projektAI/venv/Lib/site-packages/sklearn/decomposition/tests/test_kernel_pca.py

328 lines
12 KiB
Python
Raw Normal View History

2021-06-06 22:13:05 +02:00
import numpy as np
import scipy.sparse as sp
import pytest
from sklearn.utils._testing import (assert_array_almost_equal,
assert_allclose)
from sklearn.decomposition import PCA, KernelPCA
from sklearn.datasets import make_circles
from sklearn.datasets import make_blobs
from sklearn.linear_model import Perceptron
from sklearn.pipeline import Pipeline
from sklearn.preprocessing import StandardScaler
from sklearn.model_selection import GridSearchCV
from sklearn.metrics.pairwise import rbf_kernel
from sklearn.utils.validation import _check_psd_eigenvalues
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 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 X_fit_transformed.size != 0
# transform new data
X_pred_transformed = kpca.transform(X_pred)
assert (X_pred_transformed.shape[1] ==
X_fit_transformed.shape[1])
# inverse transform
if inv:
X_pred2 = kpca.inverse_transform(X_pred_transformed)
assert X_pred2.shape == X_pred.shape
def test_kernel_pca_invalid_parameters():
with pytest.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_deterministic_output():
rng = np.random.RandomState(0)
X = rng.rand(10, 10)
eigen_solver = ('arpack', 'dense')
for solver in eigen_solver:
transformed_X = np.zeros((20, 2))
for i in range(20):
kpca = KernelPCA(n_components=2, eigen_solver=solver,
random_state=rng)
transformed_X[i, :] = kpca.fit_transform(X)[0]
assert_allclose(
transformed_X, np.tile(transformed_X[0, :], 20).reshape(20, 2))
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 (X_pred_transformed.shape[1] ==
X_fit_transformed.shape[1])
# inverse transform
# X_pred2 = kpca.inverse_transform(X_pred_transformed)
# assert 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 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 Xt.shape == (3, 0)
kpca = KernelPCA(n_components=2)
Xt = kpca.fit_transform(X)
assert Xt.shape == (3, 2)
kpca = KernelPCA(n_components=2, remove_zero_eig=True)
Xt = kpca.fit_transform(X)
assert Xt.shape == (3, 0)
def test_leave_zero_eig():
"""This test checks that fit().transform() returns the same result as
fit_transform() in case of non-removed zero eigenvalue.
Non-regression test for issue #12141 (PR #12143)"""
X_fit = np.array([[1, 1], [0, 0]])
# Assert that even with all np warnings on, there is no div by zero warning
with pytest.warns(None) as record:
with np.errstate(all='warn'):
k = KernelPCA(n_components=2, remove_zero_eig=False,
eigen_solver="dense")
# Fit, then transform
A = k.fit(X_fit).transform(X_fit)
# Do both at once
B = k.fit_transform(X_fit)
# Compare
assert_array_almost_equal(np.abs(A), np.abs(B))
for w in record:
# There might be warnings about the kernel being badly conditioned,
# but there should not be warnings about division by zero.
# (Numpy division by zero warning can have many message variants, but
# at least we know that it is a RuntimeWarning so lets check only this)
assert not issubclass(w.category, RuntimeWarning)
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")
with pytest.raises(ValueError):
kpca.fit(X_fit)
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 grid_search.best_score_ == 1
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 grid_search.best_score_ == 1
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 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 train_score == 1.0
def test_kernel_conditioning():
""" Test that ``_check_psd_eigenvalues`` is correctly called
Non-regression test for issue #12140 (PR #12145)"""
# create a pathological X leading to small non-zero eigenvalue
X = [[5, 1],
[5+1e-8, 1e-8],
[5+1e-8, 0]]
kpca = KernelPCA(kernel="linear", n_components=2,
fit_inverse_transform=True)
kpca.fit(X)
# check that the small non-zero eigenvalue was correctly set to zero
assert kpca.lambdas_.min() == 0
assert np.all(kpca.lambdas_ == _check_psd_eigenvalues(kpca.lambdas_))
def test_kernel_pca_inverse_transform_reconstruction():
# Test if the reconstruction is a good approximation.
# Note that in general it is not possible to get an arbitrarily good
# reconstruction because of kernel centering that does not
# preserve all the information of the original data.
X, *_ = make_blobs(n_samples=100, n_features=4, random_state=0)
kpca = KernelPCA(
n_components=20, kernel='rbf', fit_inverse_transform=True, alpha=1e-3
)
X_trans = kpca.fit_transform(X)
X_reconst = kpca.inverse_transform(X_trans)
assert np.linalg.norm(X - X_reconst) / np.linalg.norm(X) < 1e-1
def test_32_64_decomposition_shape():
""" Test that the decomposition is similar for 32 and 64 bits data """
# see https://github.com/scikit-learn/scikit-learn/issues/18146
X, y = make_blobs(
n_samples=30,
centers=[[0, 0, 0], [1, 1, 1]],
random_state=0,
cluster_std=0.1
)
X = StandardScaler().fit_transform(X)
X -= X.min()
# Compare the shapes (corresponds to the number of non-zero eigenvalues)
kpca = KernelPCA()
assert (kpca.fit_transform(X).shape ==
kpca.fit_transform(X.astype(np.float32)).shape)
# TODO: Remove in 1.1
def test_kernel_pcc_pairwise_is_deprecated():
kp = KernelPCA(kernel='precomputed')
msg = r"Attribute _pairwise was deprecated in version 0\.24"
with pytest.warns(FutureWarning, match=msg):
kp._pairwise