06 ML logistic 回归 梯度上升法求最佳常数w

rom numpy import *

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

def sigmoid(inX):
    return 1.0/(1+exp(-inX))

def gradAscent(dataMatIn, classLabels):
    dataMatrix = mat(dataMatIn)             # 转换成 numpy 的矩阵
    labelMat = mat(classLabels).transpose() 
    m, n = shape(dataMatrix) # 矩阵的大小

    alpha = 0.001 # 移动的步长
    maxCycles = 500
    weights = ones((n,1)) # 权重

    for k in range(maxCycles):              # heavy on matrix operations
        h = sigmoid(dataMatrix*weights)     # matrix mult 向量乘法 得到 h 为列向量
        error = (labelMat - h)              # 真实类别与预测类别的差值
        # 按照差值的方法 调整回归系数
        # 一行 * 一列 结果为一个数 即权重
        weights = weights + alpha * dataMatrix.transpose()* error #matrix mult
    return weights

# 画出该拟合曲线
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()

# 随机梯度上升算法
# 思路：要找到某函数的最大值 就是在该函数的梯度方向不断叠加 探寻
# w = w + alpha * sigmoid(v) # sigmoid 为跃阶函数 alpha 为步长
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
        # 在偏差的地方 继续梯度上升
        weights = weights + alpha * error * dataMatrix[i]
    return weights

# 随机梯度上升算法改进
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):
            # 每次迭代都调整它 常数项保证了 alpha不为零
            alpha = 4/(1.0+j+i)+0.0001    #apha decreases with iteration, does not 
            # 通过随机取样来更新回归系数
            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

# 分类器
# 每个特征向量乘以最优的回归系数 再求和用 sigmoid 函数计算结果即可
def classifyVector(inX, weights):
    prob = sigmoid(sum(inX*weights))
    if prob > 0.5: 
        return 1.0
    else: 
        return 0.0

def colicTest():
    frTrain = open('horseColicTraining.txt'); frTest = open('horseColicTest.txt')
    trainingSet = []; trainingLabels = []
    for line in frTrain.readlines():
        currLine = line.strip().split('\t')
        lineArr =[]
        for i in range(21):
            lineArr.append(float(currLine[i]))
        trainingSet.append(lineArr)
        trainingLabels.append(float(currLine[21]))

    trainWeights = stocGradAscent1(array(trainingSet), trainingLabels, 1000)
    errorCount = 0; numTestVec = 0.0
    for line in frTest.readlines():
        numTestVec += 1.0
        currLine = line.strip().split('\t')
        lineArr =[]
        for i in range(21):
            lineArr.append(float(currLine[i]))
        if int(classifyVector(array(lineArr), trainWeights))!= int(currLine[21]):
            errorCount += 1
    errorRate = (float(errorCount)/numTestVec)
    print "the error rate of this test is: %f" % errorRate
    return errorRate

def multiTest():
    numTests = 10; errorSum=0.0
    for k in range(numTests):
        errorSum += colicTest()
    print "after %d iterations the average error rate is: %f" % (numTests, errorSum/float(numTests))
        
Status API Training Shop Blog About