线性回归和梯度下降

最新推荐文章于 2025-05-28 15:31:15 发布

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本文详细介绍了如何利用随机梯度下降算法实现多变量线性回归模型，通过核函数将属性映射到更高维空间，提高了模型的泛化能力。文章包含代码实现和可视化结果，展示了模型训练过程和最终预测效果。

# -*- coding: utf-8 -*-
import numpy as np
import mkdata as mk
import matplotlib.pyplot as plt
import random

N = 100
iterNums = 10000
#核函数 将属性(x1,x2)映射为(x1,x2,x1*x2,x1*x1,x2*x2)
def kernel(X,y):
    m,n = X.shape
    X_copy = np.zeros((m+3, n))
    
    X_copy[0]=X[0]
    X_copy[1]=X[1]
    
    for i in range(n):
        X_copy[2][i] = X[0][i]*X[1][i]
        X_copy[3][i] = X[0][i]*X[0][i]
        X_copy[4][i] = X[1][i]*X[1][i]
    return X_copy    

#随机梯度下降
def gradientDescent_stochastic(X,y):
    m,n = X.shape
    w = np.zeros(m)
    b = 0
    
    for i in range(iterNums):
        j = random.choice(range(n))
        w = w - (np.dot(w, X[:,j].T)+b - y[0][j])*X[:,j]
        b = b - (np.dot(w, X[:,j].T)+b-y[0][j])
    return w,b
  #批量梯度下降      
def gradientDescent_batch(X, y):
    
    
    m,n = X.shape
    w = np.zeros(m)
    b = 0
    
    for i in range(iterNums):
        diff = np.zeros(m)
        bb = 0
        for j in range(n):
            diff += (np.dot(w, X[:,j].T)+b-y[0][j])*X[:,j]
            bb += np.dot(w,X[:,j].T)+b-y[0][j]
        w = w - 0.01 * diff
        b = b - 0.01 * bb
    return w, b
    
if __name__ == "__main__":
    X,y,w = mk.mk_data(N)
    theta, bias = gradientDescent_batch(X,y)
    #theta, bias = gradientDescent_stochastic(X,y)
    plt.scatter(X[0,y[0]==1], X[1, y[0]==1], color='red')
    plt.scatter(X[0,y[0]==-1], X[1, y[0]==-1], color='g')
    
    x=np.arange(-2,2,0.1)
    x2 = (-bias-theta[0]*x)/theta[1]
    
    plt.plot(x,x2)
    
    plt.show()