PCA主成分分析的簡單示例-opencv、python

pca：principal component analysis，常見的降維技術

生成一組多元正態分布的數據，兩個隨機分布的協方差矩陣：cov(x,x)=5 cov(x,y)=5 cov(y,y)=5 cov(y,x)=25

import numpy as np
import matplotlib.pyplot as plt

mean = [20, 20]
cov = [[5, 5], [5, 25]]
x, y = np.random.multivariate_normal(mean, cov, 500).T

plt.plot(x, y, '.')
plt.axis([0, 40, 0, 40])
plt.xlabel('feature 1')
plt.ylabel('feature 2')

plt.show()

展示出兩個特征向量，一個是數據分布最大方向，也稱第一主成分，另一個是方差方向，第二主成分。

import numpy as np
import matplotlib.pyplot as plt
import cv2

mean = [20, 20]
cov = [[5, 5], [5, 25]]
X = np.random.multivariate_normal(mean, cov, 500)
x, y = X.T

mu, eig = cv2.PCACompute(X, np.array([]))

plt.plot(x, y, '.', zorder=1)
plt.quiver(mean[0], mean[1], eig[0, 0], eig[0, 1],zorder=3, scale=0.2, units='xy')
plt.quiver(mean[0], mean[1], eig[1, 0], eig[1, 1],zorder=3, scale=0.2, units='xy')
plt.axis([0, 40, 0, 40])
plt.xlabel('feature 1')
plt.ylabel('feature 2')
plt.show()

利用opencv的PCAProject來旋轉數據

import numpy as np
import matplotlib.pyplot as plt
import cv2

mean = [20, 20]
cov = [[5, 5], [5, 25]]
X = np.random.multivariate_normal(mean, cov, 500)
x, y = X.T

mu, eig = cv2.PCACompute(X, np.array([]))
X2 = cv2.PCAProject(X,mu,eig)

# plt.plot(x, y, '.', zorder=1)
# plt.quiver(mean[0], mean[1], eig[0, 0], eig[0, 1],zorder=3, scale=0.2, units='xy')
# plt.quiver(mean[0], mean[1], eig[1, 0], eig[1, 1],zorder=3, scale=0.2, units='xy')
plt.plot(X2[:,0],X2[:,1],'.')
plt.axis([-20, 20, -20, 20])
plt.xlabel('feature 1')
plt.ylabel('feature 2')
plt.show()

當人，箭頭方向是還是原來的(⊙ˍ⊙)