kappa系数

kappa计算结果为-1~1，通常kappa是落在 0~1 间，可分为五组来表示不同级别的一致性：

计算公式：

p_o是每一类正确分类的样本数量之和除以总样本数.

假设每一类的真实样本个数分别为a1,a2,...,aC，预测出来的每一类的样本个数分别为b1,b2,...,bC，总样本个数为n，则有：p_e=（a1×b1+a2×b2+...+aC×bC） / （n×n）.

举例分析：

学生考试的作文成绩，由两个老师给出 好、中、差三档的打分，现在已知两位老师的打分结果，需要计算两位老师打分之间的相关性kappa系数：

Po = (10+35+15) / 87 = 0.689

a1 = 10+2+8 = 20; a2 = 5+35+5 = 45; a3 = 5+2+15 = 22;

b1 = 10+5+5 = 20; b2 = 2+35+2 = 39; b3 = 8+5+15 = 28;

Pe = (a1*b1 + a2*b2 + a3*b3) / (87*87) = 0.455 

K = (Po-Pe) / (1-Pe) = 0.4293578

from sklearn.svm import SVC
from sklearn.datasets import make_classification
from sklearn.model_selection import train_test_split
from sklearn.metrics import confusion_matrix



X,y = make_classification()
X_train,X_test,y_train,y_test = train_test_split(X,y,test_size=0.3)

svc = SVC()
svc.fit(X_train,y_train)
y_pred = svc.predict(X_test)

result = confusion_matrix(y_test, y_pred)




def kappa_coefficient(confusion_matrix):
    """
    descibe:compute kappa coefficient
    param confusion_matrix:matrix
    return kappa coefficient
    """ 
    import numpy as np
    
    P_0 = 0
    for i in range(len(confusion_matrix)):
        P_0 = P_0+confusion_matrix[i,i]
    
    a = []
    b = []
    for i in range(len(confusion_matrix)):
        a.append(sum(confusion_matrix[i]))
        b.append(sum(confusion_matrix[:,i]))
        
    P_e = sum(np.array(a)*np.array(b))/(sum(a)*sum(a))
    kappa = (P_0/sum(a)-P_e)/(1-P_e)
    
    return kappa
    
kappa_coefficient(confusion_matrix=result)