Faces dataset decompositions

This example applies to The Olivetti faces dataset different unsupervised matrix decomposition (dimension reduction) methods from the module sklearn.decomposition (see the documentation chapter Decomposing signals in components (matrix factorization problems)) .

print(__doc__)

# Authors: Vlad Niculae, Alexandre Gramfort
# License: BSD 3 clause

import logging
from time import time

from numpy.random import RandomState
import matplotlib.pyplot as plt

from sklearn.datasets import fetch_olivetti_faces
from sklearn.cluster import MiniBatchKMeans
from sklearn import decomposition

# Display progress logs on stdout
logging.basicConfig(level=logging.INFO,
                    format='%(asctime)s %(levelname)s %(message)s')
n_row, n_col = 2, 3
n_components = n_row * n_col
image_shape = (64, 64)
rng = RandomState(0)

Load faces data

dataset = fetch_olivetti_faces(shuffle=True, random_state=rng)
faces = dataset.data

n_samples, n_features = faces.shape

# global centering
faces_centered = faces - faces.mean(axis=0)

# local centering
faces_centered -= faces_centered.mean(axis=1).reshape(n_samples, -1)

print("Dataset consists of %d faces" % n_samples)

Out:

Dataset consists of 400 faces

def plot_gallery(title, images, n_col=n_col, n_row=n_row):
    plt.figure(figsize=(2. * n_col, 2.26 * n_row))
    plt.suptitle(title, size=16)
    for i, comp in enumerate(images):
        plt.subplot(n_row, n_col, i + 1)
        vmax = max(comp.max(), -comp.min())
        plt.imshow(comp.reshape(image_shape), cmap=plt.cm.gray,
                   interpolation='nearest',
                   vmin=-vmax, vmax=vmax)
        plt.xticks(())
        plt.yticks(())
    plt.subplots_adjust(0.01, 0.05, 0.99, 0.93, 0.04, 0.)

List of the different estimators, whether to center and transpose the problem, and whether the transformer uses the clustering API.

estimators = [
    ('Eigenfaces - PCA using randomized SVD',
     decomposition.PCA(n_components=n_components, svd_solver='randomized',
                       whiten=True),
     True),

    ('Non-negative components - NMF',
     decomposition.NMF(n_components=n_components, init='nndsvda', tol=5e-3),
     False),

    ('Independent components - FastICA',
     decomposition.FastICA(n_components=n_components, whiten=True),
     True),

    ('Sparse comp. - MiniBatchSparsePCA',
     decomposition.MiniBatchSparsePCA(n_components=n_components, alpha=0.8,
                                      n_iter=100, batch_size=3,
                                      random_state=rng),
     True),

    ('MiniBatchDictionaryLearning',
        decomposition.MiniBatchDictionaryLearning(n_components=15, alpha=0.1,
                                                  n_iter=50, batch_size=3,
                                                  random_state=rng),
     True),

    ('Cluster centers - MiniBatchKMeans',
        MiniBatchKMeans(n_clusters=n_components, tol=1e-3, batch_size=20,
                        max_iter=50, random_state=rng),
     True),

    ('Factor Analysis components - FA',
     decomposition.FactorAnalysis(n_components=n_components, max_iter=2),
     True),
]

Plot a sample of the input data

plot_gallery("First centered Olivetti faces", faces_centered[:n_components])

Do the estimation and plot it

for name, estimator, center in estimators:
    print("Extracting the top %d %s..." % (n_components, name))
    t0 = time()
    data = faces
    if center:
        data = faces_centered
    estimator.fit(data)
    train_time = (time() - t0)
    print("done in %0.3fs" % train_time)
    if hasattr(estimator, 'cluster_centers_'):
        components_ = estimator.cluster_centers_
    else:
        components_ = estimator.components_
    if (hasattr(estimator, 'noise_variance_') and
            estimator.noise_variance_.shape != ()):
        plot_gallery("Pixelwise variance",
                     estimator.noise_variance_.reshape(1, -1), n_col=1,
                     n_row=1)
    plot_gallery('%s - Train time %.1fs' % (name, train_time),
                 components_[:n_components])

plt.show()

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Out:

  Extracting the top 6 Eigenfaces - PCA using randomized SVD...
done in 0.094s
Extracting the top 6 Non-negative components - NMF...
done in 0.660s
Extracting the top 6 Independent components - FastICA...
done in 0.319s
Extracting the top 6 Sparse comp. - MiniBatchSparsePCA...
done in 1.134s
Extracting the top 6 MiniBatchDictionaryLearning...
done in 1.007s
Extracting the top 6 Cluster centers - MiniBatchKMeans...
done in 0.096s
Extracting the top 6 Factor Analysis components - FA...
done in 0.137s

Total running time of the script: (0 minutes 6.636 seconds)

Download Python source code: plot_faces_decomposition.py

Download IPython notebook: plot_faces_decomposition.ipynb