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import numpy as np
import scipy.sparse as sp
import pytest
from sklearn.utils.testing import (assert_array_almost_equal, assert_less,
assert_equal, assert_not_equal,
assert_raises, ignore_warnings)
from sklearn.decomposition import PCA, KernelPCA
from sklearn.datasets import make_circles
from sklearn.linear_model import Perceptron
from sklearn.pipeline import Pipeline
from sklearn.model_selection import GridSearchCV
from sklearn.metrics.pairwise import rbf_kernel
def test_kernel_pca():
rng = np.random.RandomState(0)
X_fit = rng.random_sample((5, 4))
X_pred = rng.random_sample((2, 4))
def histogram(x, y, **kwargs):
# Histogram kernel implemented as a callable.
assert_equal(kwargs, {}) # no kernel_params that we didn't ask for
return np.minimum(x, y).sum()
for eigen_solver in ("auto", "dense", "arpack"):
for kernel in ("linear", "rbf", "poly", histogram):
# histogram kernel produces singular matrix inside linalg.solve
# XXX use a least-squares approximation?
inv = not callable(kernel)
# transform fit data
kpca = KernelPCA(4, kernel=kernel, eigen_solver=eigen_solver,
fit_inverse_transform=inv)
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))
# non-regression test: previously, gamma would be 0 by default,
# forcing all eigenvalues to 0 under the poly kernel
assert_not_equal(X_fit_transformed.size, 0)
# transform new data
X_pred_transformed = kpca.transform(X_pred)
assert_equal(X_pred_transformed.shape[1],
X_fit_transformed.shape[1])
# inverse transform
if inv:
X_pred2 = kpca.inverse_transform(X_pred_transformed)
assert_equal(X_pred2.shape, X_pred.shape)
def test_kernel_pca_invalid_parameters():
assert_raises(ValueError, KernelPCA, 10, fit_inverse_transform=True,
kernel='precomputed')
def test_kernel_pca_consistent_transform():
# X_fit_ needs to retain the old, unmodified copy of X
state = np.random.RandomState(0)
X = state.rand(10, 10)
kpca = KernelPCA(random_state=state).fit(X)
transformed1 = kpca.transform(X)
X_copy = X.copy()
X[:, 0] = 666
transformed2 = kpca.transform(X_copy)
assert_array_almost_equal(transformed1, transformed2)
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_remove_zero_eig():
X = np.array([[1 - 1e-30, 1], [1, 1], [1, 1 - 1e-20]])
# n_components=None (default) => remove_zero_eig is True
kpca = KernelPCA()
Xt = kpca.fit_transform(X)
assert_equal(Xt.shape, (3, 0))
kpca = KernelPCA(n_components=2)
Xt = kpca.fit_transform(X)
assert_equal(Xt.shape, (3, 2))
kpca = KernelPCA(n_components=2, remove_zero_eig=True)
Xt = kpca.fit_transform(X)
assert_equal(Xt.shape, (3, 0))
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, eigen_solver=eigen_solver, kernel='precomputed').fit(
np.dot(X_fit, X_fit.T)).transform(np.dot(X_pred, X_fit.T))
X_kpca_train = KernelPCA(
4, eigen_solver=eigen_solver,
kernel='precomputed').fit_transform(np.dot(X_fit, X_fit.T))
X_kpca_train2 = KernelPCA(
4, eigen_solver=eigen_solver, kernel='precomputed').fit(
np.dot(X_fit, X_fit.T)).transform(np.dot(X_fit, X_fit.T))
assert_array_almost_equal(np.abs(X_kpca),
np.abs(X_kpca2))
assert_array_almost_equal(np.abs(X_kpca_train),
np.abs(X_kpca_train2))
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)
@pytest.mark.filterwarnings('ignore: The default of the `iid`') # 0.22
# 0.23. warning about tol not having its correct default value.
@pytest.mark.filterwarnings('ignore:max_iter and tol parameters have been')
def test_gridsearch_pipeline():
# Test if we can do a grid-search to find parameters to separate
# circles with a perceptron model.
X, y = make_circles(n_samples=400, factor=.3, noise=.05,
random_state=0)
kpca = KernelPCA(kernel="rbf", n_components=2)
pipeline = Pipeline([("kernel_pca", kpca),
("Perceptron", Perceptron(max_iter=5))])
param_grid = dict(kernel_pca__gamma=2. ** np.arange(-2, 2))
grid_search = GridSearchCV(pipeline, cv=3, param_grid=param_grid)
grid_search.fit(X, y)
assert_equal(grid_search.best_score_, 1)
@pytest.mark.filterwarnings('ignore: The default of the `iid`') # 0.22
# 0.23. warning about tol not having its correct default value.
@pytest.mark.filterwarnings('ignore:max_iter and tol parameters have been')
def test_gridsearch_pipeline_precomputed():
# Test if we can do a grid-search to find parameters to separate
# circles with a perceptron model using a precomputed kernel.
X, y = make_circles(n_samples=400, factor=.3, noise=.05,
random_state=0)
kpca = KernelPCA(kernel="precomputed", n_components=2)
pipeline = Pipeline([("kernel_pca", kpca),
("Perceptron", Perceptron(max_iter=5))])
param_grid = dict(Perceptron__max_iter=np.arange(1, 5))
grid_search = GridSearchCV(pipeline, cv=3, param_grid=param_grid)
X_kernel = rbf_kernel(X, gamma=2.)
grid_search.fit(X_kernel, y)
assert_equal(grid_search.best_score_, 1)
# 0.23. warning about tol not having its correct default value.
@pytest.mark.filterwarnings('ignore:max_iter and tol parameters have been')
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(max_iter=5).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=2.)
X_kpca = kpca.fit_transform(X)
# The data is perfectly linearly separable in that space
train_score = Perceptron(max_iter=5).fit(X_kpca, y).score(X_kpca, y)
assert_equal(train_score, 1.0)
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