機器學習實戰筆記三——Logistic迴歸

# -*- coding: utf-8 -*-
"""
Created on Wed Apr 18 09:41:09 2018

@author: zhangsh
"""

'''
Logistic 迴歸的一般工程：
    1、收集數據
    2、準備數據：數值型數據
    3、分析數據
    4、訓練數據：尋找最佳的分類迴歸係數
    5、測試算法
    6、使用算法
'''
from numpy import *
import matplotlib.pyplot as plt

def loadDataSet():
    dataMat = []
    labelMat = []
    fr = open('testSet.txt')
    for line in fr.readlines():
        linArr = line.strip().split()  # 去掉每一行的'\n',再按照空格切分，切分後的各個元素保存爲一個列表
        dataMat.append([1.0,float(linArr[0]),float(linArr[1])]) # (w0,w1,w2) * (1,x1,x2)^T
        labelMat.append(int(linArr[2]))
    return dataMat,labelMat

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

# 梯度上升算法，求出最佳的 W 參數
def gradAscent(dataMatIn,classLabels):
    dataMatrix = mat(dataMatIn)  # 將列表轉換爲 numpy 數組 100*3 (1.0,X1,X2)
    labelMat = mat(classLabels).transpose()  # 轉換成 100*1 列向量
    m,n = shape(dataMatrix)  # 返回數據集的行數與列數，m 爲行數 100，n 爲列數 3
    alpha = 0.001  # 梯度表示移動方向，步長表示每次移動量
    maxCycles = 500  # 移動500次
    weights = ones((n,1))  # weights 爲 n*1=3*1 列向量。z=w0+w1*x1+w2*x2
    for k in range(maxCycles):
        h = sigmoid(dataMatrix * weights)  # 100*1 列向量，z = w0 +w1*X1+w2*X2
        error = (labelMat - h)
        weights = weights + alpha * dataMatrix.transpose() * error
    return weights

# 根據求出的 w 畫出擬合曲線
def plotBestFit(weights):
    dataMat,labelMat = loadDataSet()
    dataArr = array(dataMat)
    n = shape(dataArr)[0]  # 返回 dataArr 的行數
    
    xcord1 = []
    ycord1 = []
    
    xcord2 = []
    ycord2 = []
    
    for i in range(n):
        if int(labelMat[i]) == 1:    # 第一類
            xcord1.append(dataArr[i,1])
            ycord1.append(dataArr[i,2])
        else:                           # 第二類
            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()

# 改進隨機梯度上升法
'''
梯度上升法：每次更新系數需要遍歷數據集中所有的數據
隨機梯度上升法：一次用一個樣本點更新系數
改進的隨機梯度上升算法：1、alpha隨迭代次數增加而減小  2、隨機的用樣本點更新系數
'''
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

# 改進的隨機梯度上升算法
# numpy.random.uniform(low,high,size)
# 從一個均勻分佈[low,high)中隨機採樣，定義域是左閉右開。size：輸出樣本個數，默認值爲 1
def stocGradAscent1(dataMatrix,classLabels,numIter=150):    
    m,n = shape(dataMatrix)
    weights = ones(n)  # 初始化權值
    for j in range(numIter):
        dataIndex = list(range(m))  # python 3.x range 返回的是 range 對象
        for i in range(m):
            alpha = 4/(1.0 + j + i) +0.01  # alpha 隨着迭代次數增多變小
            randIndex = int(random.uniform(0,len(dataIndex))) # 隨機選取樣本來更新迴歸係數
            h = sigmoid(sum(dataMatrix[randIndex] * weights))
            error = classLabels[randIndex] - h
            weights = weights + alpha * error * dataMatrix[randIndex]
            del(dataIndex[randIndex])
    return weights

# 分類函數
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 = []  # 保存訓練集
    trainingLabels = []  # 保存標籤集
    for line in frTrain.readlines():
        currLine = line.strip().split('\t')
        lineArr = []
        for i in range(21):  # 前21列爲屬性，第21列爲標籤
            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('\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)))