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)) .

• 
• 
• 
• 
• 
• 
• 
• 
• 
• 
• 
• 
• 
• 

Out:

Dataset consists of 400 faces
Extracting the top 6 Eigenfaces - PCA using randomized SVD...
done in 0.025s
Extracting the top 6 Non-negative components - NMF...
done in 0.115s
Extracting the top 6 Independent components - FastICA...
done in 0.131s
Extracting the top 6 Sparse comp. - MiniBatchSparsePCA...
done in 0.577s
Extracting the top 6 MiniBatchDictionaryLearning...
done in 0.353s
Extracting the top 6 Cluster centers - MiniBatchKMeans...
done in 0.045s
Extracting the top 6 Factor Analysis components - FA...
done in 0.186s
Extracting the top 6 Dictionary learning...
done in 0.342s
Extracting the top 6 Dictionary learning - positive dictionary...
done in 0.378s
Extracting the top 6 Dictionary learning - positive code...
done in 0.130s
Extracting the top 6 Dictionary learning - positive dictionary & code...
done in 0.160s

# 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
faces, _ = fetch_olivetti_faces(return_X_y=True, shuffle=True, random_state=rng)
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)


def plot_gallery(title, images, n_col=n_col, n_row=n_row, cmap=plt.cm.gray):
    plt.figure(figsize=(2.0 * 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=cmap,
            interpolation="nearest",
            vmin=-vmax,
            vmax=vmax,
        )
        plt.xticks(())
        plt.yticks(())
    plt.subplots_adjust(0.01, 0.05, 0.99, 0.93, 0.04, 0.0)


# #############################################################################
# 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=20),
        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_

    # Plot an image representing the pixelwise variance provided by the
    # estimator e.g its noise_variance_ attribute. The Eigenfaces estimator,
    # via the PCA decomposition, also provides a scalar noise_variance_
    # (the mean of pixelwise variance) that cannot be displayed as an image
    # so we skip it.
    if (
        hasattr(estimator, "noise_variance_") and estimator.noise_variance_.ndim > 0
    ):  # Skip the Eigenfaces case
        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()

# #############################################################################
# Various positivity constraints applied to dictionary learning.
estimators = [
    (
        "Dictionary learning",
        decomposition.MiniBatchDictionaryLearning(
            n_components=15, alpha=0.1, n_iter=50, batch_size=3, random_state=rng
        ),
        True,
    ),
    (
        "Dictionary learning - positive dictionary",
        decomposition.MiniBatchDictionaryLearning(
            n_components=15,
            alpha=0.1,
            n_iter=50,
            batch_size=3,
            random_state=rng,
            positive_dict=True,
        ),
        True,
    ),
    (
        "Dictionary learning - positive code",
        decomposition.MiniBatchDictionaryLearning(
            n_components=15,
            alpha=0.1,
            n_iter=50,
            batch_size=3,
            fit_algorithm="cd",
            random_state=rng,
            positive_code=True,
        ),
        True,
    ),
    (
        "Dictionary learning - positive dictionary & code",
        decomposition.MiniBatchDictionaryLearning(
            n_components=15,
            alpha=0.1,
            n_iter=50,
            batch_size=3,
            fit_algorithm="cd",
            random_state=rng,
            positive_dict=True,
            positive_code=True,
        ),
        True,
    ),
]


# #############################################################################
# Plot a sample of the input data

plot_gallery(
    "First centered Olivetti faces", faces_centered[:n_components], cmap=plt.cm.RdBu
)

# #############################################################################
# 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)
    components_ = estimator.components_
    plot_gallery(name, components_[:n_components], cmap=plt.cm.RdBu)

plt.show()