Python机器学习与实战笔记之逻辑斯蒂回归Logistic Regression, LR

理论参考-特别是梯度下降权值更新向量化的过程
http://www.cnblogs.com/nsnow/p/4540700.html

http://blog.youkuaiyun.com/zouxy09/article/details/20319673

1定义特征与标签矩阵
2定义sigmoid函数
3根据推出的权值更新公式进行迭代-最后算出权值
可选的训练方式有梯度上升，随机梯度上升，改进的随机梯度上升(alpha会变化)
4测试样本乘以权值，结果输入sigmoid函数，输出大于0.5为1类,小于等于0.5为0类

#coding:utf-8
from numpy import *

#获取数据，拼接成两个矩阵
def loadDataSet():
    dataMat = [];
    labelMat = []
    fr = open('F:/python/pythonwork/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

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

#定义梯度上升训练方法(负号梯度下降)-每次全部样本参与更新迭代
def gradAscent(dataMatIn, classLabels):
    dataMatrix = mat(dataMatIn)  # convert to NumPy matrix
    labelMat = mat(classLabels).transpose()  # convert to NumPy matrix
    m, n = shape(dataMatrix)  #矩阵的行，列
    alpha = 0.001
    maxCycles = 500   #迭代次数
    weights = ones((n, 1))  #初始权重 3x1
    for k in range(maxCycles):  # heavy on matrix operations
        h = sigmoid(dataMatrix * weights)  # matrix mult 100x3  3x1
        error = (labelMat - h)  # vector subtraction
        weights = weights + alpha * dataMatrix.transpose() * error  # matrix mult  transpose矩阵转账-梯度下降权值更新向量化
    return weights

#随机梯度上升算法-单个样本值更新迭代
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算法--alpha每次调整-会随着迭代次数不断减小， 但永远不会减小到0
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

#测试样本分类
def classifyVector(inX, weights):
    prob = sigmoid(sum(inX * weights))
    if prob > 0.5:
        return 1.0
    else:
        return 0.0