原理
最小二乘法进行线性拟合分为训练过程和预测过程
训练过程分为如下3步：
①导入训练数据集，得到特征值feature（即X）和标签label（即Y）
②利用最小二乘法进行训练，根据公式得到W
③将W保存
预测过程分为如下4步：
①导入测试数据集，得到测试集的特征值feature
②导入W
③根据公式得预测值predict
④将预测值保存
权重向量
w = np.matmul(np.matmul(feature.T, feature).I, np.matmul(feature.T, label))
预测结果
即：
predict = np.matmul(testData, w.T)
源数据(200行)
最小二乘法完整代码
训练过程
import numpy as np# 导入训练数据集data.txtdef load_data(file_name):'''导入数据input: file_path(string):训练数据output: feature(mat):特征label(mat):标签'''f = open(file_name)feature = []label = []for line in f.readlines():feature_tmp = []lines = line.strip().split("\t")# print(lines)feature_tmp.append(1) # x0for i in range(len(lines) - 1):feature_tmp.append(float(lines[i]))feature.append(feature_tmp)label.append(float(lines[-1]))f.close()# print(np.mat(feature))# print(np.mat(label).T)# 矩阵化return np.mat(feature), np.mat(label).T # 至此导入数据已经完成# 导入数据后，用最小二乘法对参数进行训练def least_square(feature, label):'''input: feature,labeloutput: w'''# print(feature.shape)# print(label.shape)# print(label)# 叉乘w = np.matmul(np.matmul(feature.T, feature).I, np.matmul(feature.T, label))# print(w.shape)return w.T# 训练完成后，将最终的线性回归模型参数保存在文件"weights.txt"def save_model(file_name, w):'''保存最终的模型input：file_name(string):要保存的文件的名称w(mat):训练好的线性回归模型'''f_result = open(file_name, "w") # 以写的模式打开m, n = np.shape(w) # m表示行数，n表示列数# print(m,n)for i in range(m):w_tmp = []for j in range(n):w_tmp.append(str(w[i, j]))f_result.write("\t".join(w_tmp) + "\n")f_result.close()# 训练过程的主函数if __name__ == "__main__":# 1、导入数据集print("----------- 1.load data ----------")# 用feature,label接收两个返回值feature, label = load_data(r"C:\Users\YouthUpward\Desktop\机器学习\实验2 线性回归\data.txt")# 2、最小二乘法求解print("----------- 2.training ----------")print("\t ---------- least_square ----------")w_ls = least_square(feature, label)print("w_ls :\n",w_ls)# 3、保存最终的结果print("----------- 3.save result ----------")save_model(r"C:\Users\YouthUpward\Desktop\机器学习\实验2 线性回归\weights.txt", w_ls)
预测过程
import numpy as np# 导入数据def load_data(file_name):'''导入数据input: file_path(string):测试数据output: feature 转化成矩阵形式的特征值'''f = open(file_name)feature = []for line in f.readlines():feature_tmp = []lines = line.strip().split("\t")# print(lines)feature_tmp.append(1) # x0for i in range(len(lines)):feature_tmp.append(float(lines[i]))feature.append(feature_tmp)f.close()return np.mat(feature) # 至此导入数据已经完成# 导入线性回归模型def load_model(file_name):f = open(file_name) # 读入文件w = []for line in f.readlines(): # 对于文件的每一行w_tmp = []lines = line.strip().split("\t")for i in range(len(lines)):w_tmp.append(float(lines[i]))w.append(w_tmp)# print("w = ", w)f.close()return np.mat(w)# 得到预测结果，X值与w叉乘def get_prediction(testData, w):# print(testData.shape)# print(w.T.shape)predict = np.matmul(testData, w.T)return np.mat(predict)# 保存预测结果,将Y值保存在“predict_result.txt”文件中def save_predict(file_name, predict):f = open(file_name, "w") # 写入文件m, n = np.shape(predict) # m表示行数，n表示列数for i in range(m):predict_tmp = []for j in range(n):predict_tmp.append(str(predict[i, j]))f.write("\t".join(predict_tmp) + "\n")f.close()# 测试过程的主函数if __name__ == "__main__":# 1、导入测试数据testData = load_data(r"C:\Users\YouthUpward\Desktop\机器学习\实验2 线性回归\data_test.txt")# 2、导入线性回归模型w = load_model(r"C:\Users\YouthUpward\Desktop\机器学习\实验2 线性回归\weights.txt")# 3、得到预测结果predict = get_prediction(testData, w)print(predict)# 4、保存最终的结果save_predict(r"C:\Users\YouthUpward\Desktop\机器学习\实验2 线性回归\predict_result.txt", predict)
最小二乘法图的绘制
import matplotlib.pyplot as pltimport numpy as np#首先要绘制散点图，其次要绘制一次函数f = open(r"C:\Users\YouthUpward\Desktop\机器学习\实验2 线性回归\data.txt")feature = []label = []for line in f.readlines():lines = line.strip().split("\t")feature.append(float(lines[0]))label.append(float(lines[1]))#print(feature)#print(label)f.close()f = open(r"C:\Users\YouthUpward\Desktop\机器学习\实验2 线性回归\weights.txt")w = []for line in f.readlines():lines = line.strip().split("\t")w.append(lines[0])w.append(lines[1])f.close()plt.figure()plt.scatter(feature,label) #散点图x = np.arange(0,0.8,0.1)y = []for i in range(len(x)):y.append(float(w[0]) + float(w[1]) * x[i])plt.plot(x,y)plt.show()
