Logistic回归

话说网上记录这本书内容的博客好多，而且挺多写的不错的。emmmmm，我写的这么渣我都不好意思写了。

3点半睡7点起，困困的一天，看懂了原理但愣是没看懂Logistic回归的代码，这里先贴个代码暂存一下，改天弄懂了再补。

from 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)
    labelMat = mat(classLabels).transpose()
    m, n = shape(dataMatrix)
    alpha = 0.001
    maxCycles = 500
    weights = ones((n, 1))
    for k in range(maxCycles):
        h = sigmoid(dataMatrix * weights)
        error = (labelMat - h)
        weights = weights + alpha * dataMatrix.transpose() * error
    return weights


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 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()


def stocGradAscent0(dataMatrix, classLabels):
    m, n = shape(dataMatrix)
    alpha = 0.01
    weights = ones(n)
    for i in range(m):
        h = sigmoid(sum(dataMatrix[i] * weights))
        error = classLabels[i] - h
        weights = weights + alpha * error * dataMatrix[i]
    return weights


def stocGradAscent1(dataMatrix, classLabels, numIter=150):
    m, n = shape(dataMatrix)
    alpha = 0.01
    weights = ones(n)
    for j in range(numIter):
        dataIndex = list(range(m))
        for i in range(m):
            alpha = 4 / (1.0 + j + i) + 0.01
            randIndex = int(random.uniform(0, len(dataIndex)))
            h = sigmoid(sum(dataMatrix[randIndex] * weights))
            error = classLabels[randIndex] - h
            weights = weights + alpha * error * dataMatrix[randIndex]
            del (dataIndex[randIndex])

    return weights


def classifyVector(inX, weights):
    prob = sigmoid(sum(inX * weights))
    if prob > 0.5:
        return 1
    else:
        return 0


def colicTest():
    frTrain = open('horseColicTraining.txt')
    frTest = open('horseColicTest.txt')
    trainingSet = []
    trainingLabels = []
    for line in frTrain.readlines():
        currLine = line.strip().split('	')
        lineArr = []
        for i in range(21):
            lineArr.append(float(currLine[i]))
        trainingSet.append(lineArr)
        trainingLabels.append(float(currLine[21]))
    trainWeights = stocGradAscent1(array(trainingSet), trainingLabels, 500)
    errorCount = 0
    numTestVec = 0.0
    for line in frTest.readlines():
        numTestVec += 1.0
        currLine = line.strip().split('	')
        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)))


if __name__ == '__main__':
    dataArr, labelMat = loadDataSet()
    # weights = gradAscent(dataArr, labelMat)
    # weights = stocGradAscent0(array(dataArr), labelMat)
    weights = stocGradAscent1(array(dataArr), labelMat)
    # plotBestFit(weights.getA())
    plotBestFit(weights)

    multiTest()

 

 

 

Logistic回归的目的是寻找一个非线性函数Sigmoid的最佳拟合参数，求解过程可以由最优化算法来完成。

在最优化算法中，最常用的就是梯度上升算法，而它又可以简化为随机梯度上升算法。

两者效果相当，但后者占用更少的计算资源。

此外它还是一个在线算法，可以在新数据到来时就完成参数更新，而不需要重新读取整个数据集来进行批处理运算。