def test_nystroem_approximation():
# some basic tests
rnd = np.random.RandomState(0)
X = rnd.uniform(size=(10, 4))
# With n_components = n_samples this is exact
X_transformed = Nystroem(n_components=X.shape[0]).fit_transform(X)
K = rbf_kernel(X)
assert_array_almost_equal(np.dot(X_transformed, X_transformed.T), K)
trans = Nystroem(n_components=2, random_state=rnd)
X_transformed = trans.fit(X).transform(X)
assert X_transformed.shape == (X.shape[0], 2)
# test callable kernel
def linear_kernel(X, Y):
return np.dot(X, Y.T)
trans = Nystroem(n_components=2, kernel=linear_kernel, random_state=rnd)
X_transformed = trans.fit(X).transform(X)
assert X_transformed.shape == (X.shape[0], 2)
# test that available kernels fit and transform
kernels_available = kernel_metrics()
for kern in kernels_available:
trans = Nystroem(n_components=2, kernel=kern, random_state=rnd)
X_transformed = trans.fit(X).transform(X)
assert X_transformed.shape == (X.shape[0], 2)
def test_decision_function():
# Test decision_function
# Sanity check, test that decision_function implemented in python
# returns the same as the one in libsvm
# multi class:
clf = svm.SVC(kernel='linear', C=0.1,
decision_function_shape='ovo').fit(iris.data, iris.target)
dec = np.dot(iris.data, clf.coef_.T) + clf.intercept_
assert_array_almost_equal(dec, clf.decision_function(iris.data))
# binary:
clf.fit(X, Y)
dec = np.dot(X, clf.coef_.T) + clf.intercept_
prediction = clf.predict(X)
assert_array_almost_equal(dec.ravel(), clf.decision_function(X))
assert_array_almost_equal(
prediction,
clf.classes_[(clf.decision_function(X) > 0).astype(np.int)])
expected = np.array([-1., -0.66, -1., 0.66, 1., 1.])
assert_array_almost_equal(clf.decision_function(X), expected, 2)
# kernel binary:
clf = svm.SVC(kernel='rbf', gamma=1, decision_function_shape='ovo')
clf.fit(X, Y)
rbfs = rbf_kernel(X, clf.support_vectors_, gamma=clf.gamma)
dec = np.dot(rbfs, clf.dual_coef_.T) + clf.intercept_
assert_array_almost_equal(dec.ravel(), clf.decision_function(X))
def test_pairwise_kernels_callable():
# Test the pairwise_kernels helper function
# with a callable function, with given keywords.
rng = np.random.RandomState(0)
X = rng.random_sample((5, 4))
Y = rng.random_sample((2, 4))
metric = callable_rbf_kernel
kwds = {'gamma': 0.1}
K1 = pairwise_kernels(X, Y=Y, metric=metric, **kwds)
K2 = rbf_kernel(X, Y=Y, **kwds)
assert_array_almost_equal(K1, K2)
# callable function, X=Y
K1 = pairwise_kernels(X, Y=X, metric=metric, **kwds)
K2 = rbf_kernel(X, Y=X, **kwds)
assert_array_almost_equal(K1, K2)
def test_spectral_embedding_deterministic():
# Test that Spectral Embedding is deterministic
random_state = np.random.RandomState(36)
data = random_state.randn(10, 30)
sims = rbf_kernel(data)
embedding_1 = spectral_embedding(sims)
embedding_2 = spectral_embedding(sims)
assert_array_almost_equal(embedding_1, embedding_2)
def test_pairwise_kernels_filter_param():
rng = np.random.RandomState(0)
X = rng.random_sample((5, 4))
Y = rng.random_sample((2, 4))
K = rbf_kernel(X, Y, gamma=0.1)
params = {"gamma": 0.1, "blabla": ":)"}
K2 = pairwise_kernels(X, Y, metric="rbf", filter_params=True, **params)
assert_array_almost_equal(K, K2)
assert_raises(TypeError, pairwise_kernels, X, Y, "rbf", **params)
def test_spectral_embedding_callable_affinity(seed=36):
# Test spectral embedding with callable affinity
gamma = 0.9
kern = rbf_kernel(S, gamma=gamma)
se_callable = SpectralEmbedding(
n_components=2,
affinity=(lambda x: rbf_kernel(x, gamma=gamma)),
gamma=gamma,
random_state=np.random.RandomState(seed))
se_rbf = SpectralEmbedding(n_components=2,
affinity="rbf",
gamma=gamma,
random_state=np.random.RandomState(seed))
embed_rbf = se_rbf.fit_transform(S)
embed_callable = se_callable.fit_transform(S)
assert_array_almost_equal(se_callable.affinity_matrix_,
se_rbf.affinity_matrix_)
assert_array_almost_equal(kern, se_rbf.affinity_matrix_)
assert _check_with_col_sign_flipping(embed_rbf, embed_callable, 0.05)
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_nystroem_singular_kernel():
# test that nystroem works with singular kernel matrix
rng = np.random.RandomState(0)
X = rng.rand(10, 20)
X = np.vstack([X] * 2) # duplicate samples
gamma = 100
N = Nystroem(gamma=gamma, n_components=X.shape[0]).fit(X)
X_transformed = N.transform(X)
K = rbf_kernel(X, gamma=gamma)
assert_array_almost_equal(K, np.dot(X_transformed, X_transformed.T))
assert np.all(np.isfinite(Y))
def test_spectral_embedding_precomputed_affinity(seed=36):
# Test spectral embedding with precomputed kernel
gamma = 1.0
se_precomp = SpectralEmbedding(n_components=2,
affinity="precomputed",
random_state=np.random.RandomState(seed))
se_rbf = SpectralEmbedding(n_components=2,
affinity="rbf",
gamma=gamma,
random_state=np.random.RandomState(seed))
embed_precomp = se_precomp.fit_transform(rbf_kernel(S, gamma=gamma))
embed_rbf = se_rbf.fit_transform(S)
assert_array_almost_equal(se_precomp.affinity_matrix_,
se_rbf.affinity_matrix_)
assert _check_with_col_sign_flipping(embed_precomp, embed_rbf, 0.05)
def test_rbf_sampler():
# test that RBFSampler approximates kernel on random data
# compute exact kernel
gamma = 10.
