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from unittest.mock import Mock
import numpy as np
import pytest
from numpy.testing import assert_allclose, assert_array_almost_equal, assert_equal
from sklearn.datasets import load_digits
from sklearn.manifold import _mds as mds
from sklearn.metrics import euclidean_distances
def test_smacof():
# test metric smacof using the data of "Modern Multidimensional Scaling",
# Borg & Groenen, p 154
sim = np.array([[0, 5, 3, 4], [5, 0, 2, 2], [3, 2, 0, 1], [4, 2, 1, 0]])
Z = np.array([[-0.266, -0.539], [0.451, 0.252], [0.016, -0.238], [-0.200, 0.524]])
X, _ = mds.smacof(sim, init=Z, n_components=2, max_iter=1, n_init=1)
X_true = np.array(
[[-1.415, -2.471], [1.633, 1.107], [0.249, -0.067], [-0.468, 1.431]]
)
assert_array_almost_equal(X, X_true, decimal=3)
def test_nonmetric_lower_normalized_stress():
# Testing that nonmetric MDS results in lower normalized stress compared
# compared to metric MDS (non-regression test for issue 27028)
sim = np.array([[0, 5, 3, 4], [5, 0, 2, 2], [3, 2, 0, 1], [4, 2, 1, 0]])
Z = np.array([[-0.266, -0.539], [0.451, 0.252], [0.016, -0.238], [-0.200, 0.524]])
_, stress1 = mds.smacof(
sim, init=Z, n_components=2, max_iter=1000, n_init=1, normalized_stress=True
)
_, stress2 = mds.smacof(
sim,
init=Z,
n_components=2,
max_iter=1000,
n_init=1,
normalized_stress=True,
metric=False,
)
assert stress1 > stress2
def test_nonmetric_mds_optimization():
# Test that stress is decreasing during nonmetric MDS optimization
# (non-regression test for issue 27028)
X, _ = load_digits(return_X_y=True)
rng = np.random.default_rng(seed=42)
ind_subset = rng.choice(len(X), size=200, replace=False)
X = X[ind_subset]
mds_est = mds.MDS(
n_components=2,
n_init=1,
max_iter=2,
metric=False,
random_state=42,
).fit(X)
stress_after_2_iter = mds_est.stress_
mds_est = mds.MDS(
n_components=2,
n_init=1,
max_iter=3,
metric=False,
random_state=42,
).fit(X)
stress_after_3_iter = mds_est.stress_
assert stress_after_2_iter > stress_after_3_iter
@pytest.mark.parametrize("metric", [True, False])
def test_mds_recovers_true_data(metric):
X = np.array([[1, 1], [1, 4], [1, 5], [3, 3]])
mds_est = mds.MDS(
n_components=2,
n_init=1,
eps=1e-15,
max_iter=1000,
metric=metric,
random_state=42,
).fit(X)
stress = mds_est.stress_
assert_allclose(stress, 0, atol=1e-6)
def test_smacof_error():
# Not symmetric similarity matrix:
sim = np.array([[0, 5, 9, 4], [5, 0, 2, 2], [3, 2, 0, 1], [4, 2, 1, 0]])
with pytest.raises(ValueError):
mds.smacof(sim, n_init=1)
# Not squared similarity matrix:
sim = np.array([[0, 5, 9, 4], [5, 0, 2, 2], [4, 2, 1, 0]])
with pytest.raises(ValueError):
mds.smacof(sim, n_init=1)
# init not None and not correct format:
sim = np.array([[0, 5, 3, 4], [5, 0, 2, 2], [3, 2, 0, 1], [4, 2, 1, 0]])
Z = np.array([[-0.266, -0.539], [0.016, -0.238], [-0.200, 0.524]])
with pytest.raises(ValueError):
mds.smacof(sim, init=Z, n_init=1)
def test_MDS():
sim = np.array([[0, 5, 3, 4], [5, 0, 2, 2], [3, 2, 0, 1], [4, 2, 1, 0]])
mds_clf = mds.MDS(
metric=False,
n_jobs=3,
n_init=3,
dissimilarity="precomputed",
)
mds_clf.fit(sim)
# TODO(1.9): remove warning filter
@pytest.mark.filterwarnings("ignore::FutureWarning")
@pytest.mark.parametrize("k", [0.5, 1.5, 2])
def test_normed_stress(k):
"""Test that non-metric MDS normalized stress is scale-invariant."""
