def variable_batch_size_comparison(data):
batch_sizes = [i.astype(int) for i in np.linspace(data.shape[0] // 10,
data.shape[0], num=10)]
for n_components in [i.astype(int) for i in
np.linspace(data.shape[1] // 10,
data.shape[1], num=4)]:
all_times = defaultdict(list)
all_errors = defaultdict(list)
pca = PCA(n_components=n_components)
rpca = PCA(n_components=n_components, svd_solver='randomized',
random_state=1999)
results_dict = {k: benchmark(est, data) for k, est in [('pca', pca),
('rpca', rpca)]}
# Create flat baselines to compare the variation over batch size
all_times['pca'].extend([results_dict['pca']['time']] *
len(batch_sizes))
all_errors['pca'].extend([results_dict['pca']['error']] *
len(batch_sizes))
all_times['rpca'].extend([results_dict['rpca']['time']] *
len(batch_sizes))
all_errors['rpca'].extend([results_dict['rpca']['error']] *
len(batch_sizes))
for batch_size in batch_sizes:
ipca = IncrementalPCA(n_components=n_components,
batch_size=batch_size)
results_dict = {k: benchmark(est, data) for k, est in [('ipca',
ipca)]}
all_times['ipca'].append(results_dict['ipca']['time'])
all_errors['ipca'].append(results_dict['ipca']['error'])
plot_batch_times(all_times, n_components, batch_sizes, data)
plot_batch_errors(all_errors, n_components, batch_sizes, data)
def test_feature_union_weights():
# test feature union with transformer weights
iris = load_iris()
X = iris.data
y = iris.target
pca = PCA(n_components=2, svd_solver='randomized', random_state=0)
select = SelectKBest(k=1)
# test using fit followed by transform
fs = FeatureUnion([("pca", pca), ("select", select)],
transformer_weights={"pca": 10})
fs.fit(X, y)
X_transformed = fs.transform(X)
# test using fit_transform
fs = FeatureUnion([("pca", pca), ("select", select)],
transformer_weights={"pca": 10})
X_fit_transformed = fs.fit_transform(X, y)
# test it works with transformers missing fit_transform
fs = FeatureUnion([("mock", Transf()), ("pca", pca), ("select", select)],
transformer_weights={"mock": 10})
X_fit_transformed_wo_method = fs.fit_transform(X, y)
# check against expected result
# We use a different pca object to control the random_state stream
assert_array_almost_equal(X_transformed[:, :-1], 10 * pca.fit_transform(X))
assert_array_equal(X_transformed[:, -1],
select.fit_transform(X, y).ravel())
assert_array_almost_equal(X_fit_transformed[:, :-1],
10 * pca.fit_transform(X))
assert_array_equal(X_fit_transformed[:, -1],
select.fit_transform(X, y).ravel())
assert X_fit_transformed_wo_method.shape == (X.shape[0], 7)
def test_incremental_pca_sparse(matrix_class):
