X, T = datasets.make_circles(n_samples, noise=sigma, factor=0.5)
n_components = 2
plt.figure(figsize=(8, 6))
n_rows, n_cols = 2, 2
marker = 'x'
color = T
cmap = plt.cm.Paired
plt.subplot(n_rows, n_cols, 1)
plt.scatter(X[:, 0], X[:, 1], marker=marker, color=T, cmap=cmap)
plt.title('Origin')
pca = PCA(n_components)
Y_pca = pca.fit(X)
plt.subplot(n_rows, n_cols, 2)
plt.scatter(Y_pca[:, 0], Y_pca[:, 1], marker=marker, color=T, cmap=cmap)
plt.title('PCA')
sigma_gaussian = 0.2
kpca = KernelPCA(n_components, kernel='gaussian', sigma=sigma_gaussian)
Y_kpca = kpca.fit(X)
plt.subplot(n_rows, n_cols, 3)
plt.scatter(Y_kpca[:, 0], Y_kpca[:, 1], marker=marker, color=T, cmap=cmap)
plt.title('KPCA(Gaussian): $\sigma$={0}'.format(sigma_gaussian))
degree = 9
coef0 = 1
kpca = KernelPCA(n_components, kernel='polynomial', degree=degree, coef0=coef0)
Y_kpca = kpca.fit(X)
from mlpy.model import PCA
from mlpy.util import loadMNISTImages, loadMNISTLabels
X = loadMNISTImages('../../mnist/train-images-idx3-ubyte')
T = loadMNISTLabels('../../mnist/train-labels-idx1-ubyte')
digit3_idx = sp.nonzero(T == 3)[0]
digit3_T = T[digit3_idx]
digit3_X = X[digit3_idx]
n_digit3, n_features = digit3_X.shape
n_sqrt_features = int(sp.sqrt(n_features))
n_components = 4
pca = PCA(M=n_components)
Y = pca.fit(digit3_X)
cov = sp.cov(digit3_X, rowvar=0)
eigvals, eigvecs = pca.eigvals, pca.eigvecs
digit3_mean = digit3_X.mean(axis=0)
# Show the Figures 12.3 on Page 566 of the book
n_figrows, n_figcols = 2, n_components + 1
plt.figure(figsize=(10, 4))
plt.subplot(n_figrows, n_figcols, 1)
plt.imshow(
digit3_mean.reshape((n_sqrt_features, n_sqrt_features)),
cmap=plt.cm.Greys_r,
interpolation='none')
plt.title('Mean')