Performing PCA

Let's perform PCA from scratch in Python:

1. Compute the correlation or covariance matrix of a given dataset.
2. Find the eigenvalues and eigenvectors of the correlation or covariance matrix.
3. Multiply the eigenvector matrix by the original dataset and you will get the principal component matrix.

Let's implement PCA from scratch:

1. We will begin by importing libraries and defining the dataset:

# Import numpy
import numpy as np
# Import linear algebra module
from scipy import linalg as la
# Create dataset
data=np.array([[7., 4., 3.],
[4., 1., 8.],
[6., 3., 5.],
[8., 6., 1.],
[8., 5., 7.],
[7., 2., 9.],
[5., 3., 3.],
[9., 5., 8.],
[7., 4., 5.],
[8., 2., 2.]])

2. Calculate the covariance matrix:

# Calculate the covariance matrix
# Center your data
data -= data.mean(axis=0)
cov = np.cov(data, rowvar=False)

3. Calculate the eigenvalues and eigenvector of the covariance matrix:

# Calculate eigenvalues and eigenvector of the covariance matrix
evals, evecs = la.eig(cov)

4. Multiply the original...