# Incremental PCA on sparse arrays.
X = iris.data
pca = PCA(n_components=2)
pca.fit_transform(X)
X_sparse = matrix_class(X)
batch_size = X_sparse.shape[0] // 3
ipca = IncrementalPCA(n_components=2, batch_size=batch_size)
X_transformed = ipca.fit_transform(X_sparse)
assert X_transformed.shape == (X_sparse.shape[0], 2)
np.testing.assert_allclose(ipca.explained_variance_ratio_.sum(),
pca.explained_variance_ratio_.sum(), rtol=1e-3)
for n_components in [1, 2, X.shape[1]]:
ipca = IncrementalPCA(n_components, batch_size=batch_size)
ipca.fit(X_sparse)
cov = ipca.get_covariance()
precision = ipca.get_precision()
np.testing.assert_allclose(np.dot(cov, precision),
np.eye(X_sparse.shape[1]), atol=1e-13)
with pytest.raises(
TypeError,
match="IncrementalPCA.partial_fit does not support "
"sparse input. Either convert data to dense "
"or use IncrementalPCA.fit to do so in batches."):
ipca.partial_fit(X_sparse)
def plot_figs(fig_num, elev, azim):
fig = plt.figure(fig_num, figsize=(4, 3))
plt.clf()
ax = Axes3D(fig, rect=[0, 0, .95, 1], elev=elev, azim=azim)
ax.scatter(a[::10],
b[::10],
c[::10],
c=density[::10],
marker='+',
alpha=.4)
Y = np.c_[a, b, c]
# Using SciPy's SVD, this would be:
# _, pca_score, V = scipy.linalg.svd(Y, full_matrices=False)
pca = PCA(n_components=3)
pca.fit(Y)
pca_score = pca.explained_variance_ratio_
V = pca.components_
x_pca_axis, y_pca_axis, z_pca_axis = 3 * V.T
x_pca_plane = np.r_[x_pca_axis[:2], -x_pca_axis[1::-1]]
y_pca_plane = np.r_[y_pca_axis[:2], -y_pca_axis[1::-1]]
z_pca_plane = np.r_[z_pca_axis[:2], -z_pca_axis[1::-1]]
x_pca_plane.shape = (2, 2)
y_pca_plane.shape = (2, 2)
z_pca_plane.shape = (2, 2)
ax.plot_surface(x_pca_plane, y_pca_plane, z_pca_plane)
ax.w_xaxis.set_ticklabels([])
ax.w_yaxis.set_ticklabels([])
ax.w_zaxis.set_ticklabels([])
def test_pca_score_consistency_solvers(svd_solver):
# Check the consistency of score between solvers
X, _ = datasets.load_digits(return_X_y=True)
pca_full = PCA(n_components=30, svd_solver='full', random_state=0)
pca_other = PCA(n_components=30, svd_solver=svd_solver, random_state=0)
pca_full.fit(X)
pca_other.fit(X)
assert_allclose(pca_full.score(X), pca_other.score(X), rtol=5e-6)
def test_pca_check_projection_list(svd_solver):
# Test that the projection of data is correct
X = [[1.0, 0.0], [0.0, 1.0]]
pca = PCA(n_components=1, svd_solver=svd_solver, random_state=0)
X_trans = pca.fit_transform(X)
assert X_trans.shape, (2, 1)
assert_allclose(X_trans.mean(), 0.00, atol=1e-12)
assert_allclose(X_trans.std(), 0.71, rtol=5e-3)
def test_pca_sparse_input(svd_solver):
X = np.random.RandomState(0).rand(5, 4)
X = sp.sparse.csr_matrix(X)
assert sp.sparse.issparse(X)
pca = PCA(n_components=3, svd_solver=svd_solver)
with pytest.raises(TypeError):
pca.fit(X)
def test_pca_explained_variance_empirical(X, svd_solver):
pca = PCA(n_components=2, svd_solver=svd_solver, random_state=0)
X_pca = pca.fit_transform(X)
assert_allclose(pca.explained_variance_, np.var(X_pca, ddof=1, axis=0))
expected_result = np.linalg.eig(np.cov(X, rowvar=False))[0]
expected_result = sorted(expected_result, reverse=True)[:2]
assert_allclose(pca.explained_variance_, expected_result, rtol=5e-3)
def test_n_components_mle(svd_solver):
# Ensure that n_components == 'mle' doesn't raise error for auto/full
rng = np.random.RandomState(0)
n_samples, n_features = 600, 10
X = rng.randn(n_samples, n_features)
pca = PCA(n_components='mle', svd_solver=svd_solver)
pca.fit(X)
assert pca.n_components_ == 0
def test_no_empty_slice_warning():
# test if we avoid numpy warnings for computing over empty arrays
n_components = 10