kernel = rbf_kernel(X, Y, gamma=gamma)
# approximate kernel mapping
rbf_transform = RBFSampler(gamma=gamma, n_components=1000, random_state=42)
X_trans = rbf_transform.fit_transform(X)
Y_trans = rbf_transform.transform(Y)
kernel_approx = np.dot(X_trans, Y_trans.T)
error = kernel - kernel_approx
assert np.abs(np.mean(error)) <= 0.01 # close to unbiased
np.abs(error, out=error)
assert np.max(error) <= 0.1 # nothing too far off
assert np.mean(error) <= 0.05 # mean is fairly close
def test_spectral_embedding_first_eigen_vector():
# Test that the first eigenvector of spectral_embedding
# is constant and that the second is not (for a connected graph)
random_state = np.random.RandomState(36)
data = random_state.randn(10, 30)
sims = rbf_kernel(data)
n_components = 2
for seed in range(10):
embedding = spectral_embedding(sims,
norm_laplacian=False,
n_components=n_components,
drop_first=False,
random_state=seed)
assert np.std(embedding[:, 0]) == pytest.approx(0)
assert np.std(embedding[:, 1]) > 1e-3
def test_nystroem_default_parameters():
rnd = np.random.RandomState(42)
X = rnd.uniform(size=(10, 4))
# rbf kernel should behave as gamma=None by default
# aka gamma = 1 / n_features
nystroem = Nystroem(n_components=10)
X_transformed = nystroem.fit_transform(X)
K = rbf_kernel(X, gamma=None)
K2 = np.dot(X_transformed, X_transformed.T)
assert_array_almost_equal(K, K2)
# chi2 kernel should behave as gamma=1 by default
nystroem = Nystroem(kernel='chi2', n_components=10)
X_transformed = nystroem.fit_transform(X)
K = chi2_kernel(X, gamma=1)
K2 = np.dot(X_transformed, X_transformed.T)
assert_array_almost_equal(K, K2)
def test_spectral_embedding_unnormalized():
# Test that spectral_embedding is also processing unnormalized laplacian
# correctly
random_state = np.random.RandomState(36)
data = random_state.randn(10, 30)
sims = rbf_kernel(data)
n_components = 8
embedding_1 = spectral_embedding(sims,
norm_laplacian=False,
n_components=n_components,
drop_first=False)
# Verify using manual computation with dense eigh
laplacian, dd = csgraph.laplacian(sims, normed=False, return_diag=True)
_, diffusion_map = eigh(laplacian)
embedding_2 = diffusion_map.T[:n_components]
embedding_2 = _deterministic_vector_sign_flip(embedding_2).T
assert_array_almost_equal(embedding_1, embedding_2)
def test_svr_predict():
# Test SVR's decision_function
# Sanity check, test that predict implemented in python
# returns the same as the one in libsvm
X = iris.data
y = iris.target
# linear kernel
reg = svm.SVR(kernel='linear', C=0.1).fit(X, y)
dec = np.dot(X, reg.coef_.T) + reg.intercept_
assert_array_almost_equal(dec.ravel(), reg.predict(X).ravel())
# rbf kernel
reg = svm.SVR(kernel='rbf', gamma=1).fit(X, y)
rbfs = rbf_kernel(X, reg.support_vectors_, gamma=reg.gamma)
dec = np.dot(rbfs, reg.dual_coef_.T) + reg.intercept_
assert_array_almost_equal(dec.ravel(), reg.predict(X).ravel())
from mrex.metrics.pairwise import rbf_kernel
from mrex.datasets import make_classification
from mrex.exceptions import ConvergenceWarning
from numpy.testing import assert_array_almost_equal
from numpy.testing import assert_array_equal
ESTIMATORS = [
(label_propagation.LabelPropagation, {
'kernel': 'rbf'
}),
(label_propagation.LabelPropagation, {
'kernel': 'knn',
'n_neighbors': 2
}),
(label_propagation.LabelPropagation, {
'kernel': lambda x, y: rbf_kernel(x, y, gamma=20)
}),
(label_propagation.LabelSpreading, {
'kernel': 'rbf'
}),
(label_propagation.LabelSpreading, {
'kernel': 'knn',
'n_neighbors': 2
}),
(label_propagation.LabelSpreading, {
'kernel': lambda x, y: rbf_kernel(x, y, gamma=20)
}),
]
def test_fit_transduction():
def callable_rbf_kernel(x, y, **kwds):
# Callable version of pairwise.rbf_kernel.
K = rbf_kernel(np.atleast_2d(x), np.atleast_2d(y), **kwds)
return K
def test_rbf_kernel():
rng = np.random.RandomState(0)
X = rng.random_sample((5, 4))
K = rbf_kernel(X, X)
# the diagonal elements of a rbf kernel are 1
assert_array_almost_equal(K.flat[::6], np.ones(5))
