#!/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)