一、二元输入特征线性回归
测试数据为：ex1data2.txt
2104,3,399900 1600,3,329900 2400,3,369000 1416,2,232000 3000,4,539900 1985,4,299900 1534,3,314900 1427,3,198999 1380,3,212000 1494,3,242500 1940,4,239999 2000,3,347000 1890,3,329999 4478,5,699900 1268,3,259900 2300,4,449900 1320,2,299900 1236,3,199900 2609,4,499998 3031,4,599000 1767,3,252900 1888,2,255000 1604,3,242900 1962,4,259900 3890,3,573900 1100,3,249900 1458,3,464500 2526,3,469000 2200,3,475000 2637,3,299900 1839,2,349900 1000,1,169900 2040,4,314900 3137,3,579900 1811,4,285900 1437,3,249900 1239,3,229900 2132,4,345000 4215,4,549000 2162,4,287000 1664,2,368500 2238,3,329900 2567,4,314000 1200,3,299000 852,2,179900 1852,4,299900 1203,3,239500
Python代码如下：
#-*- coding: UTF-8 -*- import random import numpy as np import matplotlib.pyplot as plt #加载数据 def load_exdata(filename): data = [] with open(filename, 'r') as f: for line in f.readlines(): line = line.split(',') current = [int(item) for item in line] //根据数据输入的不同确定是int 还是其他类型 #5.5277,9.1302 data.append(current) return data data = load_exdata('ex1data2.txt'); data = np.array(data,np.int64)//根据数据输入的不同确定是int 还是其他类型 #特征缩放 def featureNormalize(X): X_norm = X; mu = np.zeros((1,X.shape[1])) sigma = np.zeros((1,X.shape[1])) for i in range(X.shape[1]): mu[0,i] = np.mean(X[:,i]) # 均值 sigma[0,i] = np.std(X[:,i]) # 标准差 # print(mu) # print(sigma) X_norm = (X - mu) / sigma return X_norm,mu,sigma #计算损失 def computeCost(X, y, theta): m = y.shape[0] # J = (np.sum((X.dot(theta) - y)**2)) / (2*m) C = X.dot(theta) - y J2 = (C.T.dot(C))/ (2*m) return J2 #梯度下降 def gradientDescent(X, y, theta, alpha, num_iters): m = y.shape[0] #print(m) # 存储历史误差 J_history = np.zeros((num_iters, 1)) for iter in range(num_iters): # 对J求导，得到 alpha/m * (WX - Y)*x(i)， (3,m)*(m,1) X (m,3)*(3,1) = (m,1) theta = theta - (alpha/m) * (X.T.dot(X.dot(theta) - y)) J_history[iter] = computeCost(X, y, theta) return J_history,theta iterations = 10000 #迭代次数 alpha = 0.01 #学习率 x = data[:,(0,1)].reshape((-1,2)) y = data[:,2].reshape((-1,1)) m = y.shape[0] x,mu,sigma = featureNormalize(x) X = np.hstack([x,np.ones((x.shape[0], 1))]) # X = X[range(2),:] # y = y[range(2),:] theta = np.zeros((3, 1)) j = computeCost(X,y,theta) J_history,theta = gradientDescent(X, y, theta, alpha, iterations) print('Theta found by gradient descent',theta) def predict(data): testx = np.array(data) testx = ((testx - mu) / sigma) testx = np.hstack([testx,np.ones((testx.shape[0], 1))]) price = testx.dot(theta) print('price is %d ' % (price)) predict([1650,3])
二、多元线性回归，以三个特征输入为例
输入数据：testdata.txt。其中第一列是指输入的数据序列，不可读入
