機器學習Python版 ex1：單變量線性迴歸

import numpy as np
import cv2 as cv
import matplotlib.pyplot as plt
import pandas as pd

#獲取數據
data = pd.read_csv('ex1data1.txt',names=['population', 'profit'])
X = data['population']
y = data['profit']           #使用列名作爲索引
m = len(y)

#爲矩陣X增加列
ones = pd.DataFrame({'ones': np.ones(m)})   #學習一下
X = pd.concat([ones, X], axis=1)

#參數個數即爲X特徵值
theta = np.zeros(X.shape[1])

#獲取代價函數，單獨定義是：theta不同對應的代價函數不同
def J_function(X,y,theta):
    h_theta = X.dot(theta)    #矩陣乘積
    cost = ( (h_theta - y).dot((h_theta - y).T) ) / (2*m)
    return cost

#梯度下降算法
def gradient(X,y,theta):
    gradient = (X.T).dot( X.dot(theta) - y )
    return gradient/m

def batch_gradient_descent(X,y,theta,alpha,iterations):
    cost_data = [J_function(X,y,theta)]
    _theta = theta.copy()

    for _ in range(iterations):
        _theta = _theta - alpha * gradient(X,y, _theta)
        cost_data.append( J_function(X,y,theta) )

    return _theta, cost_data

alpha = 0.01
iterations = 500
final_theta, cost_data = batch_gradient_descent(X, y, theta ,alpha, iterations)
final_costdata = J_function( X,y,final_theta)


b = final_theta[0]
k = final_theta[1]
plt.scatter(data['population'],data['profit'], label='Training data')
plt.plot(data['population'],data['population']*k + b , label='Prediction')
plt.xlabel(('Population of City in 10,000s')),plt.ylabel(('Profit in $10,000s'))
plt.show()