机器学习|第一周:单变量线性回归例子

1%matplotlib notebook # jupyter notebook 的魔法方法
2import numpy as np
3import matplotlib.pyplot as plt
4import pandas as pd

1# 加载数据
2data = pd.read_csv('ex1data1.txt', header=None, names=['Population', 'Profit'])

1# 数据查看
2data.describe() # jupyter notebook 直接用来显示数据的，以下非Python 语法是 jupyter notebook 用来显示数据的

1# 数据可视化，绘制散点图
2data.plot(kind='scatter', x='Population', y='Profit', figsize=(12, 8))

1def costFunction(X, y, theta):
2    inner = np.power((X*theta.T)-y, 2)
3    return np.sum(inner) / (2*X.shape[0])

1# 在第 0 列插入一列数据 1 标签是 'Ones'
2data.insert(0, 'Ones', 1)
3data.head() # 查看前5 行数据

1# 设置训练集数据
2cols = data.shape[1] # 获取列数下标为 1 ；行数下标为 0 
3X = data.iloc[:,0:-1] #  取所有行，去掉所有一列
4y = data.iloc[:,cols-1:cols] # 取所有行，最后一列
5# 数据集转化为矩阵
6X = np.matrix(X.values)
7y = np.matrix(y.values)
8theta = np.matrix(np.array([0, 0]))

1#shape 属性是查看维数的
2X.shape, y.shape, theta.shape

1#测试
2theta_1 = np.matrix(np.array([-1, 2]))
3J = costFunction(X, y, theta_1)
4print('\nWith theta = [-1 ; 2]\nCost computed =', J)
5print('Expected cost value (approx) 54.24\n');

1def gradientDescent(X, y, theta, alpha, iteration):
2    J_history = np.zeros(iteration)
3    for iter in range(iteration):
4        h = X*theta.T 
5        theta = theta - alpha * (h - y).T*X / y.shape[0]
6        J_history[iter] = costFunction(X, y, theta)#记录
7    return theta, J_history

1alpha = 0.01
2iteration = 1000
3trained_theta, J = gradientDescent(X, y, theta, alpha, iteration)

1trained_theta[0, 1],J.shape

 1x_axis = np.linspace(data.Population.min(), data.Population.max(), 100)#设置x轴
 2y_axis = trained_theta[0, 0] + (trained_theta[0, 1] * x_axis)#设置Y轴
 3fig, ax = plt.subplots(figsize=(12,8))
 4ax.plot(x_axis, y_axis, 'r', label='Prediction')      # 绘制拟合曲线
 5ax.scatter(data.Population, data.Profit, label='Traning Data')#绘制散点图
 6ax.legend(loc=2)
 7ax.set_xlabel('Population')
 8ax.set_ylabel('Profit')
 9ax.set_title('Predicted Profit vs. Population Size')
10plt.show()

1fig1, ax1 = plt.subplots()
2x=np.linspace(1, iteration, iteration)
3ax1.plot(x, J)