python 实现信息熵、条件熵、信息增益、基尼系数

在这里插入代码片注：该代码为慕课网课程中老师讲解

```python
import pandas as pd
import numpy as np
import math
## 计算信息熵
def getEntropy(s):
    # 找到各个不同取值出现的次数
    if not isinstance(s, pd.core.series.Series):
        s = pd.Series(s)
    prt_ary = pd.groupby(s , by = s).count().values / float(len(s))
    return -(np.log2(prt_ary) * prt_ary).sum()
## 计算条件熵: 条件s1下s2的条件熵
def getCondEntropy(s1 , s2):
    d = dict()
    for i in list(range(len(s1))):
        d[s1[i]] = d.get(s1[i] , []) + [s2[i]]
    return sum([getEntropy(d[k]) * len(d[k]) / float(len(s1)) for k in d])


## 计算信息增益
def getEntropyGain(s1, s2):
    return getEntropy(s2) - getCondEntropy(s1, s2)

## 计算增益率
def getEntropyGainRadio(s1, s2):
    return getEntropyGain(s1, s2) / getEntropy(s2)


## 衡量离散值的相关性
import  math
def getDiscreteCorr(s1, s2):
    return getEntropyGain(s1,s2) / math.sqrt(getEntropy(s1) * getEntropy(s2))

# ######## 计算概率平方和
def getProbSS(s):
    if not isinstance(s, pd.core.series.Series):
        s = pd.Series(s)
    prt_ary = pd.groupby(s, by = s).count().values / float(len(s))
    return sum(prt_ary ** 2)
######## 计算基尼系数
def getGini(s1, s2):
    d = dict()
    for i in list(range(len(s1))):
        d[s1[i]] = d.get(s1[i] , []) + [s2[i]]
    return 1-sum([getProbSS(d[k]) * len(d[k]) / float(len(s1)) for k in d])
## 对离散型变量计算相关系数，并画出热力图, 返回相关性矩阵
def DiscreteCorr(C_data):
    ## 对离散型变量(C_data)进行相关系数的计算
    C_data_column_names =  C_data.columns.tolist()
    ## 存储C_data相关系数的矩阵
    import numpy as np
    dp_corr_mat = np.zeros([len(C_data_column_names) , len(C_data_column_names)])
    for i in range(len(C_data_column_names)):
        for j in range(len(C_data_column_names)):
            # 计算两个属性之间的相关系数
            temp_corr = getDiscreteCorr(C_data.iloc[:,i] , C_data.iloc[:,j])
            dp_corr_mat[i][j] = temp_corr
    # 画出相关系数图
    fig = plt.figure()
    fig.add_subplot(2,2,1)
    sns.heatmap(dp_corr_mat ,vmin= - 1, vmax= 1, cmap= sns.color_palette('RdBu' , n_colors= 128) , xticklabels= C_data_column_names , yticklabels= C_data_column_names)
    return pd.DataFrame(dp_corr_mat)
## 计算离散变量间的相关系数矩阵，并画出相关性热力图
## C_data: 离散变量数据
## 返回相关系数矩阵

def corr_vars(C_data):
    C_data_column_names =  C_data.columns.tolist()
    dp_corr_mat = np.zeros([len(C_data_column_names) , len(C_data_column_names)])
    for i in range(len(C_data_column_names)):
        for j in range(len(C_data_column_names)):
            # 计算两个属性之间的相关系数
            temp_corr = getDiscreteCorr(C_data.iloc[:,i] , C_data.iloc[:,j])
            dp_corr_mat[i][j] = temp_corr
    # 画出相关系数图
    fig = plt.figure()
    fig.add_subplot(2,2,1)
    sns.heatmap(dp_corr_mat ,vmin= - 1, vmax= 1,
                cmap= sns.color_palette('RdBu' , n_colors= 128) , 
                xticklabels= C_data_column_names ,
                yticklabels= C_data_column_names)
    return dp_corr_mat

if __name__ == "__main__":
    s1 = pd.Series(['X1' , 'X1' , 'X2' , 'X2' , 'X2' , 'X2'])
    s2 = pd.Series(['Y1' , 'Y1' , 'Y1' , 'Y2' , 'Y2' , 'Y2'])
    print('CondEntropy:',getCondEntropy(s1, s2))
    print('EntropyGain:' , getEntropyGain(s1, s2))
    print('EntropyGainRadio' , getEntropyGainRadio(s1 , s2))
    print('DiscreteCorr:' , getDiscreteCorr(s1, s1))
    print('Gini' , getGini(s1, s2))