average_macro)
print('f1_score_average_weighted = ', f1_score_average_weighted)
打印结果：
measure_result =
precision recall f1-score support
0 1.00 0.50 0.67 4
1 0.50 0.67 0.57 3
2 0.33 0.50 0.40 2
accuracy 0.56 9
macro avg 0.61 0.56 0.55 9
weighted avg 0.69 0.56 0.58 9
----------------------------- precision（精确率）-----------------------------
precision_score_average_None = [1. 0.5 0.33333333]
precision_score_average_micro = 0.5555555555555556
precision_score_average_macro = 0.611111111111111
precision_score_average_weighted = 0.6851851851851852
----------------------------- recall（召回率）-----------------------------
recall_score_average_None = [0.5 0.66666667 0.5 ]
recall_score_average_micro = 0.5555555555555556
recall_score_average_macro = 0.5555555555555555
recall_score_average_weighted = 0.5555555555555556
----------------------------- F1-value-----------------------------
f1_score_average_None = [0.66666667 0.57142857 0.4 ]
f1_score_average_micro = 0.5555555555555556
f1_score_average_macro = 0.546031746031746
f1_score_average_weighted = 0.5756613756613757
Process finished with exit code 0
2、数据02
true_lable = [0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 3]
prediction = [3, 0, 0, 0, 0, 0, 0, 0, 2, 3, 3, 1, 1, 1, 1, 1, 1, 3, 1, 2, 2, 2, 2, 2, 3, 0, 3, 3, 3, 3]
from sklearn.metrics import classification_report
from sklearn.metrics import precision_score, recall_score, f1_score
true_lable = [0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 3]
prediction = [3, 0, 0, 0, 0, 0, 0, 0, 2, 3, 3, 1, 1, 1, 1, 1, 1, 3, 1, 2, 2, 2, 2, 2, 3, 0, 3, 3, 3, 3]
measure_result = classification_report(true_lable, prediction)
print('measure_result = \n', measure_result)
print("----------------------------- precision（精确率）-----------------------------")
precision_score_average_None = precision_score(true_lable, prediction, average=None)
precision_score_average_micro = precision_score(true_lable, prediction, average='micro')
precision_score_average_macro = precision_score(true_lable, prediction, average='macro')
precision_score_average_weighted = precision_score(true_lable, prediction, average='weighted')
print('precision_score_average_None = ', precision_score_average_None)
print('precision_score_average_micro = ', precision_score_average_micro)
print('precision_score_average_macro = ', precision_score_average_macro)
print('precision_score_average_weighted = ', precision_score_average_weighted)
print("\n\n----------------------------- recall（召回率）-----------------------------")
recall_score_average_None = recall_score(true_lable, prediction, average=None)
recall_score_average_micro = recall_score(true_lable, prediction, average='micro')
recall_score_average_macro = recall_score(true_lable, prediction, average='macro')
recall_score_average_weighted = recall_score(true_lable, prediction, average='weighted')
print('recall_score_average_None = ', recall_score_average_None)
print('recall_score_average_micro = ', recall_score_average_micro)
print('recall_score_average_macro = ', recall_score_average_macro)
print('recall_score_average_weighted = ', recall_score_average_weighted)
print("\n\n----------------------------- F1-value-----------------------------")
f1_score_average_None = f1_score(true_lable, prediction, average=None)
f1_score_average_micro = f1_score(true_lable, prediction, average='micro')
f1_score_average_macro = f1_score(true_lable, prediction, average='macro')
f1_score_average_weighted = f1_score(true_lable, prediction, average='weighted')
print('f1_score_average_None = ', f1_score_average_None)
print('f1_score_average_micro = ', f1_score_average_micro)
print('f1_score_average_macro = ', f1_score_average_macro)
print('f1_score_average_weighted = ', f1_score_average_weighted)
打印结果：
measure_result =
precision recall f1-score support
0 0.88 0.78 0.82 9
1 0.86 0.75 0.80 8
2 0.83 0.71 0.77 7
3 0.56 0.83 0.67 6
accuracy 0.77 30
macro avg 0.78 0.77 0.76 30
weighted avg 0.80 0.77 0.77 30
----------------------------- precision（精确率）-----------------------------
precision_score_average_None = [0.875 0.85714286 0.83333333 0.55555556]
precision_score_average_micro = 0.7666666666666667
precision_score_average_macro = 0.7802579365079365
precision_score_average_weighted = 0.7966269841269841
----------------------------- recall（召回率）-----------------------------
recall_score_average_None = [0.77777778 0.75 0.71428571 0.83333333]
recall_score_average_micro = 0.7666666666666667
recall_score_average_macro = 0.7688492063492064
recall_score_average_weighted = 0.7666666666666667
----------------------------- F1-value-----------------------------
f1_score_average_None = [0.82352941 0.8 0.76923077 0.66666667]
f1_score_average_micro = 0.7666666666666667
f1_score_average_macro = 0.7648567119155354
f1_score_average_weighted = 0.7732126696832579
Process finished with exit code 0
参考资料：
Macro-F1 Score与Micro-F1 Score
分类问题的几个评价指标（Precision、Recall、F1-Score、Micro-F1、Macro-F1）
分类问题中的各种评价指标——precision，recall，F1-score，macro-F1，micro-F1
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