机器学习算法笔记系列之深入理解主成分分析PCA

https://blog.csdn.net/shizhixin/article/details/51181379

https://blog.csdn.net/shizhixin/article/details/51192031

相关Python代码

import numpy as np
import matplotlib.pyplot as plt

sampleDataSet =np.array(
  [[1, 1, 2, 4, 2],
  [1, 3, 3, 4, 4]])
mean_data = np.mean(sampleDataSet,1)
move_mean_sample = (sampleDataSet.transpose() - mean_data).transpose()

p1 = plt.subplot(121)
p1.plot(sampleDataSet[0,:],sampleDataSet[1,:],'*')
p1.axis([0,5,0,5])
p2 = plt.subplot(122)
p2.plot(move_mean_sample[0,:],move_mean_sample[1,:],'*')
p2.axis([-5,5,-5,5])

np_cov = np.cov(move_mean_sample,rowvar=1)

print 'sampleDataSet =\n',sampleDataSet
print 'move_mean_sample =\n',move_mean_sample
print 'np_cov =\n',np_cov

mat_cov = np.mat(np_cov)
(eigV, eigVector) = np.linalg.eigh(mat_cov)
pca_mat = eigVector[:,-1]
pca_data = pca_mat.T * np.mat(move_mean_sample)#Y = P^T * X

recon_data = ((pca_mat * pca_data).transpose() + mean_data).transpose() #X = P*Y
p1.plot(recon_data[0,:],recon_data[1,:],'o')
p1.axis([0,5,0,5])

k = pca_mat[1,0]/pca_mat[0,0]
b = recon_data[1,0] - k*recon_data[0,0]
xx = [0,5]
yy = k * xx +b
p1.plot(xx,yy)

print 'eigV=\n',eigV
print 'eigVector=\n',eigVector
print 'pca_data=\n',pca_data
plt.show()