def __init__(self, X, y):
# Initialize a fake NCA and variables needed to call the loss
# function:
self.fake_nca = NeighborhoodComponentsAnalysis()
self.fake_nca.n_iter_ = np.inf
self.X, y, _ = self.fake_nca._validate_params(X, y)
self.same_class_mask = y[:, np.newaxis] == y[np.newaxis, :]
def __init__(self, X, y):
self.loss = np.inf # initialize the loss to very high
# Initialize a fake NCA and variables needed to compute the loss:
self.fake_nca = NeighborhoodComponentsAnalysis()
self.fake_nca.n_iter_ = np.inf
self.X, y, _ = self.fake_nca._validate_params(X, y)
self.same_class_mask = y[:, np.newaxis] == y[np.newaxis, :]
def test_no_verbose(capsys):
# assert by default there is no output (verbose=0)
nca = NeighborhoodComponentsAnalysis()
nca.fit(iris_data, iris_target)
out, _ = capsys.readouterr()
# check output
assert(out == '')
def test_expected_transformation_shape():
"""Test that the transformation has the expected shape."""
X = iris_data
y = iris_target
class TransformationStorer:
def __init__(self, X, y):
# Initialize a fake NCA and variables needed to call the loss
# function:
self.fake_nca = NeighborhoodComponentsAnalysis()
self.fake_nca.n_iter_ = np.inf
self.X, y, _ = self.fake_nca._validate_params(X, y)
self.same_class_mask = y[:, np.newaxis] == y[np.newaxis, :]
def callback(self, transformation, n_iter):
"""Stores the last value of the transformation taken as input by
the optimizer"""
self.transformation = transformation
transformation_storer = TransformationStorer(X, y)
cb = transformation_storer.callback
nca = NeighborhoodComponentsAnalysis(max_iter=5, callback=cb)
nca.fit(X, y)
assert transformation_storer.transformation.size == X.shape[1]**2
def test_parameters_valid_types(param, value):
# check that no error is raised when parameters have numpy integer or
# floating types.
nca = NeighborhoodComponentsAnalysis(**{param: value})
X = iris_data
y = iris_target
nca.fit(X, y)
def test_one_class():
X = iris_data[iris_target == 0]
y = iris_target[iris_target == 0]
nca = NeighborhoodComponentsAnalysis(max_iter=30,
n_components=X.shape[1],
init='identity')
nca.fit(X, y)
assert_array_equal(X, nca.transform(X))
def test_n_components():
rng = np.random.RandomState(42)
X = np.arange(12).reshape(4, 3)
y = [1, 1, 2, 2]
init = rng.rand(X.shape[1] - 1, 3)
# n_components = X.shape[1] != transformation.shape[0]
n_components = X.shape[1]
nca = NeighborhoodComponentsAnalysis(init=init, n_components=n_components)
assert_raise_message(ValueError,
'The preferred dimensionality of the '
'projected space `n_components` ({}) does not match '
'the output dimensionality of the given '
'linear transformation `init` ({})!'
.format(n_components, init.shape[0]),
nca.fit, X, y)
# n_components > X.shape[1]
n_components = X.shape[1] + 2
nca = NeighborhoodComponentsAnalysis(init=init, n_components=n_components)
assert_raise_message(ValueError,
'The preferred dimensionality of the '
'projected space `n_components` ({}) cannot '
'be greater than the given data '
'dimensionality ({})!'
.format(n_components, X.shape[1]),
nca.fit, X, y)
# n_components < X.shape[1]
nca = NeighborhoodComponentsAnalysis(n_components=2, init='identity')
nca.fit(X, y)
class LossStorer:
def __init__(self, X, y):
self.loss = np.inf # initialize the loss to very high
# Initialize a fake NCA and variables needed to compute the loss:
self.fake_nca = NeighborhoodComponentsAnalysis()
self.fake_nca.n_iter_ = np.inf
self.X, y, _ = self.fake_nca._validate_params(X, y)
self.same_class_mask = y[:, np.newaxis] == y[np.newaxis, :]
def callback(self, transformation, n_iter):
"""Stores the last value of the loss function"""
self.loss, _ = self.fake_nca._loss_grad_lbfgs(transformation,
self.X,
self.same_class_mask,
-1.0)
def test_simple_example():
"""Test on a simple example.
Puts four points in the input space where the opposite labels points are
next to each other. After transform the samples from the same class
should be next to each other.
