机器学习(周志华) 西瓜书 第三章课后习题3.3—— Python实现
机器学习(周志华) 西瓜书 第三章课后习题3.3—— Python实现
个人原创，禁止转载——Zetrue_Li
复制下列数据并粘贴到记事本，保存为data.txt：
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
Python代码：
# 对率回归 西瓜数据集3.0ɑ
# -*- coding: utf-8 -*-
import numpy as np
import pandas as pd
import matplotlib.pyplot as plt
def loadData(filename):
dataSet = pd.read_csv(filename)
return dataSet
def processData(dataSet):
dataSet['b'] = 1
x = np.array(dataSet[['密度', '含糖率', 'b']])
y = np.array(dataSet[['好瓜']].replace(['是', '否'], [1, 0]))
return x, y
def p0_function(xi, beta):
return 1 - p1_function(xi, beta)
def p1_function(xi, beta):
beta_T_x = np.dot(beta.T, xi)
exp_beta_T_x = np.exp(beta_T_x)
return exp_beta_T_x / (1+exp_beta_T_x)
def l_function(beta, x, y):
#计算当前3.27式的l值
result = 0
for xi, yi in zip(x, y):
xi = xi.reshape(xi.shape[0], 1)
# beta.T与x相乘, beta_T_x表示β转置乘以x
beta_T_x = np.dot(beta.T, xi)
exp_beta_T_x = np.exp(beta_T_x)
result += -yi*beta_T_x + np.log(1+exp_beta_T_x)
return result
def run(x, y, iterate=100):
#定义初始参数
#β列向量
beta = np.zeros((x.shape[1], 1))
beta[-1] = 1
old_l = 0 #3.27式l值的记录，这是上一次迭代的l值
cur_iter = 0
while cur_iter < iterate:
cur_iter += 1
cur_l = l_function(beta, x, y)
# 迭代终止条件
if np.abs(cur_l - old_l) <= 10e-5:
# 精度，二者差在0.00001以内就认为收敛
# 满足条件直接跳出循环
break
# print(cur_l)
old_l = cur_l
d1_beta, d2_beta = 0, 0
# 牛顿迭代法更新β
for xi, yi in zip(x, y):
xi = xi.reshape(xi.shape[0], 1)
p1 = p1_function(xi, beta)
# 求关于β的一阶导数
d1_beta -= np.dot(xi, yi-p1)
# 求关于β的一阶导数
d2_beta += np.dot(xi, xi.T) * p1 * (1-p1)
#print(beta)
try:
beta = beta - np.dot(np.linalg.inv(d2_beta), d1_beta)
except Exception as e:
break
return beta
def test(beta, x, y):
for xi, yi in zip(x, y):
xi = xi.reshape(xi.shape[0], 1)
beta_T_x = np.dot(beta.T, xi)
y_test = np.exp(beta_T_x)
print(yi, y_test)
if __name__=="__main__":
# 读取数据
filename = 'data.txt'
dataSet = loadData(filename)
# 预处理数据
x, y = processData(dataSet)
beta = run(x, y)
accuracy = 0
for xi, yi in zip(x, y):
p1 = p1_function(xi, beta)
judge = 0 if p1 < 0.5 else 1
# print(yi[0], judge)
accuracy += (judge == yi[0])
error = 1 - accuracy/dataSet.shape[0]
print('Error:', error*100, '%')
实现结果：
错误率：
