机器学习模型和算法 -----监督学习，线性回归算法，最小二乘法

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Python 代码实现：

#导入numpy 和 matplotlib.pyplot 画图工具

import numpy as np 
import matplotlib.pyplot as plt

# 导入数据 data.csv （关于学习时间和学习成绩的向量数据）

points = np.genfromtxt('data.csv',delimiter=',')

x = points[:, 0] # python 可以直接使用[x,y]取得一组, 切片操作[a:b:c] 所以[:, 0]表示取所有行的第一列
y = points[:, 1] # [:, 0]表示取所有行的第二列

plt.scatter(x, y)# 散点图 
plt.show() # 查看散点图

 

 

 # 定义损失函数

def compute_cost(w, b, points):
    total_cost = 0
    M = len(points)
    
    #逐点计算平方损失误差，然后求平均数
    for i in range(M):
        x = points[i, 0]
        y = points[i, 1]
        total_cost += (y - w * x -b) ** 2
        
    return total_cost/M
        

 # 定义均值函数
def average(data):
    sum = 0
    num = len(data)
    for i in range(num):
        sum += data[i]
    return sum/num

# 定义核心拟合合函数
def fit(points):
    M = len(points)
    x_bar = average(points[:, 0])
    
    sum_yx = 0
    sum_x2 = 0
    sum_delta = 0
    
    for i in range(M):
        x = points[i, 0]
        y = points[i, 1]
        sum_yx += y * (x - x_bar)
        sum_x2 += x ** 2

        
    w = sum_yx / (sum_x2 - M *(x_bar ** 2))
    
    for i in range(M):
        x = points[i, 0]
        y = points[i, 1]
        
        sum_delta += ( y - w * x )
    b = sum_delta / M
    
    return w, b

# 调用
w, b = fit(points)

print("w is: ", w)
print("b is: ", b)

cost = compute_cost(w, b, points)

print("cost is: ", cost)

画出拟合曲线

plt.scatter(x, y)

pred_y = w * x + b

plt.plot(x, pred_y, c='r')
plt.show()