逻辑回归正则化（# 使用训练集的X1，X2两组特征画出0-1分布散点图及分割线m,n = train

import numpy as np,matplotlib.pyplot as plt,copy
plt.rcParams['font.sans-serif']=['SimHei']
plt.rcParams['axes.unicode_minus']=False
#1.数据预处理
import sklearn.datasets as dts
def data_process():
    data_cancer=dts.load_breast_cancer()
    x=data_cancer.data[:,:-1]
    y=data_cancer.target
    #特征缩放(标准化)
    x=(x-np.mean(x,axis=0))/np.std(x,axis=0,ddof=1)
    #截距拼接
    m,n=x.shape
    x=np.c_[np.ones((m,1)),x]
    y=np.c_[y]
    #洗牌
    np.random.seed(5)
    order=np.random.permutation(m)
    x=x[order]
    y=y[order]
    # 分割训练集和测试集 6:4
    num = int(m * 0.6)
    train_x, test_x = np.split(x, [num])
    train_y, test_y = np.split(y, [num])
    return train_x, test_x, train_y, test_y

#线性模型
def lh(x,theta):
    z=x.dot(theta)
    return z
# 实现Sigmoid函数
def sigmoid(z):
    h=1/(1+np.exp(-z))
    return h
# 实现逻辑回归的代价函数 交叉熵+正则化
def loss_func(h,y,lamda,thetaR):
    m=len(h)
    R=lamda/(2*m)*np.sum(thetaR**2)
    J=-1/m*np.sum(y*np.log(h)+(1-y)*np.log(1-h))+R
    return J
# 实现梯度下降函数
def grad_decent(x,h,y,lamda,thetaR):
    e=h-y
    m=len(h)
    dt=1/m*x.T.dot(e)+lamda/m*thetaR
    return dt
# 实现逻辑回归模型精度函数
def acc_func(h,y):
    acc=np.mean(y==(h>=0.5))
    return acc
# 通过梯度下降训练逻辑回归模型
def train_mode(x,y,lamda=0.1,alpha=0.7,iters=100):
    m,n=x.shape
    theta=np.zeros((n,1))
    loss_list=[]
    for i in range(iters):
        z=lh(x,theta)
        h=sigmoid(z)
        thetaR=copy.copy(theta)
        thetaR[0]=0
        loss=loss_func(h,y,lamda,thetaR)
        loss_list.append(loss)
        dt=grad_decent(x,h,y,lamda,thetaR)
        theta=theta-alpha*dt
    return loss_list,theta
train_x, test_x, train_y, test_y=data_process()
loss_list01,theta=train_mode(train_x,train_y)
print('迭代过程中的损失值:',loss_list01)
plt.plot(loss_list01,c='r')
plt.show()
# 用所得模型对测试集的数据进行预测，并计算准确率
test_z = lh(test_x,theta)
test_h = sigmoid(test_z)
print('测试精度：',acc_func(test_h,test_y))
# 使用训练集的X1，X2两组特征画出0-1分布散点图及分割线
m,n = train_x.shape
for i in range(m):
    if train_y[i] == 0:
        plt.plot(train_x[i,1],train_x[i,2],'ob')
    elif train_y[i] == 1:
        plt.plot(train_x[i,1],train_x[i,2],'*r')
x1_min=np.min(train_x[:,1],axis=0)
x1_max=np.max(train_x[:,1],axis=0)
x2_min=(-theta[0]-theta[1]*x1_min)/theta[2]
x2_max=(-theta[0]-theta[1]*x1_max)/theta[2]
plt.plot([x1_min,x1_max],[x2_min,x2_max],'m')
plt.xlabel('x1')
plt.ylabel('x2')
plt.show()