PCA 只有代码

机器学习

%matplotlib inline
import numpy as np
import scipy
from matplotlib import pyplot as plt

points = np.random.randn(50, 2)

plt.scatter(points[:, 0], points[:, 1])

<matplotlib.collections.PathCollection at 0x7f378f2f7f50>

cov = np.cov(points.T)
cov.shape

(2, 2)

w, v = np.linalg.eig(cov)
w, v

(array([0.95331384, 0.82559234]), array([[ 0.99782635, -0.06589818],
        [ 0.06589818,  0.99782635]]))

y_axis = v[np.argmax(w)]
x_axis = v[np.argmin(w)]
y_axis, x_axis

(array([ 0.99782635, -0.06589818]), array([0.06589818, 0.99782635]))

x = np.dot(points, x_axis)
y = np.dot(points, y_axis)

x1 = np.dot(x.reshape(-1, 1), x_axis.reshape(1, -1))
y1 = np.dot(y.reshape(-1, 1), y_axis.reshape(1, -1))

l = np.linspace(-1, 1)

lx = np.dot(l.reshape(-1, 1), x_axis.reshape(1, -1))
ly = np.dot(l.reshape(-1, 1), y_axis.reshape(1, -1))

plt.scatter(points[:, 0], points[:, 1])
plt.scatter(x1[:, 0], x1[:, 1])
plt.scatter(y1[:, 0], y1[:, 1])
plt.plot(lx[:, 0], lx[:, 1])
plt.plot(ly[:, 0], ly[:, 1])

[<matplotlib.lines.Line2D at 0x7f378f2a79d0>]