sim = np.array([[0, 5, 3, 4], [5, 0, 2, 2], [3, 2, 0, 1], [4, 2, 1, 0]])
X1, stress1 = mds.smacof(sim, metric=False, max_iter=5, random_state=0)
X2, stress2 = mds.smacof(k * sim, metric=False, max_iter=5, random_state=0)
assert_allclose(stress1, stress2, rtol=1e-5)
assert_allclose(X1, X2, rtol=1e-5)
# TODO(1.9): remove warning filter
@pytest.mark.filterwarnings("ignore::FutureWarning")
@pytest.mark.parametrize("metric", [True, False])
def test_normalized_stress_auto(metric, monkeypatch):
rng = np.random.RandomState(0)
X = rng.randn(4, 3)
dist = euclidean_distances(X)
mock = Mock(side_effect=mds._smacof_single)
monkeypatch.setattr("sklearn.manifold._mds._smacof_single", mock)
est = mds.MDS(metric=metric, normalized_stress="auto", random_state=rng)
est.fit_transform(X)
assert mock.call_args[1]["normalized_stress"] != metric
mds.smacof(dist, metric=metric, normalized_stress="auto", random_state=rng)
assert mock.call_args[1]["normalized_stress"] != metric
def test_isotonic_outofbounds():
# This particular configuration can trigger out of bounds error
# in the isotonic regression (non-regression test for issue 26999)
dis = np.array(
[
[0.0, 1.732050807568877, 1.7320508075688772],
[1.732050807568877, 0.0, 6.661338147750939e-16],
[1.7320508075688772, 6.661338147750939e-16, 0.0],
]
)
init = np.array(
[
[0.08665881585055124, 0.7939114643387546],
[0.9959834154297658, 0.7555546025640025],
[0.8766008278401566, 0.4227358815811242],
]
)
mds.smacof(dis, init=init, metric=False, n_init=1)
# TODO(1.9): remove warning filter
@pytest.mark.filterwarnings("ignore::FutureWarning")
@pytest.mark.parametrize("normalized_stress", [True, False])
def test_returned_stress(normalized_stress):
# Test that the final stress corresponds to the final embedding
# (non-regression test for issue 16846)
X = np.array([[1, 1], [1, 4], [1, 5], [3, 3]])
D = euclidean_distances(X)
mds_est = mds.MDS(
n_components=2,
random_state=42,
normalized_stress=normalized_stress,
).fit(X)
Z = mds_est.embedding_
stress = mds_est.stress_
D_mds = euclidean_distances(Z)
stress_Z = ((D_mds.ravel() - D.ravel()) ** 2).sum() / 2
if normalized_stress:
stress_Z = np.sqrt(stress_Z / ((D_mds.ravel() ** 2).sum() / 2))
assert_allclose(stress, stress_Z)
# TODO(1.9): remove warning filter
@pytest.mark.filterwarnings("ignore::FutureWarning")
@pytest.mark.parametrize("metric", [True, False])
def test_convergence_does_not_depend_on_scale(metric):
# Test that the number of iterations until convergence does not depend on
# the scale of the input data
X = np.array([[1, 1], [1, 4], [1, 5], [3, 3]])
mds_est = mds.MDS(
n_components=2,
random_state=42,
metric=metric,
)
mds_est.fit(X * 100)
n_iter1 = mds_est.n_iter_
mds_est.fit(X / 100)
n_iter2 = mds_est.n_iter_
assert_equal(n_iter1, n_iter2)
# TODO(1.9): delete this test
def test_future_warning_n_init():
X = np.array([[1, 1], [1, 4], [1, 5], [3, 3]])
sim = np.array([[0, 5, 3, 4], [5, 0, 2, 2], [3, 2, 0, 1], [4, 2, 1, 0]])
with pytest.warns(FutureWarning):
mds.smacof(sim)
with pytest.warns(FutureWarning):
mds.MDS().fit(X)
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