1 # Author Qian Chenglong 2 3 from numpy import * 4 from numpy.ma import arange 5 6 7 def loadDataSet(): 8 dataMat = [] 9 labelMat = [] 10 fr = open('testSet.txt') 11 for line in fr.readlines(): 12 lineArr = line.strip().split() 13 dataMat.append([1.0, float(lineArr[0]), float(lineArr[1])]) 14 labelMat.append(int(lineArr[2])) 15 return dataMat, labelMat 16 17 #sigmoid归一化函数 18 #输入：z=w1x1+w2x2+w3x3...... 19 #s输出：归一化结果 20 def sigmoid(inX): 21 return 1.0 / (1 + exp(-inX)) 22 23 24 ''' 25 logistic回归梯度上升优化算法 26 param dataMatIn: 处理后的数据集 27 param classLabels: 分类标签 28 return: 权重值 29 ''' 30 def gradAscent(dataMatIn, classLabels): 31 dataMatrix = mat(dataMatIn) # convert to NumPy matrix（矩阵） 32 labelMat = mat(classLabels).transpose() # convert to NumPy matrix 33 m, n = shape(dataMatrix) #m行 n列 34 alpha = 0.001 #步长 35 maxCycles = 500 36 weights = ones((n, 1)) #系数，权重 37 for k in range(maxCycles): # heavy on matrix operations 38 h = sigmoid(dataMatrix * weights) # matrix mult 39 error = (labelMat - h) # vector subtraction 40 weights = weights + alpha * dataMatrix.transpose() * error # transpose()矩阵转置 41 return weights 42 43 ''' 44 画出数据集和logisitic回归最佳拟合直线的函数 45 param weights: 46 return: 47 最后的分割方程是y=(-w0-w1*x)/w2 48 ''' 49 def plotBestFit(weights): 50 import matplotlib.pyplot as plt 51 dataMat, labelMat = loadDataSet() 52 dataArr = array(dataMat) 53 n = shape(dataArr)[0] 54 xcord1 = [] 55 ycord1 = [] 56 xcord2 = [] 57 ycord2 = [] 58 for i in range(n): 59 if int(labelMat[i]) == 1: 60 xcord1.append(dataArr[i, 1]); 61 ycord1.append(dataArr[i, 2]) 62 else: 63 xcord2.append(dataArr[i, 1]); 64 ycord2.append(dataArr[i, 2]) 65 fig = plt.figure() 66 ax = fig.add_subplot(111) 67 ax.scatter(xcord1, ycord1, s=30, c='red', marker='s') 68 ax.scatter(xcord2, ycord2, s=30, c='green') 69 x = arange(-3.0, 3.0, 0.1) 70 y = (-weights[0] - weights[1] * x) / weights[2] 71 ax.plot(x, y) 72 plt.xlabel('X1') 73 plt.ylabel('X2') 74 plt.show() 75 76 '''随机梯度上升 77 param dataMatIn: 处理后的数据集 78 param classLabels: 分类标签 79 return: 权重值''' 80 def stocGradAscent0(dataMatrix, classLabels): 81 m, n = shape(dataMatrix) 82 alpha = 0.01 83 weights = ones(n) # initialize to all ones 84 for i in range(m): 85 h = sigmoid(sum(dataMatrix[i] * weights)) 86 error = classLabels[i] - h 87 weights = weights + alpha * error * dataMatrix[i] 88 return weights 89 90 '''改进的随机梯度上升 91 param dataMatIn: 处理后的数据集 92 param classLabels: 分类标签 93 return: 权重值''' 94 def stocGradAscent1(dataMatrix, classLabels, numIter=150): 95 m, n = shape(dataMatrix) 96 weights = ones(n) # initialize to all ones 97 for j in range(numIter): 98 dataIndex = range(m) 99 for i in range(m): 100 alpha = 4 / (1.0 + j + i) + 0.0001 # apha decreases with iteration, does not 101 randIndex = int(random.uniform(0, len(dataIndex))) # go to 0 because of the constant 102 h = sigmoid(sum(dataMatrix[randIndex] * weights)) 103 error = classLabels[randIndex] - h 104 weights = weights + alpha * error * dataMatrix[randIndex] 105 del (dataIndex[randIndex]) 106 return weights