232 lines
7.5 KiB
Python
Executable File
232 lines
7.5 KiB
Python
Executable File
#!/usr/bin/env python3
|
||
# -*- coding:UTF-8 -*-
|
||
from matplotlib.font_manager import FontProperties
|
||
import matplotlib.pyplot as plt
|
||
import numpy as np
|
||
import random
|
||
|
||
|
||
"""
|
||
函数说明:加载数据
|
||
|
||
Parameters:
|
||
无
|
||
Returns:
|
||
dataMat - 数据列表
|
||
labelMat - 标签列表
|
||
Author:
|
||
Jack Cui
|
||
Blog:
|
||
http://blog.csdn.net/c406495762
|
||
Zhihu:
|
||
https://www.zhihu.com/people/Jack--Cui/
|
||
Modify:
|
||
2017-08-28
|
||
"""
|
||
def loadDataSet():
|
||
dataMat = [] #创建数据列表
|
||
labelMat = [] #创建标签列表
|
||
fr = open('testSet.txt') #打开文件
|
||
for line in fr.readlines(): #逐行读取
|
||
lineArr = line.strip().split() #去回车，放入列表
|
||
dataMat.append([1.0, float(lineArr[0]), float(lineArr[1])]) #添加数据
|
||
labelMat.append(int(lineArr[2])) #添加标签
|
||
fr.close() #关闭文件
|
||
return dataMat, labelMat #返回
|
||
|
||
"""
|
||
函数说明:sigmoid函数
|
||
|
||
Parameters:
|
||
inX - 数据
|
||
Returns:
|
||
sigmoid函数
|
||
Author:
|
||
Jack Cui
|
||
Blog:
|
||
http://blog.csdn.net/c406495762
|
||
Zhihu:
|
||
https://www.zhihu.com/people/Jack--Cui/
|
||
Modify:
|
||
2017-08-28
|
||
"""
|
||
def sigmoid(inX):
|
||
return 1.0 / (1 + np.exp(-inX))
|
||
|
||
"""
|
||
函数说明:梯度上升算法
|
||
|
||
Parameters:
|
||
dataMatIn - 数据集
|
||
classLabels - 数据标签
|
||
Returns:
|
||
weights.getA() - 求得的权重数组(最优参数)
|
||
weights_array - 每次更新的回归系数
|
||
Author:
|
||
Jack Cui
|
||
Blog:
|
||
http://blog.csdn.net/c406495762
|
||
Zhihu:
|
||
https://www.zhihu.com/people/Jack--Cui/
|
||
Modify:
|
||
2017-08-28
|
||
"""
|
||
def gradAscent(dataMatIn, classLabels):
|
||
dataMatrix = np.mat(dataMatIn) #转换成numpy的mat
|
||
labelMat = np.mat(classLabels).transpose() #转换成numpy的mat,并进行转置
|
||
m, n = np.shape(dataMatrix) #返回dataMatrix的大小。m为行数,n为列数。
|
||
alpha = 0.01 #移动步长,也就是学习速率,控制更新的幅度。
|
||
maxCycles = 500 #最大迭代次数
|
||
weights = np.ones((n,1))
|
||
weights_array = np.array([])
|
||
for k in range(maxCycles):
|
||
h = sigmoid(dataMatrix * weights) #梯度上升矢量化公式
|
||
error = labelMat - h
|
||
weights = weights + alpha * dataMatrix.transpose() * error
|
||
weights_array = np.append(weights_array,weights)
|
||
weights_array = weights_array.reshape(maxCycles,n)
|
||
return weights.getA(),weights_array #将矩阵转换为数组，并返回
|
||
|
||
"""
|
||
函数说明:改进的随机梯度上升算法
|
||
|
||
Parameters:
|
||
dataMatrix - 数据数组
|
||
classLabels - 数据标签
|
||
numIter - 迭代次数
|
||
Returns:
|
||
weights - 求得的回归系数数组(最优参数)
|
||
weights_array - 每次更新的回归系数
|
||
Author:
|
||
Jack Cui
|
||
Blog:
|
||
http://blog.csdn.net/c406495762
|
||
Zhihu:
|
||
https://www.zhihu.com/people/Jack--Cui/
|
||
Modify:
|
||
2017-08-31
|
||
"""
|
||
def stocGradAscent1(dataMatrix, classLabels, numIter=150):
|
||
m,n = np.shape(dataMatrix) #返回dataMatrix的大小。m为行数,n为列数。
|
||
weights = np.ones(n) #参数初始化
|
||
weights_array = np.array([]) #存储每次更新的回归系数
|
||
for j in range(numIter):
|
||
dataIndex = list(range(m))
|
||
for i in range(m):
|
||
alpha = 4/(1.0+j+i)+0.01 #降低alpha的大小，每次减小1/(j+i)。
|
||
randIndex = int(random.uniform(0,len(dataIndex))) #随机选取样本
|
||
h = sigmoid(sum(dataMatrix[randIndex]*weights)) #选择随机选取的一个样本，计算h
|
||
error = classLabels[randIndex] - h #计算误差
|
||
weights = weights + alpha * error * dataMatrix[randIndex] #更新回归系数
|
||
weights_array = np.append(weights_array,weights,axis=0) #添加回归系数到数组中
|
||
del(dataIndex[randIndex]) #删除已经使用的样本
|
||
weights_array = weights_array.reshape(numIter*m,n) #改变维度
|
||
return weights,weights_array #返回
|
||
|
||
"""
|
||
函数说明:绘制数据集
|
||
|
||
Parameters:
|
||
weights - 权重参数数组
|
||
Returns:
|
||
无
|
||
Author:
|
||
Jack Cui
|
||
Blog:
|
||
http://blog.csdn.net/c406495762
|
||
Zhihu:
|
||
