logistic回归梯度上升优化算法

 # Author Qian Chenglong

 from numpy import *
 from numpy.ma import arange

 def loadDataSet():
     dataMat = []
     labelMat = []
     fr = open('testSet.txt')
     for line in fr.readlines():
         lineArr = line.strip().split()
         dataMat.append([1.0, float(lineArr[0]), float(lineArr[1])])
         labelMat.append(int(lineArr[2]))
     return dataMat, labelMat

 #sigmoid归一化函数
 #输入：z=w1x1+w2x2+w3x3......
 #s输出：归一化结果
 def sigmoid(inX):
     return 1.0 / (1 + exp(-inX))

 '''
 logistic回归梯度上升优化算法
 param dataMatIn: 处理后的数据集
 param classLabels: 分类标签
 return: 权重值
  '''
 def gradAscent(dataMatIn, classLabels):
     dataMatrix = mat(dataMatIn)  # convert to NumPy matrix（矩阵）
     labelMat = mat(classLabels).transpose()  # convert to NumPy matrix
     m, n = shape(dataMatrix)          #m行  n列
     alpha = 0.001                       #步长
     maxCycles = 500
     weights = ones((n, 1))              #系数，权重
     for k in range(maxCycles):  # heavy on matrix operations
         h = sigmoid(dataMatrix * weights)  # matrix mult
         error = (labelMat - h)  # vector subtraction
         weights = weights + alpha * dataMatrix.transpose() * error  # transpose()矩阵转置
     return weights

 '''
 画出数据集和logisitic回归最佳拟合直线的函数
 param weights:
 return:
 最后的分割方程是y=(-w0-w1*x)/w2
 '''
 def plotBestFit(weights):
     import matplotlib.pyplot as plt
     dataMat, labelMat = loadDataSet()
     dataArr = array(dataMat)
     n = shape(dataArr)[0]
     xcord1 = []
     ycord1 = []
     xcord2 = []
     ycord2 = []
     for i in range(n):
         if int(labelMat[i]) == 1:
             xcord1.append(dataArr[i, 1]);
             ycord1.append(dataArr[i, 2])
         else:
             xcord2.append(dataArr[i, 1]);
             ycord2.append(dataArr[i, 2])
     fig = plt.figure()
     ax = fig.add_subplot(111)
     ax.scatter(xcord1, ycord1, s=30, c='red', marker='s')
     ax.scatter(xcord2, ycord2, s=30, c='green')
     x = arange(-3.0, 3.0, 0.1)
     y = (-weights[0] - weights[1] * x) / weights[2]
     ax.plot(x, y)
     plt.xlabel('X1')
     plt.ylabel('X2')
     plt.show()

 '''随机梯度上升
 param dataMatIn: 处理后的数据集
 param classLabels: 分类标签
 return: 权重值'''
 def stocGradAscent0(dataMatrix, classLabels):
     m, n = shape(dataMatrix)
     alpha = 0.01
     weights = ones(n)  # initialize to all ones
     for i in range(m):
         h = sigmoid(sum(dataMatrix[i] * weights))
         error = classLabels[i] - h
         weights = weights + alpha * error * dataMatrix[i]
     return weights

 '''改进的随机梯度上升
 param dataMatIn: 处理后的数据集
 param classLabels: 分类标签
 return: 权重值'''
 def stocGradAscent1(dataMatrix, classLabels, numIter=150):
     m, n = shape(dataMatrix)
     weights = ones(n)  # initialize to all ones
     for j in range(numIter):
         dataIndex = range(m)
         for i in range(m):
             alpha = 4 / (1.0 + j + i) + 0.0001  # apha decreases with iteration, does not
             randIndex = int(random.uniform(0, len(dataIndex)))  # go to 0 because of the constant
             h = sigmoid(sum(dataMatrix[randIndex] * weights))
             error = classLabels[randIndex] - h
             weights = weights + alpha * error * dataMatrix[randIndex]
             del (dataIndex[randIndex])
     return weights