深度学习数学基础一--最小二乘法

import numpy as np
from matplotlib import pyplot as plt
A = np.array([[3], [1]])
B = np.array([[1], [3]])
P = A * np.linalg.inv(A.T.dot(A)) * (A.T.dot(B))
# print(P)
plt.plot(A[0], A[1], 'k-o')
plt.plot(B[0], B[1], 'r-o')
plt.plot(P[0], P[1], 'r-o')
plt.plot([B[0], P[0]], [B[1], P[1]], 'y-o')
plt.plot([0, A[0]], [0, A[1]], 'k-')
plt.ylim(0, 3)
plt.xlim(0, 3.5)
plt.text(A[0]+0.1, A[1], 'A')
plt.text(B[0], B[1]-0.1, 'B')
plt.text(P[0]+0.1, P[1]+0.1, 'P')
plt.show()

import numpy as np
from matplotlib import pyplot as plt
x = np.linspace(-1, 1, 100)
y = 2.3*x*x + 3.5*x + 0.04
y_ = y + np.random.rand(len(x)) - 0.5
A = []
times = 2
for i in range(times+1):
    A.append(x**(times-i))
A = np.array(A).T
B = y_.reshape(y_.shape[0], 1)
w = np.linalg.inv(A.T.dot(A)).dot(A.T).dot(B)
pred_y = A.dot(w)
print(w)
plt.scatter(x, y_)
plt.plot(x, y, 'k-')
plt.plot(x, pred_y, 'r-')
plt.show()

[[ 2.28283947]
 [ 3.46918764]
 [ 0.05473155]]