Python计算信息熵实例

计算信息熵的公式：n是类别数，p(xi)是第i类的概率

假设数据集有m行，即m个样本，每一行最后一列为该样本的标签，计算数据集信息熵的代码如下：

from math import log

def calcShannonEnt(dataSet):
 numEntries = len(dataSet) # 样本数
 labelCounts = {} # 该数据集每个类别的频数
 for featVec in dataSet: # 对每一行样本
   currentLabel = featVec[-1] # 该样本的标签
   if currentLabel not in labelCounts.keys(): labelCounts[currentLabel] = 0
   labelCounts[currentLabel] += 1
 shannonEnt = 0.0
 for key in labelCounts:
   prob = float(labelCounts[key])/numEntries # 计算p(xi)
   shannonEnt -= prob * log(prob, 2) # log base 2
 return shannonEnt

补充知识：python 实现信息熵、条件熵、信息增益、基尼系数

我就废话不多说了，大家还是直接看代码吧~

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)

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))

来源：https://blog.csdn.net/weixin_38314865/article/details/84073484