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