Factor analysis and PCA blog post

Digits analysis

import numpy as np
import matplotlib.pyplot as plt
from sklearn.decomposition import PCA, FactorAnalysis, SparsePCA
from sklearn import datasets

dset = datasets.load_digits()
x = dset.data
y = dset.target

model = PCA(n_components=2)
x_reduced = model.fit_transform(x)
plt.figure(figsize=(3*1.618,3))
plt.scatter(x_reduced[:, 0], x_reduced[:, 1], c=y, cmap=plt.cm.Set1)
# plt.savefig('digits_PCA.png')

print np.dot(model.components_[0], model.components_[1])
print model.noise_variance_

v = model.transform(x)
v_samples = np.random.multivariate_normal(np.mean(v, axis=0), np.cov(v.T), size=100)
x_samples = model.inverse_transform(v_samples)

n_row = 5
n_col = 20
plt.figure(figsize=(10, 2.5))
for i in xrange(n_row*n_col):
	comp = x_samples[i]
	plt.subplot(n_row, n_col, i + 1)
	vmax = max(comp.max(), -comp.min())
	plt.imshow(comp.reshape([8,8]), cmap=plt.cm.gray, interpolation='nearest')
	plt.xticks(())
	plt.yticks(())
plt.tight_layout(h_pad=0, w_pad=0)
plt.savefig('gen_PCA.png')


model = FactorAnalysis(n_components=2)
x_reduced = model.fit_transform(x)
plt.figure(figsize=(3*1.618,3))
plt.scatter(x_reduced[:, 0], x_reduced[:, 1], c=y, cmap=plt.cm.Set1)
# plt.savefig('digits_FA.png')

print np.dot(model.components_[0], model.components_[1])
print model.noise_variance_

model = SparsePCA(n_components=10)
x_reduced = model.fit_transform(x)
plt.figure(figsize=(3*1.618,3))
plt.scatter(x_reduced[:, 0], x_reduced[:, 1], c=y, cmap=plt.cm.Set1)
plt.savefig('digits_SPCA.png')

print np.dot(model.components_[0], model.components_[1])
n_row = 5
n_col = 2
plt.figure(figsize=(6, 15))
for i in xrange(n_row*n_col):
	comp = model.components_[i]
	plt.subplot(n_row, n_col, i + 1)
	vmax = max(comp.max(), -comp.min())
	plt.imshow(comp.reshape([8,8]), cmap=plt.cm.gray, interpolation='nearest')
	plt.xticks(())
	plt.yticks(())
plt.tight_layout()
plt.savefig('digits_SPCA_rec.png')

Iris analysis

import numpy as np
import matplotlib.pyplot as plt
from scipy import linalg

from sklearn.decomposition import PCA, FactorAnalysis
from sklearn.covariance import ShrunkCovariance, LedoitWolf
from sklearn.cross_validation import cross_val_score
from sklearn.grid_search import GridSearchCV
from sklearn import datasets

iris = datasets.load_iris()
x = iris.data
y = iris.target

model = PCA(n_components=2)
x_reduced = model.fit_transform(x)
plt.figure(figsize=(3*1.618,3))
plt.scatter(x_reduced[:, 0], x_reduced[:, 1], c=y, cmap=plt.cm.Paired)
plt.savefig('iris_PCA.png')

print np.dot(model.components_[0], model.components_[1])
print model.noise_variance_

model = PCA(n_components=1)
x_reduced = model.fit_transform(x)
y_rand = np.random.normal(scale=0.1, size=x_reduced.shape)
plt.figure(figsize=(3*1.618,1))
plt.scatter(x_reduced[:, 0], y_rand, c=y, cmap=plt.cm.Paired)
plt.ylim(-1,1)
plt.yticks([-1,1])
plt.setp(plt.gca().get_yticklabels(), visible=False)
plt.tight_layout()
plt.savefig('iris_PCA_hist.png')

model = FactorAnalysis(n_components=2)
x_reduced = model.fit_transform(x)
plt.figure(figsize=(3*1.618,3))
plt.scatter(x_reduced[:, 0], x_reduced[:, 1], c=y, cmap=plt.cm.Paired)
plt.savefig('iris_FA.png')

print np.dot(model.components_[0], model.components_[1])
print model.noise_variance_

model = FactorAnalysis(n_components=1)
x_reduced = model.fit_transform(x)
y_rand = np.random.normal(scale=0.1, size=x_reduced.shape)
plt.figure(figsize=(3*1.618,1))
plt.scatter(x_reduced[:, 0], y_rand, c=y, cmap=plt.cm.Paired)
plt.ylim(-1,1)
plt.yticks([-1,1])
plt.setp(plt.gca().get_yticklabels(), visible=False)
plt.tight_layout()
plt.savefig('iris_FA_hist.png')

print model.noise_variance_