题目:给定数据集dataSet,每一行代表一组数据记录,每组数据记录中,第一个值为房屋面积(单位:平方英尺),第二个值为房屋中的房间数,第三个值为房价(单位:千美元),试用梯度下降法,构造损失函数,在函数gradientDescent中实现房价price关于房屋面积area和房间数rooms的线性回归,返回值为线性方程𝑝𝑟𝑖𝑐𝑒=𝜃0+𝜃1∗𝑎𝑟𝑒𝑎+𝜃2∗𝑟𝑜𝑜𝑚𝑠中系数𝜃𝑖(𝑖=0,1,2)的列表。
python
%matplotlib inline
import numpy as np
import pandas as pd
import matplotlib.pyplot as plt
from numpy import genfromtxt
dataPath = r"./Input/data1.csv"
dataSet = pd.read_csv(dataPath,header=None)
print(dataSet)
price = []
rooms = []
area = []
for data in range(0,len(dataSet)):
area.append(dataSet[0][data])
rooms.append(dataSet[1][data])
price.append(dataSet[2][data])
print(area)
执行结果:
python
def gradientDescent(rooms, price, area):
epochs = 500
alpha = 0.00000001
theta_gradient = [0,0,0]
const = [1,1,1,1,1]
theta = [1,2,1]
loss = []
for i in range(epochs):
theta0 = np.dot(theta[0],const)
theta1 = np.dot(theta[1],area)
theat2 = np.dot(theta[2],rooms)
predict_tmp = np.add(theta0,theta1)
predict = np.add(predict_tmp,theat2)
loss_ = predict - price
theta_gradient[0] = (theta_gradient[0] + np.dot(const,loss_.transpose()))/5
theta_gradient[1] = (theta_gradient[1] + np.dot(area,loss_.transpose()))/5
theta_gradient[2] = (theta_gradient[2] + np.dot(rooms,loss_.transpose()))/5
loss_t = np.sum(np.divide(np.square(loss_),2))/5
if i%50==0:
print("loss_t:",loss_t)
loss.append(loss_t)
theta[0] = theta[0] - alpha * theta_gradient[0]
theta[1] = theta[1] - alpha * theta_gradient[1]
theta[2] = theta[2] - alpha * theta_gradient[2]
plt.plot(loss,c='b')
plt.show()
return theta
python
def demo_GD():
theta_list = gradientDescent(rooms, price, area)
demo_GD()
j结果展示: