分析
线性回归分为单变量线性回归、多变量线性回归
区别 多变量比单变量多个特征缩放
代码及注释 import numpy as npimport matplotlib.pyplot as plt# 中文、负号plt.rcParams['font.sans-serif'] = ['SimHei']plt.rcParams['axes.unicode_minus'] = False# 读取数据data = np.loadtxt(r'ex1data2.txt',delimiter=',')# 洗牌np.random.seed(5)np.random.permutation(data)# 提取数据x,y = data[:,:-1],data[:,-1]# 数据预处理def preProcess(x,y): #特征缩放 x -= np.mean(x,0) x /= np.std(x,0,ddof=1) # 数据初始化 x = np.c_[np.ones(len(x)),x] y = np.c_[y] return x,yx,y = preProcess(x,y)# 切分train_x,test_x = np.split(x,[int(0.7*len(x))])train_y,test_y = np.split(y,[int(0.7*len(x))])# 模型def model(x,theta): h = np.dot(x,theta) return h# 代价函数def costFunc(h,y): e = h - y j = (1/(2*len(y)))*np.dot(e.T,e) return j# 梯度下降函数def gradDesc(x,y,alpha=0.01,max_iter = 10000): m,n = x.shape # 初始化 theta = np.zeros((n,1)) j_history = np.zeros(max_iter) for i in range(max_iter): h = model(x,theta) j_history[i] = costFunc(h,y) deltatheta = (1/m)*np.dot(x.T,h-y) theta -= deltatheta*alpha return j_history,thetaj_history,theta = gradDesc(train_x,train_y)print(theta)plt.title('代价函数图像')plt.plot(j_history)plt.show()# 测试值train_h = model(train_x,theta)test_h = model(test_x,theta)# 精度def score(h,y): u = np.sum(np.square(h-y)) v = np.sum(np.square(y-np.mean(y))) return 1-u/vprint('训练集精度:',score(train_h,train_y))print('测试集精度:',score(test_h,test_y))plt.title('真实值与测试值对比图')plt.scatter(train_y,train_y,label='真实值')plt.scatter(train_y,train_h,label='测试值')plt.legend()plt.show() 效果展示