def test_principal_angles(seed, m, n):
# Set random seed, draw random linear alignment.
rs = check_random_state(seed)
W = rs.randn(n, n)
# Create pair of matrices related by a linear transformation.
X = rand_orth(m, n)
Y = rand_orth(m, n)
# Compute metric based on principal angles.
cos_thetas = np.linalg.svd(X.T @ Y, compute_uv=False)
dist_1 = np.arccos(np.mean(cos_thetas))
# Fit model, assert two approaches match.
metric = LinearMetric(alpha=1.0, center_columns=False).fit(X, Y)
assert abs(dist_1 - metric.score(X, Y)) < TOL
def test_rand_orth(seed, m, n):
Q = rand_orth(m, n, random_state=seed)
if m == n:
assert_array_almost_equal(Q.T @ Q, np.eye(n))
assert_array_almost_equal(Q @ Q.T, np.eye(n))
elif m > n:
assert_array_almost_equal(Q.T @ Q, np.eye(n))
else:
assert_array_almost_equal(Q @ Q.T, np.eye(m))
def test_uncentered_procrustes(seed, m, n):
# Set random seed, draw random rotation
rs = check_random_state(seed)
Q = rand_orth(n, n, random_state=rs)
# Create a pair of randomly rotated matrices.
X = rs.randn(m, n)
Y = X @ Q
# Fit model, assert distance == 0.
metric = LinearMetric(alpha=1.0, center_columns=False)
metric.fit(X, Y)
assert abs(metric.score(X, Y)) < TOL
def test_gaussian(seed, n_rep, m, n):
rs = check_random_state(seed)
X = rs.randn(n_rep, m, n)
Y = np.copy(X) @ rand_orth(n)
metric = StochasticMetric(max_iter=1000)
metric.fit(X, Y)
d0 = metric.biased_score(X, Y)
assert_allclose(
2 * d0,
metric.Xself_ + metric.Yself_,
atol=1e-3,
rtol=1e-2,
)
def test_centered_procrustes(seed, m, n):
# Set random seed, draw random rotation, offset, and isotropic scaling.
rs = check_random_state(seed)
Q = rand_orth(n, n, random_state=rs)
v = rs.randn(1, n)
c = rs.exponential()
# Create a pair of randomly rotated matrices.
X = rs.randn(m, n)
Y = c * X @ Q + v
# Fit model, assert distance == 0.
metric = LinearMetric(alpha=1.0, center_columns=True)
metric.fit(X, Y)
assert abs(metric.score(X, Y)) < TOL
def fit(self, X, y=None):
X = self._validate_data(X, accept_sparse='csr')
rs = check_random_state(self.random_state)
n_features = X.shape[1]
nc = self.n_components // 2
self.random_weights_ = np.full((n_features, nc), np.nan)
i = 0
while i < nc:
Q = rand_orth(n_features, random_state=rs)
j = min(nc, i + n_features)
self.random_weights_[:, i:j] = Q[:, :(j - i)]
i = j
self.random_weights_ *= np.sqrt(2 * self.gamma)
self.random_weights_ *= np.sqrt(rs.chisquare(n_features, size=(1, nc)))
return self