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_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_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 __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 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))
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_equal(transformation_storer.transformation.size, X.shape[1]**2)
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)
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_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_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_store_opt_result(): X = iris_data y = iris_target nca = NeighborhoodComponentsAnalysis(max_iter=5, store_opt_result=True) nca.fit(X, y) transformation = nca.opt_result_.x assert_equal(transformation.size, X.shape[1]**2)
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_n_components(): X = np.arange(12).reshape(4, 3) y = [1, 1, 2, 2] init = np.random.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 embedding dimensionality ' '`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 embedding dimensionality ' '`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)
def test_verbose(): # assert there is proper output when verbose = 1 old_stdout = sys.stdout sys.stdout = StringIO() nca = NeighborhoodComponentsAnalysis(verbose=1) try: nca.fit(iris_data, iris_target) finally: out = sys.stdout.getvalue() sys.stdout.close() sys.stdout = old_stdout # check output assert("[NeighborhoodComponentsAnalysis]" in out) assert("Finding principal components" in out) assert ("Finding principal components" in out) assert ("Training took" in out) # assert by default there is no output (verbose=0) old_stdout = sys.stdout sys.stdout = StringIO() nca = NeighborhoodComponentsAnalysis() try: nca.fit(iris_data, iris_target) finally: out = sys.stdout.getvalue() sys.stdout.close() sys.stdout = old_stdout # check output assert(out == '')
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, :]
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 __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_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_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_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 same labels points 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) Xansformed = nca.transform(X) np.testing.assert_equal(pairwise_distances(Xansformed).argsort()[:, 1], np.array([2, 3, 0, 1]))
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_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_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_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_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)
def test_callback(): 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): rem_iter = max_iter - n_iter print('{} iterations remaining...'.format(rem_iter)) # assert that my_cb is called old_stdout = sys.stdout sys.stdout = StringIO() nca = NeighborhoodComponentsAnalysis(max_iter=max_iter, callback=my_cb, verbose=1) try: nca.fit(iris_data, iris_target) finally: out = sys.stdout.getvalue() sys.stdout.close() sys.stdout = old_stdout # check output assert('{} iterations remaining...'.format(max_iter-1) in out)
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_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_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)
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_finite_differences(): r"""Test gradient of loss function Test if the gradient is correct by computing the relative difference between the projected gradient PG: .. math:: PG = \mathbf d^{\top} \cdot \nabla \mathcal L(\mathbf x) and the finite differences FD: .. math:: FD = \frac{\mathcal L(\mathbf x + \epsilon \mathbf d) - \mathcal L(\mathbf x - \epsilon \mathbf d)}{2 \epsilon} where :math:`d` is a random direction (random vector of shape `n_features`, and norm 1), :math:`\epsilon` is a very small number, :math:`\mathcal L` is the loss function and :math:`\nabla \mathcal L` is its gradient. This relative difference should be zero: .. math :: \frac{|PG -FD|}{|PG|} = 0 """ # Initialize `transformation`, `X` and `y` and `NCA` X = iris_data y = iris_target point = rng.randn(rng.randint(1, X.shape[1] + 1), X.shape[1]) nca = NeighborhoodComponentsAnalysis(init=point) X, y, init = nca._validate_params(X, y) mask = y[:, np.newaxis] == y[np.newaxis, :] # (n_samples, n_samples) nca.n_iter_ = 0 point = nca._initialize(X, init) # compute the gradient at `point` _, gradient = nca._loss_grad_lbfgs(point, X, mask) # create a random direction of norm 1 random_direction = rng.randn(*point.shape) random_direction /= np.linalg.norm(random_direction) # computes projected gradient projected_gradient = random_direction.ravel().dot( gradient.ravel()) # compute finite differences eps = 1e-5 right_loss, _ = nca._loss_grad_lbfgs(point + eps * random_direction, X, mask) left_loss, _ = nca._loss_grad_lbfgs(point - eps * random_direction, X, mask) finite_differences = 1 / (2 * eps) * (right_loss - left_loss) # compute relative error relative_error = np.abs(finite_differences - projected_gradient) / \ np.abs(projected_gradient) np.testing.assert_almost_equal(relative_error, 0.)
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_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))
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_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. X, y = make_classification(n_samples=30, n_features=5, n_redundant=0, random_state=0) n_iter = 10 nca_warm = NeighborhoodComponentsAnalysis(warm_start=True, max_iter=n_iter, random_state=0) nca_warm.fit(X, y) transformation_warm = nca_warm.components_ nca_warm.max_iter = 1 nca_warm.fit(X, y) transformation_warm_plus_one = nca_warm.components_ nca_cold = NeighborhoodComponentsAnalysis(warm_start=False, max_iter=n_iter, random_state=0) nca_cold.fit(X, y) transformation_cold = nca_cold.components_ nca_cold.max_iter = 1 nca_cold.fit(X, y) 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_true(diff_warm < 2.0, "Transformer changed significantly after one iteration even " "though it was warm-started.") assert_true(diff_cold > diff_warm, "Cold-started transformer changed less significantly than " "warm-started transformer after one iteration.")
def test_init_transformation(): X, y = make_classification(n_samples=30, n_features=5, n_redundant=0, 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 PCA nca_pca = NeighborhoodComponentsAnalysis(init='pca') nca_pca.fit(X, y) init = np.random.rand(X.shape[1], X.shape[1]) nca = NeighborhoodComponentsAnalysis(init=init) nca.fit(X, y) # init.shape[1] must match X.shape[1] init = np.random.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 = np.random.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 = np.random.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 embedding dimensionality ' '`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_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)