ex3_1_4.py

# exercise 3.1.4
# (requires data structures from ex. 3.1.1)
from ex3_1_1 import *
from matplotlib.pyplot import figure, legend, plot, show, title, xlabel, ylabel
from scipy.linalg import svd

# Subtract mean value from data
Y = X - np.ones((N, 1)) * X.mean(0)

# PCA by computing SVD of Y
U, S, Vh = svd(Y, full_matrices=False)
# scipy.linalg.svd returns "Vh", which is the Hermitian (transpose)
# of the vector V. So, for us to obtain the correct V, we transpose:
V = Vh.T

# Project the centered data onto principal component space
Z = Y @ V

# Indices of the principal components to be plotted
i = 0
j = 1

# Plot PCA of the data
f = figure()
title("NanoNose data: PCA")
# Z = array(Z)
for c in range(C):
    # select indices belonging to class c:
    class_mask = y == c
    plot(Z[class_mask, i], Z[class_mask, j], "o", alpha=0.5)
legend(classNames)
xlabel("PC{0}".format(i + 1))
ylabel("PC{0}".format(j + 1))

# Output result to screen
show()

print("Ran Exercise 3.1.4")