"""
X = np.array([[0, 0], [0, 1], [2, 0], [2, 1]])
y = np.array([1, 0, 1, 0])
nca = NeighborhoodComponentsAnalysis(n_components=2, init='identity',
random_state=42)
nca.fit(X, y)
X_t = nca.transform(X)
assert_array_equal(pairwise_distances(X_t).argsort()[:, 1],
np.array([2, 3, 0, 1]))
def test_auto_init(n_samples, n_features, n_classes, n_components):
# Test that auto choose the init as expected with every configuration
# of order of n_samples, n_features, n_classes and n_components.
rng = np.random.RandomState(42)
nca_base = NeighborhoodComponentsAnalysis(init='auto',
n_components=n_components,
max_iter=1,
random_state=rng)
if n_classes >= n_samples:
pass
# n_classes > n_samples is impossible, and n_classes == n_samples
# throws an error from lda but is an absurd case
else:
X = rng.randn(n_samples, n_features)
y = np.tile(range(n_classes), n_samples // n_classes + 1)[:n_samples]
if n_components > n_features:
# this would return a ValueError, which is already tested in
# test_params_validation
pass
else:
nca = clone(nca_base)
nca.fit(X, y)
if n_components <= min(n_classes - 1, n_features):
nca_other = clone(nca_base).set_params(init='lda')
elif n_components < min(n_features, n_samples):
nca_other = clone(nca_base).set_params(init='pca')
else:
nca_other = clone(nca_base).set_params(init='identity')
nca_other.fit(X, y)
assert_array_almost_equal(nca.components_, nca_other.components_)
def test_warm_start_validation():
X, y = make_classification(n_samples=30, n_features=5, n_classes=4,
n_redundant=0, n_informative=5, random_state=0)
nca = NeighborhoodComponentsAnalysis(warm_start=True, max_iter=5)
nca.fit(X, y)
X_less_features, y = make_classification(n_samples=30, n_features=4,
n_classes=4, n_redundant=0,
n_informative=4, random_state=0)
assert_raise_message(ValueError,
'The new inputs dimensionality ({}) does not '
'match the input dimensionality of the '
'previously learned transformation ({}).'
.format(X_less_features.shape[1],
nca.components_.shape[1]),
nca.fit, X_less_features, y)
def test_toy_example_collapse_points():
"""Test on a toy example of three points that should collapse
We build a simple example: two points from the same class and a point from
a different class in the middle of them. On this simple example, the new
(transformed) points should all collapse into one single point. Indeed, the
objective is 2/(1 + exp(d/2)), with d the euclidean distance between the
two samples from the same class. This is maximized for d=0 (because d>=0),
with an objective equal to 1 (loss=-1.).
"""
rng = np.random.RandomState(42)
input_dim = 5
two_points = rng.randn(2, input_dim)
X = np.vstack([two_points, two_points.mean(axis=0)[np.newaxis, :]])
y = [0, 0, 1]
class LossStorer:
def __init__(self, X, y):
self.loss = np.inf # initialize the loss to very high
# Initialize a fake NCA and variables needed to compute the loss:
self.fake_nca = NeighborhoodComponentsAnalysis()
self.fake_nca.n_iter_ = np.inf
self.X, y, _ = self.fake_nca._validate_params(X, y)
self.same_class_mask = y[:, np.newaxis] == y[np.newaxis, :]
def callback(self, transformation, n_iter):
"""Stores the last value of the loss function"""
self.loss, _ = self.fake_nca._loss_grad_lbfgs(transformation,
self.X,
self.same_class_mask,
-1.0)
loss_storer = LossStorer(X, y)
nca = NeighborhoodComponentsAnalysis(random_state=42,
callback=loss_storer.callback)
X_t = nca.fit_transform(X, y)
print(X_t)
# test that points are collapsed into one point
assert_array_almost_equal(X_t - X_t[0], 0.)