1,230.1,37.8,69.2,22.1 2,44.5,39.3,45.1,10.4 3,17.2,45.9,69.3,9.3 4,151.5,41.3,58.5,18.5 5,180.8,10.8,58.4,12.9 6,8.7,48.9,75,7.2 7,57.5,32.8,23.5,11.8 8,120.2,19.6,11.6,13.2 9,8.6,2.1,1,4.8 10,199.8,2.6,21.2,10.6 11,66.1,5.8,24.2,8.6 12,214.7,24,4,17.4 13,23.8,35.1,65.9,9.2 14,97.5,7.6,7.2,9.7 15,204.1,32.9,46,19 16,195.4,47.7,52.9,22.4 17,67.8,36.6,114,12.5 18,281.4,39.6,55.8,24.4 19,69.2,20.5,18.3,11.3 20,147.3,23.9,19.1,14.6 21,218.4,27.7,53.4,18 22,237.4,5.1,23.5,12.5 23,13.2,15.9,49.6,5.6 24,228.3,16.9,26.2,15.5 25,62.3,12.6,18.3,9.7 26,262.9,3.5,19.5,12 27,142.9,29.3,12.6,15 28,240.1,16.7,22.9,15.9 29,248.8,27.1,22.9,18.9 30,70.6,16,40.8,10.5 31,292.9,28.3,43.2,21.4 32,112.9,17.4,38.6,11.9 33,97.2,1.5,30,9.6 34,265.6,20,0.3,17.4 35,95.7,1.4,7.4,9.5 36,290.7,4.1,8.5,12.8 37,266.9,43.8,5,25.4 38,74.7,49.4,45.7,14.7 39,43.1,26.7,35.1,10.1 40,228,37.7,32,21.5 41,202.5,22.3,31.6,16.6 42,177,33.4,38.7,17.1 43,293.6,27.7,1.8,20.7 44,206.9,8.4,26.4,12.9 45,25.1,25.7,43.3,8.5 46,175.1,22.5,31.5,14.9 47,89.7,9.9,35.7,10.6 48,239.9,41.5,18.5,23.2 49,227.2,15.8,49.9,14.8 50,66.9,11.7,36.8,9.7 51,199.8,3.1,34.6,11.4 52,100.4,9.6,3.6,10.7 53,216.4,41.7,39.6,22.6 54,182.6,46.2,58.7,21.2 55,262.7,28.8,15.9,20.2 56,198.9,49.4,60,23.7 57,7.3,28.1,41.4,5.5 58,136.2,19.2,16.6,13.2 59,210.8,49.6,37.7,23.8 60,210.7,29.5,9.3,18.4 61,53.5,2,21.4,8.1 62,261.3,42.7,54.7,24.2 63,239.3,15.5,27.3,15.7 64,102.7,29.6,8.4,14 65,131.1,42.8,28.9,18 66,69,9.3,0.9,9.3 67,31.5,24.6,2.2,9.5 68,139.3,14.5,10.2,13.4 69,237.4,27.5,11,18.9 70,216.8,43.9,27.2,22.3 71,199.1,30.6,38.7,18.3 72,109.8,14.3,31.7,12.4 73,26.8,33,19.3,8.8 74,129.4,5.7,31.3,11 75,213.4,24.6,13.1,17 76,16.9,43.7,89.4,8.7 77,27.5,1.6,20.7,6.9 78,120.5,28.5,14.2,14.2 79,5.4,29.9,9.4,5.3 80,116,7.7,23.1,11 81,76.4,26.7,22.3,11.8 82,239.8,4.1,36.9,12.3 83,75.3,20.3,32.5,11.3 84,68.4,44.5,35.6,13.6 85,213.5,43,33.8,21.7 86,193.2,18.4,65.7,15.2 87,76.3,27.5,16,12 88,110.7,40.6,63.2,16 89,88.3,25.5,73.4,12.9 90,109.8,47.8,51.4,16.7 91,134.3,4.9,9.3,11.2 92,28.6,1.5,33,7.3 93,217.7,33.5,59,19.4 94,250.9,36.5,72.3,22.2 95,107.4,14,10.9,11.5 96,163.3,31.6,52.9,16.9 97,197.6,3.5,5.9,11.7 98,184.9,21,22,15.5 99,289.7,42.3,51.2,25.4 100,135.2,41.7,45.9,17.2 101,222.4,4.3,49.8,11.7 102,296.4,36.3,100.9,23.8 103,280.2,10.1,21.4,14.8 104,187.9,17.2,17.9,14.7 105,238.2,34.3,5.3,20.7 106,137.9,46.4,59,19.2 107,25,11,29.7,7.2 108,90.4,0.3,23.2,8.7 109,13.1,0.4,25.6,5.3 110,255.4,26.9,5.5,19.8 111,225.8,8.2,56.5,13.4 112,241.7,38,23.2,21.8 113,175.7,15.4,2.4,14.1 114,209.6,20.6,10.7,15.9 115,78.2,46.8,34.5,14.6 116,75.1,35,52.7,12.6 117,139.2,14.3,25.6,12.2 118,76.4,0.8,14.8,9.4 119,125.7,36.9,79.2,15.9 120,19.4,16,22.3,6.6 121,141.3,26.8,46.2,15.5 122,18.8,21.7,50.4,7 123,224,2.4,15.6,11.6 124,123.1,34.6,12.4,15.2 125,229.5,32.3,74.2,19.7 126,87.2,11.8,25.9,10.6 127,7.8,38.9,50.6,6.6 128,80.2,0,9.2,8.8 129,220.3,49,3.2,24.7 130,59.6,12,43.1,9.7 131,0.7,39.6,8.7,1.6 132,265.2,2.9,43,12.7 133,8.4,27.2,2.1,5.7 134,219.8,33.5,45.1,19.6 135,36.9,38.6,65.6,10.8 136,48.3,47,8.5,11.6 137,25.6,39,9.3,9.5 138,273.7,28.9,59.7,20.8 139,43,25.9,20.5,9.6 140,184.9,43.9,1.7,20.7 141,73.4,17,12.9,10.9 142,193.7,35.4,75.6,19.2 143,220.5,33.2,37.9,20.1 144,104.6,5.7,34.4,10.4 145,96.2,14.8,38.9,11.4 146,140.3,1.9,9,10.3 147,240.1,7.3,8.7,13.2 148,243.2,49,44.3,25.4 149,38,40.3,11.9,10.9 150,44.7,25.8,20.6,10.1 151,280.7,13.9,37,16.1 152,121,8.4,48.7,11.6 153,197.6,23.3,14.2,16.6 