macro, micro and weighted 图解

闲言少叙，直接举例：

混淆矩阵

TP， FP，FN结果

下面就以precision这个指标作为示例进行计算：

$$Precisio{n}_{birds}=\frac{T{P}_{birds}}{T{P}_{birds}+F{P}_{birds}}=\frac{1}{1+0}=1$$
$$Precisio{n}_{cats}=\frac{T{P}_{cats}}{T{P}_{cats}+F{P}_{cats}}=\frac{4}{4+1}=0.8$$
$$Precisio{n}_{dogs}=\frac{T{P}_{dogs}}{T{P}_{dogs}+F{P}_{dogs}}=\frac{2}{2+1}=0.667$$

Micro
不论类别统一计算
$$\text{Micro-averaged Precision}=\frac{T{P}_{total}}{T{P}_{total}+F{P}_{total}}=\frac{7}{7+2}=0.7777$$

Macro
先计算各类别，然后平均
$$\text{Macro-averaged Precision}=\frac{1}{3}Precisio{n}_{birds}+Precisio{n}_{cats}+Precisio{n}_{dogs}=\frac{1}{3}(1+0.8+0.6666)=0.8222$$

Weighted
Macro plus, 考虑了样本量进行加权平均
$$\text{Weighted-averaged Precision}=\frac{Precisio{n}_{birds}\ast N_{birds}+Precisio{n}_{cats}\ast N_{birds}+Precisio{n}_{dogs}\ast N_{birds}}{\text{Total number of samples}}=\frac{1\ast 2+0.8\ast 4+0.6666\ast 3}{2+4+3}=0.8$$

文中例子来源：
MACHINE LEARNING MODEL EVALUATION METRICS PART 2: MULTI-CLASS CLASSIFICATION