信息熵信息增益率基尼系数原理和pandas实战

import numpy as np
# 进行数据整理
import pandas as pd
# 数据
import io
# 验证结果
from scipy import stats

data_str = output = io.StringIO('''编号,色泽,根蒂,敲声,纹理,脐部,触感,密度,含糖率,好瓜
1,青绿,蜷缩,浊响,清晰,凹陷,硬滑,0.697,0.46,是  
2,乌黑,蜷缩,沉闷,清晰,凹陷,硬滑,0.774,0.376,是  
3,乌黑,蜷缩,浊响,清晰,凹陷,硬滑,0.634,0.264,是  
4,青绿,蜷缩,沉闷,清晰,凹陷,硬滑,0.608,0.318,是  
5,浅白,蜷缩,浊响,清晰,凹陷,硬滑,0.556,0.215,是  
6,青绿,稍蜷,浊响,清晰,稍凹,软粘,0.403,0.237,是  
7,乌黑,稍蜷,浊响,稍糊,稍凹,软粘,0.481,0.149,是  
8,乌黑,稍蜷,浊响,清晰,稍凹,硬滑,0.437,0.211,是  
9,乌黑,稍蜷,沉闷,稍糊,稍凹,硬滑,0.666,0.091,否  
10,青绿,硬挺,清脆,清晰,平坦,软粘,0.243,0.267,否  
11,浅白,硬挺,清脆,模糊,平坦,硬滑,0.245,0.057,否  
12,浅白,蜷缩,浊响,模糊,平坦,软粘,0.343,0.099,否  
13,青绿,稍蜷,浊响,稍糊,凹陷,硬滑,0.639,0.161,否  
14,浅白,稍蜷,沉闷,稍糊,凹陷,硬滑,0.657,0.198,否  
15,乌黑,稍蜷,浊响,清晰,稍凹,软粘,0.36,0.37,否  
16,浅白,蜷缩,浊响,模糊,平坦,硬滑,0.593,0.042,否  
17,青绿,蜷缩,沉闷,稍糊,稍凹,硬滑,0.719,0.103,否''')

data = pd.read_csv(data_str)
data.set_index('编号', inplace=True)
data

def entropy(data, att_name):
    '''
    data: 数据集
    att_name: 属性名
    '''
    levels = data[att_name].unique()
    # 信息熵
    ent = 0
    for lv in levels:
        pi = sum(data[att_name]==lv) / data.shape[0]
        ent += pi*np.log(pi)
    return -ent
print('好瓜的信息熵:')
entropy(data, '好瓜')

def entropy_scipy(data, att_name):
    n = data.shape[0]
    values = data[att_name].value_counts()
    return stats.entropy(values/n)

assert entropy(data, '好瓜')==entropy_scipy(data, '好瓜')

def conditional_entropy(data, xname, yname):
    xs = data[xname].unique()
    ys = data[yname].unique()
    p_x = data[xname].value_counts() / data.shape[0]
    ce = 0
    for x in xs:
        ce += p_x[x]*entropy(data[data[xname]==x], yname)
    return ce

print('触感条件下, 好瓜的信息熵:')
conditional_entropy(data, '触感', '好瓜')

def gain(data, xname, yname):
    en = entropy(data, yname)
    ce = conditional_entropy(data, xname, yname)
    return en - ce

print('触感的引入导致的信息增益:')
gain(data, '触感', '好瓜')

data['testCol'] = 0
data.iloc[10:, -1] = 1
print(gain(data, 'testCol', '触感'))
data.iloc[14:, -1] = 2
print(gain(data, 'testCol', '触感'))
print(gain(data, '密度', '触感'))

def gain_ratio(data, xname, yname):
    g = gain(data, xname, yname)
    si = entropy(data, xname)
    return g / si
print('信息增益率:')
gain_ratio(data, '触感', '好瓜')