n_features = n_components + 2 # anything > n_comps triggered it in 0.16
X = np.random.uniform(-1, 1, size=(n_components, n_features))
pca = PCA(n_components=n_components)
with pytest.warns(None) as record:
pca.fit(X)
assert not record.list
def test_pca_sanity_noise_variance(svd_solver):
# Sanity check for the noise_variance_. For more details see
# https://github.com/scikit-learn/scikit-learn/issues/7568
# https://github.com/scikit-learn/scikit-learn/issues/8541
# https://github.com/scikit-learn/scikit-learn/issues/8544
X, _ = datasets.load_digits(return_X_y=True)
pca = PCA(n_components=30, svd_solver=svd_solver, random_state=0)
pca.fit(X)
assert np.all((pca.explained_variance_ - pca.noise_variance_) >= 0)
def test_pca_deterministic_output(svd_solver):
rng = np.random.RandomState(0)
X = rng.rand(10, 10)
transformed_X = np.zeros((20, 2))
for i in range(20):
pca = PCA(n_components=2, svd_solver=svd_solver, random_state=rng)
transformed_X[i, :] = pca.fit_transform(X)[0]
assert_allclose(transformed_X,
np.tile(transformed_X[0, :], 20).reshape(20, 2))
def test_infer_dim_3():
n, p = 100, 5
rng = np.random.RandomState(0)
X = rng.randn(n, p) * .1
X[:10] += np.array([3, 4, 5, 1, 2])
X[10:20] += np.array([6, 0, 7, 2, -1])
X[30:40] += 2 * np.array([-1, 1, -1, 1, -1])
pca = PCA(n_components=p, svd_solver='full')
pca.fit(X)
spect = pca.explained_variance_
assert _infer_dimension_(spect, n, p) > 2
def test_n_components_mle_error(svd_solver):
# Ensure that n_components == 'mle' will raise an error for unsupported
# solvers
rng = np.random.RandomState(0)
n_samples, n_features = 600, 10
X = rng.randn(n_samples, n_features)
pca = PCA(n_components='mle', svd_solver=svd_solver)
err_msg = ("n_components='mle' cannot be a string with svd_solver='{}'".
format(svd_solver))
with pytest.raises(ValueError, match=err_msg):
pca.fit(X)
def test_infer_dim_2():
# TODO: explain what this is testing
# Or at least use explicit variable names...
n, p = 1000, 5
rng = np.random.RandomState(0)
X = rng.randn(n, p) * .1
X[:10] += np.array([3, 4, 5, 1, 2])
X[10:20] += np.array([6, 0, 7, 2, -1])
pca = PCA(n_components=p, svd_solver='full')
pca.fit(X)
spect = pca.explained_variance_
assert _infer_dimension_(spect, n, p) > 1
def test_infer_dim_1():
# TODO: explain what this is testing
# Or at least use explicit variable names...
n, p = 1000, 5
rng = np.random.RandomState(0)
X = (rng.randn(n, p) * .1 + rng.randn(n, 1) * np.array([3, 4, 5, 1, 2]) +
np.array([1, 0, 7, 4, 6]))
pca = PCA(n_components=p, svd_solver='full')
pca.fit(X)
spect = pca.explained_variance_
ll = np.array([_assess_dimension_(spect, k, n, p) for k in range(p)])
assert ll[1] > ll.max() - .01 * n
def test_pca_singular_values(svd_solver):
rng = np.random.RandomState(0)
n_samples, n_features = 100, 80
X = rng.randn(n_samples, n_features)
pca = PCA(n_components=2, svd_solver=svd_solver, random_state=rng)
X_trans = pca.fit_transform(X)
# compare to the Frobenius norm
assert_allclose(np.sum(pca.singular_values_**2),
np.linalg.norm(X_trans, "fro")**2)
# Compare to the 2-norms of the score vectors
assert_allclose(pca.singular_values_, np.sqrt(np.sum(X_trans**2, axis=0)))
# set the singular values and see what er get back
n_samples, n_features = 100, 110
X = rng.randn(n_samples, n_features)
pca = PCA(n_components=3, svd_solver=svd_solver, random_state=rng)
X_trans = pca.fit_transform(X)
X_trans /= np.sqrt(np.sum(X_trans**2, axis=0))
X_trans[:, 0] *= 3.142
X_trans[:, 1] *= 2.718
X_hat = np.dot(X_trans, pca.components_)
pca.fit(X_hat)
assert_allclose(pca.singular_values_, [3.142, 2.718, 1.0])
def test_pca_inverse(svd_solver, whiten):
