Python实现 logistic 回归算法

Python实现 logistic 回归算法

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1、算法介绍

模型描述：

sigmoid函数：

原理： 优化目标：最小化 sigmoid(f(x)) 和真实标签的差别（有不同的 cost function）。运用算法（梯度上升等）更新参数w、b。

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2、Python代码实现及注释

决策边界：

代码：

import numpy as np
from matplotlib import pyplot as plt


# 加载数据集
def loadDataset(filename):
    # 数据集
    dataList = []
    # 数据样本
    labelsList = []
    fr = open(filename)
    for line in fr.readlines():
        lineArr = line.strip().split()
        # 添加一个值为1的特征，对应于参数b
        dataList.append([1.0, float(lineArr[0]), float(lineArr[1])])
        labelsList.append(int(lineArr[-1]))
    return dataList, labelsList


# sigmoid函数计算
def sigmoid(z):
    return 1.0/(1+np.exp(-z))


# 运用标准的梯度上升法更新参数
def gradAscent(dataList, labelsList):
    dataMat = np.mat(dataList)
    labelsMat = np.mat(labelsList).T
    m, n = np.shape(dataMat)
    learningRate = 0.1
    maxCycles = 1000
    weights = np.ones((n, 1))
    for i in range(maxCycles):
        a = sigmoid(dataMat*weights)
        # 梯度计算的公式
        error = labelsMat - a
        # 更新参数
        weights = weights + learningRate*dataMat.T*error/m
    return weights


# 运用随机梯度上升更新参数
def stocGradAscent(dataList, labelsList):
    m, n = np.shape(dataList)
    maxCycles = 200
    weights = np.ones(n)
    for j in range(maxCycles):
        for i in range(m):
            # 学习率递减
            learningRate = 4/(1.0+j+i)+0.01
            # randIndex = int(np.random.uniform(0, m))
            # 计算 sigmoid 一次只计算一个样本
            a = sigmoid(np.sum(dataList[i]*weights))
            error = labelsList[i] - a
            weights = weights + learningRate*error*np.array(dataList[i])
    return weights


# 绘制数据集及决策边界
def plotLine(dataSet, labels, weights):
    # 绘制数据集，不同类别颜色不同
    plt.scatter(np.array(dataSet)[:, 1], np.array(dataSet)[:, 2], 30 * (np.array(labels)+1), 15*np.array(labels))
    # 令表达式=0绘制决策边界
    x = np.expand_dims(range(-3, 3, 1), 1)
    y = (-weights[0]-x*weights[1])/weights[2]
    plt.plot(x, y)
    plt.show()


# 测试 logistic 回归分类器
def predict(sample, weights):
    # 重构样本特征向量
    sample = np.array([1.0, sample[0], sample[1]])
    prob = sigmoid(np.sum(sample*weights))
    if prob > 0.5:
        print("this is a positive")
    else:
        print('this is a negative')


if __name__ == '__main__':
    # 加载数据集
    dataList, labelsList = loadDataset('testSet.txt')
    # 得到模型参数
    # weights = gradAscent(dataList, labelsList)
    weights = stocGradAscent(dataList, labelsList)
    print(weights)
    # 绘制决策边界
    plotLine(dataList, labelsList, weights)
    # 测试分类器
    sample = np.array([1, 9])
    predict(sample, weights)

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