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