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"""Tests for module dr on Dimensionality Reduction"""
# Author: Remi Flamary <remi.flamary@unice.fr>
# Minhui Huang <mhhuang@ucdavis.edu>
# Antoine Collas <antoine.collas@inria.fr>
#
# License: MIT License
import numpy as np
import ot
import pytest
try: # test if autograd and pymanopt are installed
import ot.dr
nogo = False
except ImportError:
nogo = True
@pytest.mark.skipif(nogo, reason="Missing modules (autograd or pymanopt)")
def test_fda():
n_samples = 90 # nb samples in source and target datasets
rng = np.random.RandomState(0)
# generate gaussian dataset
xs, ys = ot.datasets.make_data_classif("gaussrot", n_samples, random_state=rng)
n_features_noise = 8
xs = np.hstack((xs, rng.randn(n_samples, n_features_noise)))
p = 1
Pfda, projfda = ot.dr.fda(xs, ys, p)
projfda(xs)
np.testing.assert_allclose(np.sum(Pfda**2, 0), np.ones(p))
@pytest.mark.skipif(nogo, reason="Missing modules (autograd or pymanopt)")
def test_wda():
n_samples = 100 # nb samples in source and target datasets
rng = np.random.RandomState(0)
# generate gaussian dataset
xs, ys = ot.datasets.make_data_classif("gaussrot", n_samples, random_state=rng)
n_features_noise = 8
xs = np.hstack((xs, rng.randn(n_samples, n_features_noise)))
p = 2
Pwda, projwda = ot.dr.wda(xs, ys, p, maxiter=10)
projwda(xs)
np.testing.assert_allclose(np.sum(Pwda**2, 0), np.ones(p))
@pytest.mark.skipif(nogo, reason="Missing modules (autograd or pymanopt)")
def test_wda_low_reg():
n_samples = 100 # nb samples in source and target datasets
rng = np.random.RandomState(0)
# generate gaussian dataset
xs, ys = ot.datasets.make_data_classif("gaussrot", n_samples, random_state=rng)
n_features_noise = 8
xs = np.hstack((xs, rng.randn(n_samples, n_features_noise)))
p = 2
Pwda, projwda = ot.dr.wda(
xs, ys, p, reg=0.01, maxiter=10, sinkhorn_method="sinkhorn_log"
)
projwda(xs)
np.testing.assert_allclose(np.sum(Pwda**2, 0), np.ones(p))
@pytest.mark.skipif(nogo, reason="Missing modules (autograd or pymanopt)")
def test_wda_normalized():
n_samples = 100 # nb samples in source and target datasets
rng = np.random.RandomState(0)
# generate gaussian dataset
xs, ys = ot.datasets.make_data_classif("gaussrot", n_samples, random_state=rng)
n_features_noise = 8
xs = np.hstack((xs, rng.randn(n_samples, n_features_noise)))
p = 2
P0 = rng.randn(10, p)
P0 /= P0.sum(0, keepdims=True)
Pwda, projwda = ot.dr.wda(xs, ys, p, maxiter=10, P0=P0, normalize=True)
projwda(xs)
np.testing.assert_allclose(np.sum(Pwda**2, 0), np.ones(p))
@pytest.mark.skipif(nogo, reason="Missing modules (autograd or pymanopt)")
def test_prw():
d = 100 # Dimension
n = 100 # Number samples
k = 3 # Subspace dimension
dim = 3
def fragmented_hypercube(n, d, dim, rng):
assert dim <= d
assert dim >= 1
assert dim == int(dim)
a = (1.0 / n) * np.ones(n)
b = (1.0 / n) * np.ones(n)
# First measure : uniform on the hypercube
X = rng.uniform(-1, 1, size=(n, d))
# Second measure : fragmentation
tmp_y = rng.uniform(-1, 1, size=(n, d))
Y = tmp_y + 2 * np.sign(tmp_y) * np.array(dim * [1] + (d - dim) * [0])
return a, b, X, Y
rng = np.random.RandomState(42)
a, b, X, Y = fragmented_hypercube(n, d, dim, rng)
tau = 0.002
reg = 0.2
pi, U = ot.dr.projection_robust_wasserstein(
X, Y, a, b, tau, reg=reg, k=k, maxiter=1000, verbose=1
)
U0 = rng.randn(d, k)
U0, _ = np.linalg.qr(U0)
pi, U = ot.dr.projection_robust_wasserstein(
X, Y, a, b, tau, U0=U0, reg=reg, k=k, maxiter=1000, verbose=1
)
@pytest.mark.skipif(nogo, reason="Missing modules (autograd or pymanopt)")
def test_ewca():
d = 5
n_samples = 50
k = 3
rng = np.random.RandomState(0)
# generate gaussian dataset
A = rng.normal(size=(d, d))
Q, _ = np.linalg.qr(A)
D = rng.normal(size=d)
D = (D / np.linalg.norm(D)) ** 4
cov = Q @ np.diag(D) @ Q.T
X = rng.multivariate_normal(np.zeros(d), cov, size=n_samples)
X = X - X.mean(0, keepdims=True)
assert X.shape == (n_samples, d)
# compute first 3 components with BCD
pi, U = ot.dr.ewca(
X, reg=0.01, method="BCD", k=k, verbose=1, sinkhorn_method="sinkhorn_log"
)
assert pi.shape == (n_samples, n_samples)
assert (pi >= 0).all()
assert np.allclose(pi.sum(0), 1 / n_samples, atol=1e-3)
assert np.allclose(pi.sum(1), 1 / n_samples, atol=1e-3)
assert U.shape == (d, k)
assert np.allclose(U.T @ U, np.eye(k), atol=1e-3)
# test that U contains the principal components
U_first_eigvec = np.linalg.svd(X.T, full_matrices=False)[0][:, :k]
_, cos, _ = np.linalg.svd(U.T @ U_first_eigvec, full_matrices=False)
assert np.allclose(cos, np.ones(k), atol=1e-3)
# compute first 3 components with MM
pi, U = ot.dr.ewca(
X, reg=0.01, method="MM", k=k, verbose=1, sinkhorn_method="sinkhorn_log"
)
assert pi.shape == (n_samples, n_samples)
assert (pi >= 0).all()
assert np.allclose(pi.sum(0), 1 / n_samples, atol=1e-3)
assert np.allclose(pi.sum(1), 1 / n_samples, atol=1e-3)
assert U.shape == (d, k)
assert np.allclose(U.T @ U, np.eye(k), atol=1e-3)
# test that U contains the principal components
U_first_eigvec = np.linalg.svd(X.T, full_matrices=False)[0][:, :k]
_, cos, _ = np.linalg.svd(U.T @ U_first_eigvec, full_matrices=False)
assert np.allclose(cos, np.ones(k), atol=1e-3)
# compute last 3 components
pi, U = ot.dr.ewca(
X, reg=100000, method="MM", k=k, verbose=1, sinkhorn_method="sinkhorn_log"
)
# test that U contains the last principal components
U_last_eigvec = np.linalg.svd(X.T, full_matrices=False)[0][:, -k:]
_, cos, _ = np.linalg.svd(U.T @ U_last_eigvec, full_matrices=False)
assert np.allclose(cos, np.ones(k), atol=1e-3)
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