assert abs(loss_storer.loss + 1) < 1e-10
def test_transformation_dimensions():
X = np.arange(12).reshape(4, 3)
y = [1, 1, 2, 2]
# Fail if transformation input dimension does not match inputs dimensions
transformation = np.array([[1, 2], [3, 4]])
assert_raises(ValueError,
NeighborhoodComponentsAnalysis(init=transformation).fit,
X, y)
# Fail if transformation output dimension is larger than
# transformation input dimension
transformation = np.array([[1, 2], [3, 4], [5, 6]])
# len(transformation) > len(transformation[0])
assert_raises(ValueError,
NeighborhoodComponentsAnalysis(init=transformation).fit,
X, y)
# Pass otherwise
transformation = np.arange(9).reshape(3, 3)
NeighborhoodComponentsAnalysis(init=transformation).fit(X, y)
class TransformationStorer:
def __init__(self, X, y):
# Initialize a fake NCA and variables needed to call the loss
# function:
self.fake_nca = NeighborhoodComponentsAnalysis()
self.fake_nca.n_iter_ = np.inf
self.X, y, _ = self.fake_nca._validate_params(X, y)
self.same_class_mask = y[:, np.newaxis] == y[np.newaxis, :]
def callback(self, transformation, n_iter):
"""Stores the last value of the transformation taken as input by
the optimizer"""
self.transformation = transformation
def test_verbose(init_name, capsys):
# assert there is proper output when verbose = 1, for every initialization
# except auto because auto will call one of the others
rng = np.random.RandomState(42)
X, y = make_blobs(n_samples=30, centers=6, n_features=5, random_state=0)
regexp_init = r'... done in \ *\d+\.\d{2}s'
msgs = {'pca': "Finding principal components" + regexp_init,
'lda': "Finding most discriminative components" + regexp_init}
if init_name == 'precomputed':
init = rng.randn(X.shape[1], X.shape[1])
else:
init = init_name
nca = NeighborhoodComponentsAnalysis(verbose=1, init=init)
nca.fit(X, y)
out, _ = capsys.readouterr()
# check output
lines = re.split('\n+', out)
# if pca or lda init, an additional line is printed, so we test
# it and remove it to test the rest equally among initializations
if init_name in ['pca', 'lda']:
assert re.match(msgs[init_name], lines[0])
lines = lines[1:]
assert lines[0] == '[NeighborhoodComponentsAnalysis]'
header = '{:>10} {:>20} {:>10}'.format('Iteration', 'Objective Value',
'Time(s)')
assert lines[1] == '[NeighborhoodComponentsAnalysis] {}'.format(header)
assert lines[2] == ('[NeighborhoodComponentsAnalysis] {}'
.format('-' * len(header)))
for line in lines[3:-2]:
# The following regex will match for instance:
# '[NeighborhoodComponentsAnalysis] 0 6.988936e+01 0.01'
assert re.match(r'\[NeighborhoodComponentsAnalysis\] *\d+ *\d\.\d{6}e'
r'[+|-]\d+\ *\d+\.\d{2}', line)
assert re.match(r'\[NeighborhoodComponentsAnalysis\] Training took\ *'
r'\d+\.\d{2}s\.', lines[-2])
assert lines[-1] == ''
def test_finite_differences():
"""Test gradient of loss function
Assert that the gradient is almost equal to its finite differences
approximation.
"""
# Initialize the transformation `M`, as well as `X` and `y` and `NCA`
rng = np.random.RandomState(42)
X, y = make_classification()
M = rng.randn(rng.randint(1, X.shape[1] + 1),
X.shape[1])
nca = NeighborhoodComponentsAnalysis()
nca.n_iter_ = 0
mask = y[:, np.newaxis] == y[np.newaxis, :]
def fun(M):
return nca._loss_grad_lbfgs(M, X, mask)[0]
def grad(M):
return nca._loss_grad_lbfgs(M, X, mask)[1]
# compute relative error
rel_diff = check_grad(fun, grad, M.ravel()) / np.linalg.norm(grad(M))
np.testing.assert_almost_equal(rel_diff, 0., decimal=5)
def test_callback(capsys):
X = iris_data
y = iris_target
nca = NeighborhoodComponentsAnalysis(callback='my_cb')
assert_raises(ValueError, nca.fit, X, y)
max_iter = 10
def my_cb(transformation, n_iter):
assert transformation.shape == (iris_data.shape[1]**2,)
rem_iter = max_iter - n_iter
print('{} iterations remaining...'.format(rem_iter))
# assert that my_cb is called
nca = NeighborhoodComponentsAnalysis(max_iter=max_iter,
callback=my_cb, verbose=1)
nca.fit(iris_data, iris_target)
out, _ = capsys.readouterr()
# check output
assert('{} iterations remaining...'.format(max_iter - 1) in out)
def test_init_transformation():
rng = np.random.RandomState(42)
X, y = make_blobs(n_samples=30, centers=6, n_features=5, random_state=0)
# Start learning from scratch
nca = NeighborhoodComponentsAnalysis(init='identity')
nca.fit(X, y)
# Initialize with random
nca_random = NeighborhoodComponentsAnalysis(init='random')
nca_random.fit(X, y)
# Initialize with auto
nca_auto = NeighborhoodComponentsAnalysis(init='auto')
nca_auto.fit(X, y)
# Initialize with PCA
nca_pca = NeighborhoodComponentsAnalysis(init='pca')
nca_pca.fit(X, y)
# Initialize with LDA
nca_lda = NeighborhoodComponentsAnalysis(init='lda')
nca_lda.fit(X, y)
init = rng.rand(X.shape[1], X.shape[1])
nca = NeighborhoodComponentsAnalysis(init=init)
nca.fit(X, y)
# init.shape[1] must match X.shape[1]
init = rng.rand(X.shape[1], X.shape[1] + 1)
nca = NeighborhoodComponentsAnalysis(init=init)
assert_raise_message(ValueError,
'The input dimensionality ({}) of the given '
'linear transformation `init` must match the '
'dimensionality of the given inputs `X` ({}).'
