%matplotlib inline
import numpy as np
from numpy import *
import os
import pandas as pd
import matplotlib.pyplot as plt

普通的梯度上升算法

可以看到21-24行的代碼，就是上面推導公式，梯度提升迭代更新參數w。

這里要注意到，算法gradAscent里的變量h 和誤差error都是向量， 用矩陣的形式把所有的樣本都帶進去算了，要區分后面的隨機梯度的算法。

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

##邏輯函數
def sigmoid(inX):    
    return 1.0/(1+np.exp(-inX))

def gradAscent(dataMatIn, classLabels):
    dataMatrix = mat(dataMatIn)             #convert to NumPy matrix
    labelMat = mat(classLabels).transpose() #convert to NumPy matrix
    m,n = shape(dataMatrix)
    alpha = 0.001
    maxCycles = 500
    weights = ones((n,1))
    for k in range(maxCycles):              #heavy on matrix operations
        h = sigmoid(dataMatrix*weights)     #matrix mult
        error = (labelMat - h)              #vector subtraction
        weights = weights + alpha * dataMatrix.transpose()* error #matrix mult
    print("h和error的形式",shape(h),shape(error))
    return weights

def plotBestFit(weights):
    dataMat,labelMat=loadDataSet()
    dataArr = array(dataMat)
    n = 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=30, c='green')
    x = arange(-3.0, 3.0, 0.1)
    y = (-weights[0]-weights[1]*x)/weights[2]+1
    ax.plot(x, y)
    plt.xlabel('X1'); plt.ylabel('X2');
    plt.show()
if __name__ == '__main__':
    dataMat, labelMat = loadDataSet()
    weights=gradAscent(dataMat,labelMat)
    weights=array(weights).ravel()
    print(weights)
    plotBestFit(weights)

h和error的形式 (100, 1) (100, 1)
[ 4.12414349  0.48007329 -0.6168482 ]

單個梯度上升法

每次都要全部的樣本進去算，很麻煩，這里只用了一個樣本就更新參數了

這里的h和誤差error都是數值。

這里我們只把整個數據過一遍而已，所以會有點差。

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]
    print("h和error的形式",h,error)
    return weights
if __name__ == '__main__':
    dataMat, labelMat = loadDataSet()
    weights=stocGradAscent0(array(dataMat),labelMat)
    print(weights)
    plotBestFit(weights)

h和error的形式 0.01686841821437535 -0.01686841821437535
[ 1.01702007  0.85914348 -0.36579921]

改進的隨機梯度上升法

第7行代碼，學習率每次迭代都會有調整，但會有個最小值的。

第8行，隨機選一個樣本，再刪掉。這樣就保證每個樣本都隨機迭代一遍，去除了樣本可能存在的周期性影響。

def stocGradAscent1(dataMatrix, classLabels, numIter=150):
    m,n = shape(dataMatrix)
    weights = ones(n)   #initialize to all ones
    for j in range(numIter):
        dataIndex = [i for i in 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]
            dataIndex.pop(randIndex)
    return weights
if __name__ == '__main__':
    dataMat, labelMat = loadDataSet()
    weights=stocGradAscent1(array(dataMat),labelMat)
    print(weights)
    plotBestFit(weights)

[13.33505316  0.89550644 -1.89817652]

使用 sklearn 包中的邏輯回歸算法

使用sklearn包，用他自己提供的接口，我們獲取到了最后的系數，然后畫出分界線。

from sklearn.linear_model import LogisticRegression
def sk_lr(X_train,y_train):
    model = LogisticRegression()
    model.fit(X_train, y_train)
    model.score(X_train,y_train)
    print('權重',model.coef_)
    print(model.intercept_)
#     return model.predict(X_train)
    return model.coef_,model.intercept_
def plotBestFit1(coef,intercept):
    weights=array(coef).ravel()
    dataMat,labelMat=loadDataSet()
    dataArr = array(dataMat)
    n = 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=30, c='green')
    x = arange(-3.0, 3.0, 0.1)
    y = (-weights[0]-weights[1]*x)/weights[2]+intercept+1
    ax.plot(x, y)
    plt.xlabel('X1'); plt.ylabel('X2');
    plt.show()
if __name__=='__main__':
    dataMat,labelMat=loadDataSet()
    coef,intercept=sk_lr(dataMat,labelMat)
    plotBestFit1(coef,intercept)

權重 [[ 2.45317293  0.51690909 -0.71377635]]
[2.45317293]