154,171.3,39.7,37.7,19 155,187.8,21.1,9.5,15.6 156,4.1,11.6,5.7,3.2 157,93.9,43.5,50.5,15.3 158,149.8,1.3,24.3,10.1 159,11.7,36.9,45.2,7.3 160,131.7,18.4,34.6,12.9 161,172.5,18.1,30.7,14.4 162,85.7,35.8,49.3,13.3 163,188.4,18.1,25.6,14.9 164,163.5,36.8,7.4,18 165,117.2,14.7,5.4,11.9 166,234.5,3.4,84.8,11.9 167,17.9,37.6,21.6,8 168,206.8,5.2,19.4,12.2 169,215.4,23.6,57.6,17.1 170,284.3,10.6,6.4,15 171,50,11.6,18.4,8.4 172,164.5,20.9,47.4,14.5 173,19.6,20.1,17,7.6 174,168.4,7.1,12.8,11.7 175,222.4,3.4,13.1,11.5 176,276.9,48.9,41.8,27 177,248.4,30.2,20.3,20.2 178,170.2,7.8,35.2,11.7 179,276.7,2.3,23.7,11.8 180,165.6,10,17.6,12.6 181,156.6,2.6,8.3,10.5 182,218.5,5.4,27.4,12.2 183,56.2,5.7,29.7,8.7 184,287.6,43,71.8,26.2 185,253.8,21.3,30,17.6 186,205,45.1,19.6,22.6 187,139.5,2.1,26.6,10.3 188,191.1,28.7,18.2,17.3 189,286,13.9,3.7,15.9 190,18.7,12.1,23.4,6.7 191,39.5,41.1,5.8,10.8 192,75.5,10.8,6,9.9 193,17.2,4.1,31.6,5.9 194,166.8,42,3.6,19.6 195,149.7,35.6,6,17.3 196,38.2,3.7,13.8,7.6 197,94.2,4.9,8.1,9.7 198,177,9.3,6.4,12.8 199,283.6,42,66.2,25.5 200,232.1,8.6,8.7,13.4
python 代码：
#-*- coding: UTF-8 -*- import random import numpy as np import matplotlib.pyplot as plt #加载数据 def load_exdata(filename): data = [] with open(filename, 'r') as f: for line in f.readlines(): line = line.split(',') current = [float(item) for item in line] #5.5277,9.1302 data.append(current) return data data = load_exdata('testdata.txt'); data = np.array(data,np.float64)//数据是浮点型 # 特征缩放 def featureNormalize(X): X_norm = X; mu = np.zeros((1, X.shape[1])) sigma = np.zeros((1, X.shape[1])) for i in range(X.shape[1]): mu[0, i] = np.mean(X[:, i]) # 均值 sigma[0, i] = np.std(X[:, i]) # 标准差 # print(mu) # print(sigma) X_norm = (X - mu) / sigma return X_norm, mu, sigma # 计算损失 def computeCost(X, y, theta): m = y.shape[0] # J = (np.sum((X.dot(theta) - y)**2)) / (2*m) C = X.dot(theta) - y J2 = (C.T.dot(C)) / (2 * m) return J2 # 梯度下降 def gradientDescent(X, y, theta, alpha, num_iters): m = y.shape[0] # print(m) # 存储历史误差 J_history = np.zeros((num_iters, 1)) for iter in range(num_iters): # 对J求导，得到 alpha/m * (WX - Y)*x(i)， (3,m)*(m,1) X (m,3)*(3,1) = (m,1) theta = theta - (alpha / m) * (X.T.dot(X.dot(theta) - y)) J_history[iter] = computeCost(X, y, theta) return J_history, theta iterations = 10000 # 迭代次数 alpha = 0.01 # 学习率 x = data[:, ( 1,2,3)].reshape((-1, 3))//数据特征输入，采用数据集一行的，第1，2，3个数据，然后将其变成一行，所以用shape y = data[:, 4].reshape((-1, 1))//输出特征，数据集的第四位 m = y.shape[0] x, mu, sigma = featureNormalize(x) X = np.hstack([x, np.ones((x.shape[0], 1))]) # X = X[range(2),:] # y = y[range(2),:] theta = np.zeros((4, 1))//因为x+y.总共有四个输入，所以theta是四维 j = computeCost(X, y, theta) J_history, theta = gradientDescent(X, y, theta, alpha, iterations) print('Theta found by gradient descent', theta) def predict(data): testx = np.array(data) testx = ((testx - mu) / sigma) testx = np.hstack([testx, np.ones((testx.shape[0], 1))]) price = testx.dot(theta) print('predit value is %f ' % (price)) predict([151.5,41.3,58.5])//输入为3维