机器学习算法的Python实现 (1)：logistics回归 与 线性判别分析（LDA）

使用的数据集：机器学习教材上的西瓜数据集3.0α

Idx	density	ratio_sugar	label
1	0.697	0.46	1
2	0.774	0.376	1
3	0.634	0.264	1
4	0.608	0.318	1
5	0.556	0.215	1
6	0.403	0.237	1
7	0.481	0.149	1
8	0.437	0.211	1
9	0.666	0.091	0
10	0.243	0.0267	0
11	0.245	0.057	0
12	0.343	0.099	0
13	0.639	0.161	0
14	0.657	0.198	0
15	0.36	0.37	0
16	0.593	0.042	0
17	0.719	0.103	0

 

# -*- coding: cp936 -*-  
from numpy import *  
import pandas as pd  
import matplotlib.pyplot as plt  
  
#读入csv文件数据  
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函数  
def sigmoid(inX):  
    return 1.0/(1+exp(-inX))  
  
#梯度上升算法  
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  
  
#随机梯度上升  
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  
  
#画图  
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)  

梯度上升法得到的结果如下：

随机梯度上升法得到的结果如下：

可以看出，两种方法的效果基本差不多。但是随机梯度上升方法所需要的迭代次数要少很多

# -*- 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)  

结果如下：

对应的w值为：

[ -6.62487509e-04,  -9.36728168e-01]

由于数据分布的关系，所以LDA的效果不太明显。所以我改了几个label=0的样例的数值，重新运行程序得到结果如下：

效果比较明显，对应的w值为：

[-0.60311161, -0.67601433]

转自：http://cache.baiducontent.com/c?m=9d78d513d9d430db4f9be0697b14c0101f4381132ba6d70209d6843890732f43506793ac57270772d7d20d1016db4d4bea81743971597deb8f8fc814d2e1d46e6d9f26476d01d61f4f860eafbc1764977c875a9ef34ea1a7b57accef8c959a49008a155e2bdea7960c57529934ae552ce4a59b49105a10bd&p=ce6fc64ad4d807f449bd9b7d0d1796&newp=c26ada15d9c041ae17a6c7710f0a88231610db2151dcd101298ffe0cc4241a1a1a3aecbf21261b01d4c67a6606a94c5de1f53373310434f1f689df08d2ecce7e60c3&user=baidu&fm=sc&query=%CF%DF%D0%D4%C5%D0%B1%F0%B7%D6%CE%F6+python&qid=ccbe92e80000a2cb&p1=1