Anaconda Spyder - Principle Coponent Analysis (PCA)

# -*- coding: utf-8 -*-
"""
Created on Sat Mar 24 09:57:46 2018

@author: username
"""
import numpy as np


X = np.array([[1, 2, 3, 1, 2],
             [3, 1, 5, 7, 9],
             [2, 2, 7, 1, 6],
             [8, 9, 2, 6, 2]])

n_sample = X.shape[0]
dim = X.shape[1]

print ('The number of data is %d and the original dimensionality of data is %d.' % (n_sample, dim))

X_mean = np.mean(X, 0)
X_hat = X - X_mean

X_hat_transpose = X_hat.T
covariance_matrix = np.cov(X_hat_transpose)
print ('The covariance matrix is \n%s' % covariance_matrix)

EigenValues, EigenVectors = np.linalg.eig(covariance_matrix)
index = EigenValues.argsort()[-1]
EigenValues_maximum = EigenValues[index]
EigenVectors_maximum = EigenVectors[:, index]

print ('The eigenvector of the maximum eigenvalue is \n%s' % EigenVectors_maximum)

X_projected_1 = np.dot(X_hat, EigenVectors_maximum)
print (X_projected_1)

U, D, V = np.linalg.svd(X_hat)

print (D)
print (V)

print (V[0, :])

X_projected_2 = np.dot(X_hat, V[0, :])

print (X_projected_2)

----

Outputs:

The number of data is 4 and the original dimensionality of data is 5.

The covariance matrix is
[[  9.66666667  10.66666667  -3.83333333   6.5         -3.16666667]
 [ 10.66666667  13.66666667  -5.5          4.16666667  -7.83333333]
 [ -3.83333333  -5.5          4.91666667  -2.25         5.41666667]
 [  6.5          4.16666667  -2.25        10.25         3.91666667]
 [ -3.16666667  -7.83333333   5.41666667   3.91666667  11.58333333]]

The eigenvector of the maximum eigenvalue is
[-0.51593529+0.j -0.65096754+0.j  0.31439697+0.j -0.25398825+0.j
  0.38300986+0.j]

X_projected_1
[ 1.51848390+0.j  2.92351431+0.j  3.79217593+0.j -8.23417413+0.j]

Print (D)
[  9.64546273e+00   6.88907160e+00   3.12341821e+00   6.66788455e-16]

Print (V)
[[-0.51593529 -0.65096754  0.31439697 -0.25398825  0.38300986]
 [ 0.26157469 -0.03763102  0.11075017  0.69562888  0.65878483]
 [-0.3182144  -0.39321581 -0.71388251  0.42748234 -0.22748964]
 [ 0.5031028  -0.22133546 -0.53150908 -0.5007761   0.40573338]
 [-0.55768864  0.60927589 -0.31106077 -0.1344343   0.45048294]]

Print (V[0, :])
[-0.51593529 -0.65096754  0.31439697 -0.25398825  0.38300986]

X_projected_2
[ 1.5184839   2.92351431  3.79217593 -8.23417413]