data.txt

2.5	2.4
0.5	0.7
2.2	2.9
1.9	2.2
3.1	3.0
2.3	2.7
2	1.6
1	1.1
1.5	1.6
1.1	0.9

pca.py

import numpy as np


data = np.loadtxt('data.txt', delimiter='\t')

# subtract mean
data_adjusted = data - data.mean(axis=0)

# covariance matrix
covariance = np.cov(data_adjusted.T)

# eigen decomposition
eigen_values, eigen_vectors = np.linalg.eig(covariance)

print(eigen_values.shape)
print(eigen_vectors.shape)
print('eigen value * I * eigen vector')
print(np.matmul(eigen_values * np.eye(2), eigen_vectors))
print('covariance matrix * eigen vector')
print(np.matmul(covariance, eigen_vectors))


ind = np.argsort(eigen_values)[::-1]
eigen_values = eigen_values[ind]
eigen_vectors = eigen_vectors[ind]

top_k = 1


eigen_values_top_k = eigen_values[:top_k]
eigen_vectors_top_k = eigen_vectors[:top_k, :]

print(eigen_values_top_k)
print(eigen_vectors_top_k)