本文為筆者在學習周志華老師的機器學習教材後，寫的課後習題的的程式設計題。之前放在答案的博文中，現在重新進行整理，將需要實現程式碼的部分單獨拿出來，慢慢積累。希望能寫一個機器學習演算法實現的系列。

本文主要包括：

1、logistics迴歸

2、線性判別分析（LDA）

使用的python庫：

• numpy
• matplotlib
• pandas

# -*- coding: cp936 -*-  
from numpy import *  
import pandas as pd  
import matplotlib.pyplot as plt  
  
#讀入csv檔案資料  
df=pd.read_csv('watermelon_3a.csv')  
m,n=shape(dataMat)  
df['norm']=ones((m,1))  
dataMat=array(df[['norm','density','ratio_sugar']].values[:,:])  
labelMat=mat(df['label'].values[:]).transpose()  
  
#sigmoid函式  
def sigmoid(inX):  
    return 1.0/(1+exp(-inX))  
  
#梯度上升演算法  
def gradAscent(dataMat,labelMat):  
    m,n=shape(df.values)  
    alpha=0.1  
    maxCycles=500  
    weights=array(ones((n,1)))  
  
    for k in range(maxCycles):   
        a=dot(dataMat,weights)  
        h=sigmoid(a)  
        error=(labelMat-h)  
        weights=weights+alpha*dot(dataMat.transpose(),error)  
    return weights  
  
#隨機梯度上升  
def randomgradAscent(dataMat,label,numIter=50):  
    m,n=shape(dataMat)  
    weights=ones(n)  
    for j in range(numIter):  
        dataIndex=range(m)  
        for i in range(m):  
            alpha=40/(1.0+j+i)+0.2  
  
            randIndex_Index=int(random.uniform(0,len(dataIndex)))  
            randIndex=dataIndex[randIndex_Index]  
            h=sigmoid(sum(dot(dataMat[randIndex],weights)))  
            error=(label[randIndex]-h)  
            weights=weights+alpha*error[0,0]*(dataMat[randIndex].transpose())  
            del(dataIndex[randIndex_Index])  
    return weights  
  
#畫圖  
def plotBestFit(weights):  
    m=shape(dataMat)[0]  
    xcord1=[]  
    ycord1=[]  
    xcord2=[]  
    ycord2=[]  
    for i in range(m):  
        if labelMat[i]==1:  
            xcord1.append(dataMat[i,1])  
            ycord1.append(dataMat[i,2])  
        else:  
            xcord2.append(dataMat[i,1])  
            ycord2.append(dataMat[i,2])  
    plt.figure(1)  
    ax=plt.subplot(111)  
    ax.scatter(xcord1,ycord1,s=30,c='red',marker='s')  
    ax.scatter(xcord2,ycord2,s=30,c='green')  
    x=arange(0.2,0.8,0.1)  
    y=array((-weights[0]-weights[1]*x)/weights[2])  
    print shape(x)  
    print shape(y)  
    plt.sca(ax)  
    plt.plot(x,y)      #ramdomgradAscent  
    #plt.plot(x,y[0])   #gradAscent  
    plt.xlabel('density')  
    plt.ylabel('ratio_sugar')  
    #plt.title('gradAscent logistic regression')  
    plt.title('ramdom gradAscent logistic regression')  
    plt.show()  
  
#weights=gradAscent(dataMat,labelMat)  
weights=randomgradAscent(dataMat,labelMat)  
plotBestFit(weights)  
 

# -*- coding: cp936 -*-  
from numpy import *  
import numpy as np  
import pandas as pd  
import matplotlib.pyplot as plt  
  
df=pd.read_csv('watermelon_3a.csv')  
  
def calulate_w():  
    df1=df[df.label==1]  
    df2=df[df.label==0]  
    X1=df1.values[:,1:3]  
    X0=df2.values[:,1:3]  
    mean1=array([mean(X1[:,0]),mean(X1[:,1])])  
    mean0=array([mean(X0[:,0]),mean(X0[:,1])])  
    m1=shape(X1)[0]  
    sw=zeros(shape=(2,2))  
    for i in range(m1):  
        xsmean=mat(X1[i,:]-mean1)  
        sw+=xsmean.transpose()*xsmean  
    m0=shape(X0)[0]  
    for i in range(m0):  
        xsmean=mat(X0[i,:]-mean0)  
        sw+=xsmean.transpose()*xsmean  
    w=(mean0-mean1)*(mat(sw).I)  
    return w  
  
def plot(w):  
    dataMat=array(df[['density','ratio_sugar']].values[:,:])  
    labelMat=mat(df['label'].values[:]).transpose()  
    m=shape(dataMat)[0]  
    xcord1=[]  
    ycord1=[]  
    xcord2=[]  
    ycord2=[]  
    for i in range(m):  
        if labelMat[i]==1:  
            xcord1.append(dataMat[i,0])  
            ycord1.append(dataMat[i,1])  
        else:  
            xcord2.append(dataMat[i,0])  
            ycord2.append(dataMat[i,1])  
    plt.figure(1)  
    ax=plt.subplot(111)  
    ax.scatter(xcord1,ycord1,s=30,c='red',marker='s')  
    ax.scatter(xcord2,ycord2,s=30,c='green')  
    x=arange(-0.2,0.8,0.1)  
    y=array((-w[0,0]*x)/w[0,1])  
    print shape(x)  
    print shape(y)  
    plt.sca(ax)  
    #plt.plot(x,y)      #ramdomgradAscent  
    plt.plot(x,y)   #gradAscent  
    plt.xlabel('density')  
    plt.ylabel('ratio_sugar')  
    plt.title('LDA')  
    plt.show()  
  
w=calulate_w()  
plot(w)  
 

對應的w值為：

[ -6.62487509e-04,  -9.36728168e-01]

由於資料分佈的關係，所以LDA的效果不太明顯。所以我改了幾個label=0的樣例的數值，重新執行程式得到結果如下：

效果比較明顯，對應的w值為：

[-0.60311161, -0.67601433]