https://www.zhihu.com/people/Jack--Cui/
|
||
Modify:
|
||
2017-08-30
|
||
"""
|
||
def plotBestFit(weights):
|
||
dataMat, labelMat = loadDataSet() #加载数据集
|
||
dataArr = np.array(dataMat) #转换成numpy的array数组
|
||
n = np.shape(dataMat)[0] #数据个数
|
||
xcord1 = []; ycord1 = [] #正样本
|
||
xcord2 = []; ycord2 = [] #负样本
|
||
for i in range(n): #根据数据集标签进行分类
|
||
if int(labelMat[i]) == 1:
|
||
xcord1.append(dataArr[i,1]); ycord1.append(dataArr[i,2]) #1为正样本
|
||
else:
|
||
xcord2.append(dataArr[i,1]); ycord2.append(dataArr[i,2]) #0为负样本
|
||
fig = plt.figure()
|
||
ax = fig.add_subplot(111) #添加subplot
|
||
ax.scatter(xcord1, ycord1, s = 20, c = 'red', marker = 's',alpha=.5)#绘制正样本
|
||
ax.scatter(xcord2, ycord2, s = 20, c = 'green',alpha=.5) #绘制负样本
|
||
x = np.arange(-3.0, 3.0, 0.1)
|
||
y = (-weights[0] - weights[1] * x) / weights[2]
|
||
ax.plot(x, y)
|
||
plt.title('BestFit') #绘制title
|
||
plt.xlabel('X1'); plt.ylabel('X2') #绘制label
|
||
plt.show()
|
||
|
||
"""
|
||
函数说明:绘制回归系数与迭代次数的关系
|
||
|
||
Parameters:
|
||
weights_array1 - 回归系数数组1
|
||
weights_array2 - 回归系数数组2
|
||
Returns:
|
||
无
|
||
Author:
|
||
Jack Cui
|
||
Blog:
|
||
http://blog.csdn.net/c406495762
|
||
Zhihu:
|
||
https://www.zhihu.com/people/Jack--Cui/
|
||
Modify:
|
||
2017-08-30
|
||
"""
|
||
def plotWeights(weights_array1,weights_array2):
|
||
#设置汉字格式
|
||
#font = FontProperties(fname=r"c:\windows\fonts\simsun.ttc", size=14)
|
||
#将fig画布分隔成1行1列,不共享x轴和y轴,fig画布的大小为(13,8)
|
||
#当nrow=3,nclos=2时,代表fig画布被分为六个区域,axs[0][0]表示第一行第一列
|
||
fig, axs = plt.subplots(nrows=3, ncols=2,sharex=False, sharey=False, figsize=(20,10))
|
||
x1 = np.arange(0, len(weights_array1), 1)
|
||
#绘制w0与迭代次数的关系
|
||
axs[0][0].plot(x1,weights_array1[:,0])
|
||
axs0_title_text = axs[0][0].set_title(u'Improved Random Gradient Rising')
|
||
axs0_ylabel_text = axs[0][0].set_ylabel(u'W0')
|
||
plt.setp(axs0_title_text, size=20, weight='bold', color='black')
|
||
plt.setp(axs0_ylabel_text, size=20, weight='bold', color='black')
|
||
#绘制w1与迭代次数的关系
|
||
axs[1][0].plot(x1,weights_array1[:,1])
|
||
axs1_ylabel_text = axs[1][0].set_ylabel(u'W1')
|
||
plt.setp(axs1_ylabel_text, size=20, weight='bold', color='black')
|
||
#绘制w2与迭代次数的关系
|
||
axs[2][0].plot(x1,weights_array1[:,2])
|
||
axs2_xlabel_text = axs[2][0].set_xlabel(u'Iteration times')
|
||
axs2_ylabel_text = axs[2][0].set_ylabel(u'W1')
|
||
plt.setp(axs2_xlabel_text, size=20, weight='bold', color='black')
|
||
plt.setp(axs2_ylabel_text, size=20, weight='bold', color='black')
|
||
|
||
|
||
x2 = np.arange(0, len(weights_array2), 1)
|
||
#绘制w0与迭代次数的关系
|
||
axs[0][1].plot(x2,weights_array2[:,0])
|
||
axs0_title_text = axs[0][1].set_title(u'Random Gradient Rising')
|
||
axs0_ylabel_text = axs[0][1].set_ylabel(u'W0')
|
||
plt.setp(axs0_title_text, size=20, weight='bold', color='black')
|
||
plt.setp(axs0_ylabel_text, size=20, weight='bold', color='black')
|
||
#绘制w1与迭代次数的关系
|
||
axs[1][1].plot(x2,weights_array2[:,1])
|
||
axs1_ylabel_text = axs[1][1].set_ylabel(u'W1')
|
||
plt.setp(axs1_ylabel_text, size=20, weight='bold', color='black')
|
||
#绘制w2与迭代次数的关系
|
||
axs[2][1].plot(x2,weights_array2[:,2])
|
||
axs2_xlabel_text = axs[2][1].set_xlabel(u'Iteration times')
|
||
axs2_ylabel_text = axs[2][1].set_ylabel(u'W1')
|
||
plt.setp(axs2_xlabel_text, size=20, weight='bold', color='black')
|
||
plt.setp(axs2_ylabel_text, size=20, weight='bold', color='black')
|
||
|
||
plt.show()
|
||
|
||
if __name__ == '__main__':
|
||
dataMat, labelMat = loadDataSet()
|
||
weights1,weights_array1 = stocGradAscent1(np.array(dataMat), labelMat)
|
||
|
||
weights2,weights_array2 = gradAscent(dataMat, labelMat)
|
||
plotWeights(weights_array1, weights_array2)
|