机器学习算法Python实现--逻辑回归

# 代价函数
def costFunction(initial_theta,X,y,inital_lambda):
    m = len(y)
    J = 0
    h = sigmoid(np.dot(X,initial_theta))    # 计算h(z)
    theta1 = initial_theta.copy()           # 因为正则化j=1从1开始，不包含0，所以复制一份，前theta(0)值为0 
    theta1[0] = 0   
    temp = np.dot(np.transpose(theta1),theta1)
    J = (-np.dot(np.transpose(y),np.log(h))-np.dot(np.transpose(1-y),np.log(1-h))+temp*inital_lambda/2)/m   # 正则化的代价方程
    return J

# 计算梯度
def gradient(initial_theta,X,y,inital_lambda):
    m = len(y)
    grad = np.zeros((initial_theta.shape[0]))
    h = sigmoid(np.dot(X,initial_theta))# 计算h(z)
    theta1 = initial_theta.copy()
    theta1[0] = 0
    grad = np.dot(np.transpose(X),h-y)/m+inital_lambda/m*theta1 #正则化的梯度
    return grad  

# S型函数    
def sigmoid(z):
    h = np.zeros((len(z),1))    # 初始化，与z的长度一置
    h = 1.0/(1.0+np.exp(-z))
    return h

# 映射为多项式 
def mapFeature(X1,X2):
    degree = 3;                     # 映射的最高次方
    out = np.ones((X1.shape[0],1))  # 映射后的结果数组（取代X）
    '''
    这里以degree=2为例，映射为1,x1,x2,x1^2,x1,x2,x2^2
    '''
    for i in np.arange(1,degree+1): 
        for j in range(i+1):
            temp = X1**(i-j)*(X2**j)    #矩阵直接乘相当于matlab中的点乘.*
            out = np.hstack((out, temp.reshape(-1,1)))
    return out

    result = optimize.fmin_bfgs(costFunction, initial_theta, fprime=gradient, args=(X,y,initial_lambda)) 

from sklearn.linear_model import LogisticRegression
from sklearn.preprocessing import StandardScaler
from sklearn.cross_validation import train_test_split
import numpy as np

    # 划分为训练集和测试集
    x_train,x_test,y_train,y_test = train_test_split(X,y,test_size=0.2)

    # 归一化
    scaler = StandardScaler()
    scaler.fit(x_train)
    x_train = scaler.fit_transform(x_train)
    x_test = scaler.fit_transform(x_test)

    #逻辑回归
    model = LogisticRegression()
    model.fit(x_train,y_train)

    # 预测
    predict = model.predict(x_test)
    right = sum(predict == y_test)
    predict = np.hstack((predict.reshape(-1,1),y_test.reshape(-1,1)))   # 将预测值和真实值放在一块，好观察
    print predict
    print ('测试集准确率：%f%%'%(right*100.0/predict.shape[0]))          #计算在测试集上的准确度