# Test that the projection of data can be inverted
rng = np.random.RandomState(0)
n, p = 50, 3
X = rng.randn(n, p) # spherical data
X[:, 1] *= .00001 # make middle component relatively small
X += [5, 4, 3] # make a large mean
# same check that we can find the original data from the transformed
# signal (since the data is almost of rank n_components)
pca = PCA(n_components=2, svd_solver=svd_solver, whiten=whiten).fit(X)
Y = pca.transform(X)
Y_inverse = pca.inverse_transform(Y)
assert_allclose(X, Y_inverse, rtol=5e-6)
def test_pca_vs_spca():
rng = np.random.RandomState(0)
Y, _, _ = generate_toy_data(3, 1000, (8, 8), random_state=rng)
Z, _, _ = generate_toy_data(3, 10, (8, 8), random_state=rng)
spca = SparsePCA(alpha=0, ridge_alpha=0, n_components=2)
pca = PCA(n_components=2)
pca.fit(Y)
spca.fit(Y)
results_test_pca = pca.transform(Z)
results_test_spca = spca.transform(Z)
assert_allclose(np.abs(spca.components_.dot(pca.components_.T)),
np.eye(2), atol=1e-5)
results_test_pca *= np.sign(results_test_pca[0, :])
results_test_spca *= np.sign(results_test_spca[0, :])
assert_allclose(results_test_pca, results_test_spca)
def test_pipeline_score_samples_pca_lof():
iris = load_iris()
X = iris.data
# Test that the score_samples method is implemented on a pipeline.
# Test that the score_samples method on pipeline yields same results as
# applying transform and score_samples steps separately.
pca = PCA(svd_solver='full', n_components='mle', whiten=True)
lof = LocalOutlierFactor(novelty=True)
pipe = Pipeline([('pca', pca), ('lof', lof)])
pipe.fit(X)
# Check the shapes
assert pipe.score_samples(X).shape == (X.shape[0],)
# Check the values
lof.fit(pca.fit_transform(X))
assert_allclose(pipe.score_samples(X), lof.score_samples(pca.transform(X)))
def test_pca_svd_solver_auto(data, n_components, expected_solver):
pca_auto = PCA(n_components=n_components, random_state=0)
pca_test = PCA(n_components=n_components,
svd_solver=expected_solver,
random_state=0)
pca_auto.fit(data)
pca_test.fit(data)
assert_allclose(pca_auto.components_, pca_test.components_)
def test_pca_score3():
# Check that probabilistic PCA selects the right model
n, p = 200, 3
rng = np.random.RandomState(0)
Xl = (rng.randn(n, p) + rng.randn(n, 1) * np.array([3, 4, 5]) +
np.array([1, 0, 7]))
Xt = (rng.randn(n, p) + rng.randn(n, 1) * np.array([3, 4, 5]) +
np.array([1, 0, 7]))
ll = np.zeros(p)
for k in range(p):
pca = PCA(n_components=k, svd_solver='full')
pca.fit(Xl)
ll[k] = pca.score(Xt)
assert ll.argmax() == 1
def test_make_union():
pca = PCA(svd_solver='full')
mock = Transf()
fu = make_union(pca, mock)
names, transformers = zip(*fu.transformer_list)
assert names == ("pca", "transf")
assert transformers == (pca, mock)
def test_pipeline_methods_preprocessing_svm():
# Test the various methods of the pipeline (preprocessing + svm).
iris = load_iris()
X = iris.data
y = iris.target
n_samples = X.shape[0]
n_classes = len(np.unique(y))
scaler = StandardScaler()
pca = PCA(n_components=2, svd_solver='randomized', whiten=True)
clf = SVC(probability=True, random_state=0, decision_function_shape='ovr')
for preprocessing in [scaler, pca]:
pipe = Pipeline([('preprocess', preprocessing), ('svc', clf)])
pipe.fit(X, y)
# check shapes of various prediction functions
predict = pipe.predict(X)
assert predict.shape == (n_samples,)
proba = pipe.predict_proba(X)
assert proba.shape == (n_samples, n_classes)
log_proba = pipe.predict_log_proba(X)
assert log_proba.shape == (n_samples, n_classes)
decision_function = pipe.decision_function(X)
assert decision_function.shape == (n_samples, n_classes)
pipe.score(X, y)
def test_incremental_pca_against_pca_iris():
