scikit-learn/examples/plot_kernel_approximation.py

"""
==================================================
Explicit feature map approximation for RBF kernels
==================================================

An example shows how to use RBFSampler to appoximate
the feature map of an RBF kernel. Results for varying
amounts of Monte Carlo samplings are shown.

"""
print __doc__

# Author: Gael Varoquaux <gael dot varoquaux at normalesup dot org>
#         modified Andreas Mueller
# License: Simplified BSD

# Standard scientific Python imports
import pylab as pl
import numpy as np

# Import datasets, classifiers and performance metrics
from sklearn import datasets, svm, pipeline
from sklearn.kernel_approximation import RBFSampler

# The digits dataset
digits = datasets.load_digits()

# To apply an classifier on this data, we need to flatten the image, to
# turn the data in a (samples, feature) matrix:
n_samples = len(digits.images)
data = digits.images.reshape((n_samples, -1))

# We learn the digits on the first half of the digits
data_train, targets_train = data[:n_samples/2], digits.target[:n_samples/2]

# Now predict the value of the digit on the second half:
data_test, targets_test = data[n_samples/2:], digits.target[n_samples/2:]

# Create a classifier: a support vector classifier
kernel_svm = svm.SVC(gamma=0.001)
linear_svm = svm.LinearSVC()

# create pipeline from kernel approximation
# and linear svm
feature_map = RBFSampler(gamma=0.001)
approx_kernel_svm = pipeline.Pipeline([("feature_map", feature_map),
    ("svm", svm.LinearSVC())])

# fit and predict using linear and kernel svm:
kernel_svm.fit(data_train, targets_train)
kernel_svm_score = kernel_svm.score(data_test, targets_test)

linear_svm.fit(data_train, targets_train)
linear_svm_score = linear_svm.score(data_test, targets_test)

sample_sizes = 20*np.arange(1,15)
approx_kernel_scores = []
for D in sample_sizes:
    approx_kernel_svm.set_params(feature_map__n_components=D)
    approx_kernel_svm.fit(data_train, targets_train)
    score = approx_kernel_svm.score(data_test, targets_test)
    approx_kernel_scores.append(score)

# plot the results:
pl.plot(sample_sizes, approx_kernel_scores, label="approximate kernel")

# horizontal lines for exact rbf and linear kernels:
pl.plot([sample_sizes[0], sample_sizes[-1]], [linear_svm_score, linear_svm_score], label="linear svm")
pl.plot([sample_sizes[0], sample_sizes[-1]], [kernel_svm_score, kernel_svm_score], label="rbf svm")

# vertical line for dataset dimensionality = 64
pl.plot([64, 64], [0.7, 1], label="original dimensionality")

# legends and labels
pl.xlim(sample_sizes[0], sample_sizes[-1])
pl.ylim(np.min(approx_kernel_scores),1)
pl.xlabel("Sampling steps = transformed feature dimension")
pl.ylabel("Classification accuracy")
pl.legend()
pl.show()