前言

代码实现

import numpy as np
import matplotlib.pyplot as plt


# 载入数据
def loadDataSet():
    dataMat = []
    labelMat = []
    with open('testSet.txt', 'r', encoding='utf8') as f:
        for line in f.readlines():
            lineArr = line.strip().split()
            # 分别为X0、X1、X2的值
            dataMat.append([1.0, float(lineArr[0]), float(lineArr[1])])
            # 对应的标签
            labelMat.append(int(lineArr[2]))
    return dataMat, labelMat


# 阶跃函数
def sigmoid(inx):
    return 1.0 / (1 + np.exp(-inx))


# 梯度上升算法
def gradAscent(dataMatIn, classLabels):
    # 转换为numpy矩阵类型；dataMatrix:100 * 3；labelMat:100 * 1
    dataMatrix = np.mat(dataMatIn)
    labelMat = np.mat(classLabels).transpose()
    m, n = np.shape(dataMatrix)
    # 步长
    alpha = 0.001
    # 迭代次数
    maxCycles = 500
    weights = np.ones((n, 1))
    for k in range(maxCycles):
        h = sigmoid(dataMatrix * weights)
        error = (labelMat - h)
        # 此处推导过程可看前沿
        weights = weights + alpha * dataMatrix.transpose() * error
    return weights


# 可视化
def plotBestFit(wei):
    weights = np.array(wei)
    dataMat, labelMat = loadDataSet()
    dataArr = np.array(dataMat)
    n = np.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=40, c='green')
    x = np.arange(-3.0, 3.0, 0.1)
    # 最佳拟合直线
    y = (-weights[0] - weights[1] * x) / weights[2]
    ax.plot(x, y)
    plt.xlabel('x1')
    plt.ylabel('y1')
    plt.show()


# 随机梯度上升算法：一次仅用1个样本来更新回归系数
def stocGradAscent0(dataMatrix, classLabels):
    m, n = np.shape(dataMatrix)
    alpha = 0.01
    weights = np.ones(n)
    # 便利所有样本，每次使用一个样本来更新回归参数
    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算法：主要是（1）alpha随着迭代次数减小但不为0（2）随机选取样本来进行参数更新
# 减少系数波动，加快手链
def stocGradAscent1(dataMatrix, classLabels, numIter=150):
    m, n = np.shape(dataMatrix)
    weights = np.ones(n)
    for j in range(numIter):
        dataIndex = list(range(m))
        # 便利所有样本，每次使用一个样本来更新回归参数
        for i in range(m):
            # alpha随着迭代次数不断减少
            alpha = 4 / (1.0+j+i) + 0.01
            # 随机选取样本进行参数更新,使用np.random.uniform在[0, m)上随机取值
            randIndex = int(np.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


if __name__ == "__main__":
    # # 使用梯度上升法获取回归系数
    dataArr, labelMat = loadDataSet()
    # weights = gradAscent(dataArr, labelMat)
    # plotBestFit(weights)
    # # 使用随机梯度上升法获取回归系数
    # weights = stocGradAscent0(np.array(dataArr), labelMat)
    # plotBestFit(weights)
    # 使用改进的随机梯度上升法获取回归系数
    weights = stocGradAscent1(np.array(dataArr), labelMat)
    plotBestFit(weights)