190 lines
5.2 KiB
Python
190 lines
5.2 KiB
Python
|
#!/usr/bin/env python3
|
|||
|
|
# -*- coding:UTF-8 -*-
|
|||
|
|
import matplotlib.pyplot as plt
|
|||
|
|
import numpy as np
|
|||
|
|
|
|||
|
|
"""
|
|||
|
|
函数说明:梯度上升算法测试函数
|
|||
|
|
|
|||
|
|
求函数f(x) = -x^2 + 4x的极大值
|
|||
|
|
|
|||
|
|
Parameters:
|
|||
|
|
无
|
|||
|
|
Returns:
|
|||
|
|
无
|
|||
|
|
Author:
|
|||
|
|
Jack Cui
|
|||
|
|
Blog:
|
|||
|
|
http://blog.csdn.net/c406495762
|
|||
|
|
Zhihu:
|
|||
|
|
https://www.zhihu.com/people/Jack--Cui/
|
|||
|
|
Modify:
|
|||
|
|
2017-08-28
|
|||
|
|
"""
|
|||
|
|
def Gradient_Ascent_test():
|
|||
|
|
def f_prime(x_old): #f(x)的导数
|
|||
|
|
return -2 * x_old + 4
|
|||
|
|
x_old = -1 #初始值，给一个小于x_new的值
|
|||
|
|
x_new = 0 #梯度上升算法初始值，即从(0,0)开始
|
|||
|
|
alpha = 0.01 #步长，也就是学习速率，控制更新的幅度
|
|||
|
|
presision = 0.00000001 #精度，也就是更新阈值
|
|||
|
|
while abs(x_new - x_old) > presision:
|
|||
|
|
x_old = x_new
|
|||
|
|
x_new = x_old + alpha * f_prime(x_old) #上面提到的公式
|
|||
|
|
print(x_new) #打印最终求解的极值近似值
|
|||
|
|
|
|||
|
|
"""
|
|||
|
|
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)
|
|||
|
|
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 = 0.001 #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))
|
|||
|
|
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
|
|||
|
|
return weights.getA() #将矩阵转换为数组，返回权重数组
|
|||
|
|
|
|||
|
|
"""
|
|||
|
|
函数说明:绘制数据集
|
|||
|
|
|
|||
|
|
Parameters:
|
|||
|
|
无
|
|||
|
|
Returns:
|
|||
|
|
无
|
|||
|
|
Author:
|
|||
|
|
Jack Cui
|
|||
|
|
Blog:
|
|||
|
|
http://blog.csdn.net/c406495762
|
|||
|
|
Zhihu:
|
|||
|
|
https://www.zhihu.com/people/Jack--Cui/
|
|||
|
|
Modify:
|
|||
|
|
2017-08-30
|
|||
|
|
"""
|
|||
|
|
def plotDataSet():
|
|||
|
|
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
|
|||
|
|
plt.title('DataSet') #绘制title
|
|||
|
|
plt.xlabel('X1'); plt.ylabel('X2') #绘制label
|
|||
|
|
plt.show() #显示
|
|||
|
|
|
|||
|
|
"""
|
|||
|
|
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()
|
|||
|
|
|
|||
|
|
if __name__ == '__main__':
|
|||
|
|
dataMat, labelMat = loadDataSet()
|
|||
|
|
weights = gradAscent(dataMat, labelMat)
|
|||
|
|
plotBestFit(weights)
|