最小二乘法-使用Python+Numpy实现的最小二乘法.zip

# -*- coding: utf-8 -*- """ Created on Tue May 19 09:47:11 2020 numpy实现最小二乘法 @author: 86186 """ import numpy as np import matplotlib.pyplot as plt def loss(w, b, x, y): total_loss = 0.0 differ = w*x + b - y for i in range(len(x)): total_loss += differ[i] ** 2 return total_loss/len(x) #根据公式计算参数w和b def compute_parameters(x, y): numerator = 0.0 #分子 denominator = 0.0 #分母 x_mean = np.mean(x) y_mean = np.mean(y) for i in range(len(x)): numerator += (x[i] - x_mean) * (y[i] - y_mean) denominator += (x[i] - x_mean) ** 2 w = numerator / denominator b = y_mean - w * x_mean return w, b x = np.linspace(1,100,200) #在[1,100]区间里生成均匀分布的200个数字 noise = np.random.normal(loc=0.0, scale=20, size=200)#生成均值为0，标准差为20的正态分布数据(200个) y = 0.8 * x + noise w, b = compute_parameters(x, y) plt.figure() plt.rcParams['font.sans-serif'] = ['Microsoft YaHei'] #plt处理中文，字体为微软雅黑 y_pred = w * x + b plt.scatter(x, y, c='r') #画散点图 plt.title("x与y的拟合函数") plt.plot(x, y_pred, c='b') #画直线图 plt.xlabel('x') plt.ylabel('y') plt.show() #矩阵求解法 #计算公式params = (X.T dot X)^-1 dot X.T dot Y x = np.array(x) y = np.array(y) x_features = [] for i in range(len(x)): x_features.append(np.array([x[i], 1]).T) #将输入特征加上偏置向并转置成列向量 x_features = np.array(x_features) #[200, 2] xTx = np.dot(x_features.T, x_features) #[2, 2] xTx_inv = np.linalg.inv(xTx) #[2, 2] xTx_inv_xT = np.dot(xTx_inv, x_features.T) params = np.dot(xTx_inv_xT, y) w,b = params[0], params[1] plt.figure() plt.rcParams['font.sans-serif'] = ['Microsoft YaHei'] #plt处理中文，字体为微软雅黑 y_pred = w * x + b plt.scatter(x, y, c='r') #画散点图 plt.title("x与y的拟合函数") plt.plot(x, y_pred, c='b') #画直线图 plt.xlabel('x') plt.ylabel('y') plt.show()