Machine_Learning（logistic回归习题：python版）

ゞ浴缸里的玫瑰 2022-11-26 08:56 172阅读 0赞

## logistic回归习题：python版 ##

**线性可分**

import numpy as np
    import pandas as pd
    import matplotlib.pyplot as plt
    
    data = pd.read_csv('E:\ML_exercise\ex2\ex2data1.txt',names=['Exam1','Exam2','Accepted'])
    data.head()

①数据可视化

fig,ax = plt.subplots()
    
    ax.scatter(data[data['Accepted']==0]['Exam1'],data[data['Accepted']==0]['Exam2'],c='r',marker='x',label='Admitted')
    ax.scatter(data[data['Accepted']==1]['Exam1'],data[data['Accepted']==1]['Exam2'],c='b',marker='o',label='Not admitted')
    ax.legend()
    
    ax.set(xlabel='Exam 1 score',
          ylabel='Exam 2 score')
    plt.show()

②构造数据集

def get_Xy(data):
        data.insert(0,'ones',1)
        X_=data.iloc[:,0:-1]
        X=X_.values
        
        y_=data.iloc[:,-1]
        y=y_.values.reshape(len(y_),1)
        
        return X,y
    
    X,y=get_Xy(data)

③构造损失函数

def sigmoid(z):
        return 1 / (1+np.exp(-z))
    
    def costFunction(X,y,theta):
        A=sigmoid(X@theta)
        inner=y*np.log(A)+(1-y)*(np.log(1-A))
        return -np.sum(inner)/len(X)
    
    #初始化
    theta=np.zeros((3,1))
    #初始代价
    init_cost=costFunction(X,y,theta)

④构造梯度下降函数

def gradientDescent(X,y,theta,alpha,iters):
        costs=[]
        
        for i in range(iters):
            A=sigmoid(X@theta)
            theta = theta - (X.T@(A-y))*alpha/len(X)
            cost = costFunction(X,y,theta)
            costs.append(cost)
            
            if i%1000 == 0:
                print(cost)
        return costs,theta
    
    #初始化
    alpha=0.004
    iters=200000
    
    costs,theta = gradientDescent(X,y,theta,alpha,iters)

⑤预测

def predict(X,theta):
        prob=sigmoid(X@theta)
        return [1 if x>=0.5 else 0 for x in prob]
    
    y_ = np.array(predict(X,theta))
    y_pre = y_.reshape(len(y_),1)
    
    acc = np.mean(y_pre == y)
    
    print(acc)

⑥决策边界

#X@theta=0 ⇒ θ0+θ1x1+θ2x2=0 ⇒ x2 = -θ0/θ2-θ1/θ2x1
    coef1 = -theta[0,0]/theta[2,0]
    coef2 = -theta[1,0]/theta[2,0]
    
    x = np.linspace(20,100,100)
    f = coef1 + coef2*x
    
    fig,ax = plt.subplots()
    
    ax.scatter(data[data['Accepted']==0]['Exam1'],data[data['Accepted']==0]['Exam2'],c='r',marker='x',label='Admitted')
    ax.scatter(data[data['Accepted']==1]['Exam1'],data[data['Accepted']==1]['Exam2'],c='b',marker='o',label='Not admitted')
    ax.legend()
    
    ax.set(xlabel='Exam 1 score',
          ylabel='Exam 2 score')
    
    ax.plot(x,f,'g')
    plt.show()

**线性不可分**

import numpy as np
    import pandas as pd
    import matplotlib.pyplot as plt
    
    data = pd.read_csv('E:\ML_exercise\ex2\ex2data2.txt',names=['Test1','Test2','Accepted'])
    data.head()

①数据可视化

fig,ax = plt.subplots()
    
    ax.scatter(data[data['Accepted']==0]['Test1'],data[data['Accepted']==0]['Test2'],c='r',marker='x',label='y=0')
    ax.scatter(data[data['Accepted']==1]['Test1'],data[data['Accepted']==1]['Test2'],c='b',marker='o',label='y=1')
    ax.legend()
    
    ax.set(xlabel='Microchip Test1',
          ylabel='Microchip Test2')
    plt.show()

②特征映射

def feature_mapping(x1,x2,power):
        data = { }
        for i in np.arange(power+1):
            for j in np.arange(i+1):
                data['F{}{}'.format(i-j,j)] = np.power(x1,i-j)*np.power(x2,j) 
        return pd.DataFrame(data)
    
    x1 = data['Test1']
    x2 = data['Test2']
    data2 = feature_mapping(x1,x2,6)

③构造数据集

X = data2.values
    y = data.iloc[:,-1].values.reshape(len(X),1)

④损失函数

def sigmoid(z):
        return 1 / (1 + np.exp(-z))
    
    def costFunction(X,y,theta,lamda):
        A = sigmoid(X@theta)
        first = y*np.log(A)
        second = (1-y)*np.log(1-A)
        reg = np.sum(np.power(theta[1:],2)) * (lamda/(2*len(X)))#正则化项
        return -np.sum(first+second)/len(X)+reg
    
    #初始化
    theta = np.zeros((28,1))
    lamda = 1
    init_cost = costFunction(X,y,theta,lamda)
    print(init_cost)#打印初始代价

⑤构造梯度下降函数

def gradientDescent(X,y,theta,alpha,iters,lamda):
        costs=[]
        
        for i in range(iters):
        
            reg = theta[1:]*(lamda/len(X))
            reg = np.insert(reg,0,values=0,axis=0)
            
            theta = theta - (X.T@(sigmoid(X@theta)-y))*alpha/len(X) - reg
            cost = costFunction(X,y,theta,lamda)
            costs.append(cost)
            
            if i%1000 == 0:
                print(cost)
        return costs,theta
    
    #初始化
    alpha = 0.001
    lamda = 0.001#lamda越大，易欠拟合，lamda越小，易过拟合
    iters = 200000
    
    costs,theta = gradientDescent(X,y,theta,alpha,iters,lamda)

⑥预测

⑦决策边界

x = np.linspace(-1.2,1.2,200)
    xx,yy = np.meshgrid(x,x)
    z = feature_mapping(xx.ravel(),yy.ravel(),6).values
    
    zz = z@theta
    zz = zz.reshape(xx.shape)
    
    fig,ax = plt.subplots()
    
    ax.scatter(data[data['Accepted']==0]['Test1'],data[data['Accepted']==0]['Test2'],c='r',marker='x',label='y=0')
    ax.scatter(data[data['Accepted']==1]['Test1'],data[data['Accepted']==1]['Test2'],c='b',marker='o',label='y=1')
    ax.legend()
    
    ax.set(xlabel='Microchip Test1',
          ylabel='Microchip Test2')
    
    plt.contour(xx,yy,zz,0)#网格形式
    plt.show()