.format(init.shape[1], X.shape[1]),
nca.fit, X, y)
# init.shape[0] must be <= init.shape[1]
init = rng.rand(X.shape[1] + 1, X.shape[1])
nca = NeighborhoodComponentsAnalysis(init=init)
assert_raise_message(ValueError,
'The output dimensionality ({}) of the given '
'linear transformation `init` cannot be '
'greater than its input dimensionality ({}).'
.format(init.shape[0], init.shape[1]),
nca.fit, X, y)
# init.shape[0] must match n_components
init = rng.rand(X.shape[1], X.shape[1])
n_components = X.shape[1] - 2
nca = NeighborhoodComponentsAnalysis(init=init, n_components=n_components)
assert_raise_message(ValueError,
'The preferred dimensionality of the '
'projected space `n_components` ({}) does not match '
'the output dimensionality of the given '
'linear transformation `init` ({})!'
.format(n_components, init.shape[0]),
nca.fit, X, y)
def test_warm_start_effectiveness():
# A 1-iteration second fit on same data should give almost same result
# with warm starting, and quite different result without warm starting.
nca_warm = NeighborhoodComponentsAnalysis(warm_start=True, random_state=0)
nca_warm.fit(iris_data, iris_target)
transformation_warm = nca_warm.components_
nca_warm.max_iter = 1
nca_warm.fit(iris_data, iris_target)
transformation_warm_plus_one = nca_warm.components_
nca_cold = NeighborhoodComponentsAnalysis(warm_start=False, random_state=0)
nca_cold.fit(iris_data, iris_target)
transformation_cold = nca_cold.components_
nca_cold.max_iter = 1
nca_cold.fit(iris_data, iris_target)
transformation_cold_plus_one = nca_cold.components_
diff_warm = np.sum(np.abs(transformation_warm_plus_one -
transformation_warm))
diff_cold = np.sum(np.abs(transformation_cold_plus_one -
transformation_cold))
assert diff_warm < 3.0, ("Transformer changed significantly after one "
"iteration even though it was warm-started.")
assert diff_cold > diff_warm, ("Cold-started transformer changed less "
"significantly than warm-started "
"transformer after one iteration.")
def test_convergence_warning():
nca = NeighborhoodComponentsAnalysis(max_iter=2, verbose=1)
cls_name = nca.__class__.__name__
assert_warns_message(ConvergenceWarning,
'[{}] NCA did not converge'.format(cls_name),
nca.fit, iris_data, iris_target)
def test_singleton_class():
X = iris_data
y = iris_target
# one singleton class
singleton_class = 1
ind_singleton, = np.where(y == singleton_class)
y[ind_singleton] = 2
y[ind_singleton[0]] = singleton_class
nca = NeighborhoodComponentsAnalysis(max_iter=30)
nca.fit(X, y)
# One non-singleton class
ind_1, = np.where(y == 1)
ind_2, = np.where(y == 2)
y[ind_1] = 0
y[ind_1[0]] = 1
y[ind_2] = 0
y[ind_2[0]] = 2
nca = NeighborhoodComponentsAnalysis(max_iter=30)
nca.fit(X, y)
# Only singleton classes
ind_0, = np.where(y == 0)
ind_1, = np.where(y == 1)
ind_2, = np.where(y == 2)
X = X[[ind_0[0], ind_1[0], ind_2[0]]]
y = y[[ind_0[0], ind_1[0], ind_2[0]]]
nca = NeighborhoodComponentsAnalysis(init='identity', max_iter=30)
nca.fit(X, y)
assert_array_equal(X, nca.transform(X))