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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')
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