Python实现线性回归与批量梯度下降法完整示例

蓝鲸

发布时间：2026-10-13 | 2人浏览过

原创

本文详细介绍如何使用Python实现线性回归及批量梯度下降算法。通过自定义dataMinning类，演示了数据读取、模型训练及参数更新过程。文章包含误差迭代曲线与数据散点拟合直线的可视化代码，帮助开发者理解批量梯度下降在简单线性回归中的应用与实现细节。

基于斯坦福大学公开课中关于线性规划与梯度下降的理论内容，参考现有代码进行了实测，并封装为一个类以便后续扩展。目前代码注释尚未完善，因近期作业较多暂且搁置。

import numpy as np
import matplotlib.pyplot as plt
import random

class dataMinning:
  datasets = []
  labelsets = []
  
  addressD = '' #Data folder
  addressL = '' #Label folder
  
  npDatasets = np.zeros(1)
  npLabelsets = np.zeros(1)
  
  cost = []
  numIterations = 0
  alpha = 0
  theta = np.ones(2)
  #pCols = 0
  #dRows = 0
  def __init__(self,addressD,addressL,theta,numIterations,alpha,datasets=None):
    if datasets is None:
      self.datasets = []
    else:
      self.datasets = datasets
    self.addressD = addressD
    self.addressL = addressL
    self.theta = theta
    self.numIterations = numIterations
    self.alpha = alpha
    
  def readFrom(self):
    fd = open(self.addressD,'r')
    for line in fd:
      tmp = line[:-1].split()
      self.datasets.append([int(i) for i in tmp])
    fd.close()
    self.npDatasets = np.array(self.datasets)

    fl = open(self.addressL,'r')
    for line in fl:
      tmp = line[:-1].split()
      self.labelsets.append([int(i) for i in tmp])
    fl.close()
    
    tm = []
    for item in self.labelsets:
      tm = tm + item
    self.npLabelsets = np.array(tm)

  def genData(self,numPoints,bias,variance):
    self.genx = np.zeros(shape = (numPoints,2))
    self.geny = np.zeros(shape = numPoints)

    for i in range(0,numPoints):
      self.genx[i][0] = 1
      self.genx[i][1] = i
      self.geny[i] = (i + bias) + random.uniform(0,1) * variance

  def gradientDescent(self):
    xTrans = self.genx.transpose() #
    i = 0
    while i < self.numIterations:
      hypothesis = np.dot(self.genx,self.theta)
      loss = hypothesis - self.geny
      #record the cost
      self.cost.append(np.sum(loss ** 2))
      #calculate the gradient
      gradient = np.dot(xTrans,loss)
      #updata, gradientDescent
      self.theta = self.theta - self.alpha * gradient
      i = i + 1
      
  
  def show(self):
    print 'yes'
    
if __name__ == "__main__":
  c = dataMinning('c:\\city.txt','c:\\st.txt',np.ones(2),100000,0.000005)
  c.genData(100,25,10)
  c.gradientDescent()
  cx = range(len(c.cost))
  plt.figure(1)
  plt.plot(cx,c.cost)
  plt.ylim(0,25000)
  plt.figure(2)
  plt.plot(c.genx[:,1],c.geny,'b.')
  x = np.arange(0,100,0.1)
  y = x * c.theta[1] + c.theta[0]
  plt.plot(x,y)
  plt.margins(0.2)
  plt.show()