%matplotlib inline
import numpy as np
import matplotlib.pyplot as plt
from scipy import stats

# use seaborn plotting defaults
import seaborn as sns; sns.set()

from sklearn.datasets import fetch_lfw_people
faces = fetch_lfw_people(min_faces_per_person=70, resize=0.4)

X, y = faces.data, faces.target

from sklearn.decomposition import PCA
pca = PCA().fit(X)
pca

pca.n_components_

plt.axes(xscale='log')
plt.plot(pca.explained_variance_ratio_.cumsum())
plt.xlabel('number of components')
plt.ylabel('cubulative variance ratio');

pca = PCA(n_components=0.90)
pca.fit(X)
pca.n_components_

imshape = faces.images.shape[-2:]

plt.axes(xticks=[], yticks=[])
plt.imshow(pca.mean_.reshape(imshape), cmap='binary_r');

fig, ax = plt.subplots(2, 5, figsize=(14, 6),
                       subplot_kw=dict(xticks=[], yticks=[]))
for i in range(10):
    ax.flat[i].imshow(pca.components_[i].reshape(imshape),
                      cmap='binary_r')

pca = PCA().fit(X)

def plot_face(i=279):
    fig, ax = plt.subplots(1, 6, figsize=(14, 3),
                           subplot_kw=dict(xticks=[], yticks=[]))
    ax[0].imshow(X[i].reshape(imshape), cmap='binary_r');
        
    for j, ncomp in enumerate([10, 20, 40, 80, 100]):
        approx = pca.mean_ + np.dot(pca.transform(X[i:i + 1])[:, :ncomp],
                                    pca.components_[:ncomp])
        ax[j + 1].imshow(approx.reshape(imshape), cmap='binary_r')
        ax[j + 1].set_title('{0} components'.format(ncomp))

plot_face(700)

from IPython.html.widgets import interact
interact(plot_face, i=(0, X.shape[0] - 1));