# Test that IncrementalPCA and PCA are approximate (to a sign flip).
X = iris.data
Y_pca = PCA(n_components=2).fit_transform(X)
Y_ipca = IncrementalPCA(n_components=2, batch_size=25).fit_transform(X)
assert_almost_equal(np.abs(Y_pca), np.abs(Y_ipca), 1)
def test_pipeline_transform():
# Test whether pipeline works with a transformer at the end.
# Also test pipeline.transform and pipeline.inverse_transform
iris = load_iris()
X = iris.data
pca = PCA(n_components=2, svd_solver='full')
pipeline = Pipeline([('pca', pca)])
# test transform and fit_transform:
X_trans = pipeline.fit(X).transform(X)
X_trans2 = pipeline.fit_transform(X)
X_trans3 = pca.fit_transform(X)
assert_array_almost_equal(X_trans, X_trans2)
assert_array_almost_equal(X_trans, X_trans3)
X_back = pipeline.inverse_transform(X_trans)
X_back2 = pca.inverse_transform(X_trans)
assert_array_almost_equal(X_back, X_back2)
def test_fit_predict_on_pipeline_without_fit_predict():
# tests that a pipeline does not have fit_predict method when final
# step of pipeline does not have fit_predict defined
scaler = StandardScaler()
pca = PCA(svd_solver='full')
pipe = Pipeline([('scaler', scaler), ('pca', pca)])
assert_raises_regex(AttributeError,
"'PCA' object has no attribute 'fit_predict'",
getattr, pipe, 'fit_predict')
def test_truncated_svd_eq_pca(X_sparse):
# TruncatedSVD should be equal to PCA on centered data
X_dense = X_sparse.toarray()
X_c = X_dense - X_dense.mean(axis=0)
params = dict(n_components=10, random_state=42)
svd = TruncatedSVD(algorithm='arpack', **params)
pca = PCA(svd_solver='arpack', **params)
Xt_svd = svd.fit_transform(X_c)
Xt_pca = pca.fit_transform(X_c)
assert_allclose(Xt_svd, Xt_pca, rtol=1e-9)
assert_allclose(pca.mean_, 0, atol=1e-9)
assert_allclose(svd.components_, pca.components_)
def test_pca_dim():
# Check automated dimensionality setting
rng = np.random.RandomState(0)
n, p = 100, 5
X = rng.randn(n, p) * .1
X[:10] += np.array([3, 4, 5, 1, 2])
pca = PCA(n_components='mle', svd_solver='full').fit(X)
assert pca.n_components == 'mle'
assert pca.n_components_ == 1
def test_whitening():
# Test that PCA and IncrementalPCA transforms match to sign flip.
X = datasets.make_low_rank_matrix(1000, 10, tail_strength=0.,
effective_rank=2, random_state=1999)
prec = 3
n_samples, n_features = X.shape
for nc in [None, 9]:
pca = PCA(whiten=True, n_components=nc).fit(X)
ipca = IncrementalPCA(whiten=True, n_components=nc,
batch_size=250).fit(X)
Xt_pca = pca.transform(X)
Xt_ipca = ipca.transform(X)
assert_almost_equal(np.abs(Xt_pca), np.abs(Xt_ipca), decimal=prec)
Xinv_ipca = ipca.inverse_transform(Xt_ipca)
Xinv_pca = pca.inverse_transform(Xt_pca)
assert_almost_equal(X, Xinv_ipca, decimal=prec)
assert_almost_equal(X, Xinv_pca, decimal=prec)
assert_almost_equal(Xinv_pca, Xinv_ipca, decimal=prec)
