tensorflow 实现 正规方程求解线性回归

正规方程是用一个方程去求解线性回归问题，是最小二乘法的矩阵形式。在吴恩达的机器学习课程上也有提及。

这里写一个简单的用tensorflow实现的方法。参考《Tensorflow机器学习实战指南》

# -*- coding: utf-8 -*-"""Created on Sat Dec  9 20:16:39 2017@author: www"""import tensorflow as tfimport matplotlib.pyplot as pltimport numpy as np#准备数据x_vals = np.linspace(0, 10, 100)y_vals = 2 * x_vals + np.random.normal(0, 1, 100)sess = tf.Session()x_vals_column = np.transpose(np.matrix(x_vals))one_column = np.transpose(np.matrix(np.repeat(1, 100)))A = np.column_stack((x_vals_column, one_column))b = np.transpose(np.matrix(y_vals))#转化为张量A_tensor = tf.constant(A)b_tensor = tf.constant(b)#使用正规方程法A_temp = tf.matmul(tf.transpose(A_tensor), A_tensor)A_temp = tf.matrix_inverse(A_temp)A_temp = tf.matmul(A_temp, tf.transpose(A_tensor))solution = tf.matmul(A_temp, b_tensor)solution_eval = sess.run(solution)#得到系数，截距slope = solution_eval[0][0]intercept = solution_eval[1][0]print('slope'+str(slope))print('intercept'+str(intercept))#画图显示best_fit = []for i in x_vals:    best_fit.append(slope * i + intercept)plt.plot(x_vals, y_vals, 'o', label ='Data')plt.plot(x_vals, best_fit, 'r-', label ='Best fit line')plt.legend(loc = 'upper left')plt.show()