pca_full.py

import matplotlib.pyplot as plt
import numpy
import random

def create_datas():
    datas = []
    for i in range(20):
        a = 10 * (random.random() -  0.5)
        datas.append((a, a + 3 * (random.random() - 0.5)))
    return datas


def pca(datas, dim):
    cov_matrix = cov(transposition(datas))
    
    evs = eigen_vectors(cov_matrix)
    
    return [tuple(sum([a*b for a, b in zip(v,d)]) for v in evs[:dim]) for d in datas]
    
def eigen_vectors(matrix):
    eigen_values, eigen_matrix = numpy.linalg.eig(matrix)
    
    eigens = sorted([
        (eigen_values[i], eigen_matrix[:, i].tolist()) for i in range(len(eigen_values))
    ], key=lambda x: x[0], reverse=True)
    
    return [e[1] for e in eigens]
    
def transposition(datas):
    return [ [d[i] for d in datas] for i in range(len(datas[1])) ]
    
def cov(td):
    variance_matrix = numpy.array([
        [covariance(td[i], td[j]) for i in range(len(td))]
        for j in range(len(td))
    ])
    return variance_matrix

def average(data_series):
    return sum(data_series) / len(data_series)

def covariance(data_series_a, data_series_b):
    return sum([(d_a - average(data_series_a)) * (d_b - average(data_series_b)) for d_a, d_b in zip(data_series_a, data_series_b)]) / len(data_series_a)


ds = create_datas()
plt.xlim([-7, 7])
plt.ylim([-7, 7])

x = [d[0] for d in ds]
y = [d[1] for d in ds]

plt.xlabel("$x$", fontsize=20, fontname='serif')
plt.ylabel("$y$", fontsize=20,fontname='serif')

plt.plot(x,y, '.')

plt.savefig('ex1.png')

plt.clf()

pca_ds = pca(ds, 2)
plt.xlim([-7, 7])
plt.ylim([-7, 7])
x = [d[0] for d in pca_ds]
y = [d[1] for d in pca_ds]

plt.xlabel("$x$", fontsize=20, fontname='serif')
plt.ylabel("$y$", fontsize=20,fontname='serif')

plt.plot(x,y, '.')

plt.savefig('ex2.png')