"""
The eigenfaces example: chaining PCA and SVMs
=============================================
The goal of this example is to show how an unsupervised method and a
supervised one can be chained for better prediction. It starts with a
didactic but lengthy way of doing things, and finishes with the
idiomatic approach to pipelining in scikit-learn.
Here we'll take a look at a simple facial recognition example. Ideally,
we would use a dataset consisting of a subset of the `Labeled Faces in
the Wild `__ data that is available
with :func:`sklearn.datasets.fetch_lfw_people`. However, this is a
relatively large download (~200MB) so we will do the tutorial on a
simpler, less rich dataset. Feel free to explore the LFW dataset.
"""
from sklearn import datasets
faces = datasets.fetch_olivetti_faces()
faces.data.shape
############################################################
# Let's visualize these faces to see what we're working with
from matplotlib import pyplot as plt
fig = plt.figure(figsize=(8, 6))
# plot several images
for i in range(15):
ax = fig.add_subplot(3, 5, i + 1, xticks=[], yticks=[])
ax.imshow(faces.images[i], cmap=plt.cm.bone)
############################################################
# .. tip::
#
# Note is that these faces have already been localized and scaled to a
# common size. This is an important preprocessing piece for facial
# recognition, and is a process that can require a large collection of
# training data. This can be done in scikit-learn, but the challenge is
# gathering a sufficient amount of training data for the algorithm to work.
# Fortunately, this piece is common enough that it has been done. One good
# resource is
# `OpenCV `__, the
# *Open Computer Vision Library*.
#
# We'll perform a Support Vector classification of the images. We'll do a
# typical train-test split on the images:
from sklearn.model_selection import train_test_split
X_train, X_test, y_train, y_test = train_test_split(faces.data,
faces.target, random_state=0)
print(X_train.shape, X_test.shape)
############################################################
# Preprocessing: Principal Component Analysis
# -------------------------------------------
#
# 1850 dimensions is a lot for SVM. We can use PCA to reduce these 1850
# features to a manageable size, while maintaining most of the information
# in the dataset.
from sklearn import decomposition
pca = decomposition.PCA(n_components=150, whiten=True)
pca.fit(X_train)
############################################################
# One interesting part of PCA is that it computes the "mean" face, which
# can be interesting to examine:
plt.imshow(pca.mean_.reshape(faces.images[0].shape),
cmap=plt.cm.bone)
############################################################
# The principal components measure deviations about this mean along
# orthogonal axes.
print(pca.components_.shape)
############################################################
# It is also interesting to visualize these principal components:
fig = plt.figure(figsize=(16, 6))
for i in range(30):
ax = fig.add_subplot(3, 10, i + 1, xticks=[], yticks=[])
ax.imshow(pca.components_[i].reshape(faces.images[0].shape),
cmap=plt.cm.bone)
############################################################
# The components ("eigenfaces") are ordered by their importance from
# top-left to bottom-right. We see that the first few components seem to
# primarily take care of lighting conditions; the remaining components
# pull out certain identifying features: the nose, eyes, eyebrows, etc.
#
# With this projection computed, we can now project our original training
# and test data onto the PCA basis:
X_train_pca = pca.transform(X_train)
X_test_pca = pca.transform(X_test)
print(X_train_pca.shape)
############################################################
print(X_test_pca.shape)
############################################################
# These projected components correspond to factors in a linear combination
# of component images such that the combination approaches the original
# face.
#
# Doing the Learning: Support Vector Machines
# -------------------------------------------
#
# Now we'll perform support-vector-machine classification on this reduced
# dataset:
from sklearn import svm
clf = svm.SVC(C=5., gamma=0.001)
clf.fit(X_train_pca, y_train)
############################################################
# Finally, we can evaluate how well this classification did. First, we
# might plot a few of the test-cases with the labels learned from the
# training set:
import numpy as np
fig = plt.figure(figsize=(8, 6))
for i in range(15):
ax = fig.add_subplot(3, 5, i + 1, xticks=[], yticks=[])
ax.imshow(X_test[i].reshape(faces.images[0].shape),
cmap=plt.cm.bone)
y_pred = clf.predict(X_test_pca[i, np.newaxis])[0]
color = ('black' if y_pred == y_test[i] else 'red')
ax.set_title(faces.target[y_pred],
fontsize='small', color=color)
############################################################
# The classifier is correct on an impressive number of images given the
# simplicity of its learning model! Using a linear classifier on 150
# features derived from the pixel-level data, the algorithm correctly
# identifies a large number of the people in the images.
#
# Again, we can quantify this effectiveness using one of several measures
# from :mod:`sklearn.metrics`. First we can do the classification
# report, which shows the precision, recall and other measures of the
# "goodness" of the classification:
from sklearn import metrics
y_pred = clf.predict(X_test_pca)
print(metrics.classification_report(y_test, y_pred))
############################################################
# Another interesting metric is the *confusion matrix*, which indicates
# how often any two items are mixed-up. The confusion matrix of a perfect
# classifier would only have nonzero entries on the diagonal, with zeros
# on the off-diagonal:
print(metrics.confusion_matrix(y_test, y_pred))
############################################################
# Pipelining
# ----------
#
# Above we used PCA as a pre-processing step before applying our support
# vector machine classifier. Plugging the output of one estimator directly
# into the input of a second estimator is a commonly used pattern; for
# this reason scikit-learn provides a ``Pipeline`` object which automates
# this process. The above problem can be re-expressed as a pipeline as
# follows:
from sklearn.pipeline import Pipeline
clf = Pipeline([('pca', decomposition.PCA(n_components=150, whiten=True)),
('svm', svm.LinearSVC(C=1.0))])
clf.fit(X_train, y_train)
y_pred = clf.predict(X_test)
print(metrics.confusion_matrix(y_pred, y_test))
plt.show()
############################################################
# A Note on Facial Recognition
# ----------------------------
#
# Here we have used PCA "eigenfaces" as a pre-processing step for facial
# recognition. The reason we chose this is because PCA is a
# broadly-applicable technique, which can be useful for a wide array of
# data types. Research in the field of facial recognition in particular,
# however, has shown that other more specific feature extraction methods
# are can be much more effective.