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import numpy as np
import scipy.sparse as sp
from numpy.testing import assert_array_almost_equal
from nose.tools import assert_equal
from nose.tools import assert_raises
from sklearn.decomposition import PCA, KernelPCA
from sklearn.datasets import make_circles
from sklearn.linear_model import Perceptron
from sklearn.utils.testing import assert_less
def test_kernel_pca():
rng = np.random.RandomState(0)
X_fit = rng.random_sample((5, 4))
X_pred = rng.random_sample((2, 4))
for eigen_solver in ("auto", "dense", "arpack"):
for kernel in ("linear", "rbf", "poly"):
# transform fit data
kpca = KernelPCA(4, kernel=kernel, eigen_solver=eigen_solver,
fit_inverse_transform=True)
X_fit_transformed = kpca.fit_transform(X_fit)
X_fit_transformed2 = kpca.fit(X_fit).transform(X_fit)
assert_array_almost_equal(np.abs(X_fit_transformed),
np.abs(X_fit_transformed2))
# transform new data
X_pred_transformed = kpca.transform(X_pred)
assert_equal(X_pred_transformed.shape[1],
X_fit_transformed.shape[1])
# inverse transform
X_pred2 = kpca.inverse_transform(X_pred_transformed)
assert_equal(X_pred2.shape, X_pred.shape)
def test_invalid_parameters():
assert_raises(ValueError, KernelPCA, 10, fit_inverse_transform=True,
kernel='precomputed')
def test_kernel_pca_sparse():
rng = np.random.RandomState(0)
X_fit = sp.csr_matrix(rng.random_sample((5, 4)))
X_pred = sp.csr_matrix(rng.random_sample((2, 4)))
for eigen_solver in ("auto", "arpack"):
for kernel in ("linear", "rbf", "poly"):
# transform fit data
kpca = KernelPCA(4, kernel=kernel, eigen_solver=eigen_solver,
fit_inverse_transform=False)
X_fit_transformed = kpca.fit_transform(X_fit)
X_fit_transformed2 = kpca.fit(X_fit).transform(X_fit)
assert_array_almost_equal(np.abs(X_fit_transformed),
np.abs(X_fit_transformed2))
# transform new data
X_pred_transformed = kpca.transform(X_pred)
assert_equal(X_pred_transformed.shape[1],
X_fit_transformed.shape[1])
# inverse transform
#X_pred2 = kpca.inverse_transform(X_pred_transformed)
#assert_equal(X_pred2.shape, X_pred.shape)
def test_kernel_pca_linear_kernel():
rng = np.random.RandomState(0)
X_fit = rng.random_sample((5, 4))
X_pred = rng.random_sample((2, 4))
# for a linear kernel, kernel PCA should find the same projection as PCA
# modulo the sign (direction)
# fit only the first four components: fifth is near zero eigenvalue, so
# can be trimmed due to roundoff error
assert_array_almost_equal(
np.abs(KernelPCA(4).fit(X_fit).transform(X_pred)),
np.abs(PCA(4).fit(X_fit).transform(X_pred)))
def test_kernel_pca_n_components():
rng = np.random.RandomState(0)
X_fit = rng.random_sample((5, 4))
X_pred = rng.random_sample((2, 4))
for eigen_solver in ("dense", "arpack"):
for c in [1, 2, 4]:
kpca = KernelPCA(n_components=c, eigen_solver=eigen_solver)
shape = kpca.fit(X_fit).transform(X_pred).shape
assert_equal(shape, (2, c))
def test_kernel_pca_precomputed():
rng = np.random.RandomState(0)
X_fit = rng.random_sample((5, 4))
X_pred = rng.random_sample((2, 4))
for eigen_solver in ("dense", "arpack"):
X_kpca = KernelPCA(4, eigen_solver=eigen_solver).\
fit(X_fit).transform(X_pred)
X_kpca2 = KernelPCA(4, kernel="precomputed",
eigen_solver=eigen_solver).\
fit(np.dot(X_fit, X_fit.T)).\
transform(np.dot(X_pred, X_fit.T))
assert_array_almost_equal(np.abs(X_kpca),
np.abs(X_kpca2))
def test_kernel_pca_invalid_kernel():
rng = np.random.RandomState(0)
X_fit = rng.random_sample((2, 4))
kpca = KernelPCA(kernel="tototiti")
assert_raises(ValueError, kpca.fit, X_fit)
def test_nested_circles():
"""Test the linear separability of the first 2D KPCA transform"""
X, y = make_circles(n_samples=400, factor=.3, noise=.05,
random_state=0)
# 2D nested circles are not linearly separable
train_score = Perceptron().fit(X, y).score(X, y)
assert_less(train_score, 0.8)
# Project the circles data into the first 2 components of a RBF Kernel
# PCA model.
# Note that the gamma value is data dependent. If this test breaks
# and the gamma value has to be updated, the Kernel PCA example will
# have to be updated too.
kpca = KernelPCA(kernel="rbf", n_components=2,
fit_inverse_transform=True, gamma=10.)
X_kpca = kpca.fit_transform(X)
# The data is perfectly linearly separable in that space
train_score = Perceptron().fit(X_kpca, y).score(X_kpca, y)
assert_equal(train_score, 1.0)
if __name__ == '__main__':
import nose
nose.run(argv=['', __file__])
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