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Batuhan Berk Başoğlu 2020-11-12 11:05:57 -05:00
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import sys
from io import StringIO
import numpy as np
from numpy.testing import assert_allclose
import scipy.sparse as sp
import pytest
from sklearn.neighbors import NearestNeighbors
from sklearn.neighbors import kneighbors_graph
from sklearn.exceptions import EfficiencyWarning
from sklearn.utils._testing import ignore_warnings
from sklearn.utils._testing import assert_almost_equal
from sklearn.utils._testing import assert_array_equal
from sklearn.utils._testing import assert_array_almost_equal
from sklearn.utils._testing import skip_if_32bit
from sklearn.utils import check_random_state
from sklearn.manifold._t_sne import _joint_probabilities
from sklearn.manifold._t_sne import _joint_probabilities_nn
from sklearn.manifold._t_sne import _kl_divergence
from sklearn.manifold._t_sne import _kl_divergence_bh
from sklearn.manifold._t_sne import _gradient_descent
from sklearn.manifold._t_sne import trustworthiness
from sklearn.manifold import TSNE
# mypy error: Module 'sklearn.manifold' has no attribute '_barnes_hut_tsne'
from sklearn.manifold import _barnes_hut_tsne # type: ignore
from sklearn.manifold._utils import _binary_search_perplexity
from sklearn.datasets import make_blobs
from scipy.optimize import check_grad
from scipy.spatial.distance import pdist
from scipy.spatial.distance import squareform
from sklearn.metrics.pairwise import pairwise_distances
from sklearn.metrics.pairwise import manhattan_distances
from sklearn.metrics.pairwise import cosine_distances
x = np.linspace(0, 1, 10)
xx, yy = np.meshgrid(x, x)
X_2d_grid = np.hstack([
xx.ravel().reshape(-1, 1),
yy.ravel().reshape(-1, 1),
])
def test_gradient_descent_stops():
# Test stopping conditions of gradient descent.
class ObjectiveSmallGradient:
def __init__(self):
self.it = -1
def __call__(self, _, compute_error=True):
self.it += 1
return (10 - self.it) / 10.0, np.array([1e-5])
def flat_function(_, compute_error=True):
return 0.0, np.ones(1)
# Gradient norm
old_stdout = sys.stdout
sys.stdout = StringIO()
try:
_, error, it = _gradient_descent(
ObjectiveSmallGradient(), np.zeros(1), 0, n_iter=100,
n_iter_without_progress=100, momentum=0.0, learning_rate=0.0,
min_gain=0.0, min_grad_norm=1e-5, verbose=2)
finally:
out = sys.stdout.getvalue()
sys.stdout.close()
sys.stdout = old_stdout
assert error == 1.0
assert it == 0
assert("gradient norm" in out)
# Maximum number of iterations without improvement
old_stdout = sys.stdout
sys.stdout = StringIO()
try:
_, error, it = _gradient_descent(
flat_function, np.zeros(1), 0, n_iter=100,
n_iter_without_progress=10, momentum=0.0, learning_rate=0.0,
min_gain=0.0, min_grad_norm=0.0, verbose=2)
finally:
out = sys.stdout.getvalue()
sys.stdout.close()
sys.stdout = old_stdout
assert error == 0.0
assert it == 11
assert("did not make any progress" in out)
# Maximum number of iterations
old_stdout = sys.stdout
sys.stdout = StringIO()
try:
_, error, it = _gradient_descent(
ObjectiveSmallGradient(), np.zeros(1), 0, n_iter=11,
n_iter_without_progress=100, momentum=0.0, learning_rate=0.0,
min_gain=0.0, min_grad_norm=0.0, verbose=2)
finally:
out = sys.stdout.getvalue()
sys.stdout.close()
sys.stdout = old_stdout
assert error == 0.0
assert it == 10
assert("Iteration 10" in out)
def test_binary_search():
# Test if the binary search finds Gaussians with desired perplexity.
random_state = check_random_state(0)
data = random_state.randn(50, 5)
distances = pairwise_distances(data).astype(np.float32)
desired_perplexity = 25.0
P = _binary_search_perplexity(distances, desired_perplexity, verbose=0)
P = np.maximum(P, np.finfo(np.double).eps)
mean_perplexity = np.mean([np.exp(-np.sum(P[i] * np.log(P[i])))
for i in range(P.shape[0])])
assert_almost_equal(mean_perplexity, desired_perplexity, decimal=3)
def test_binary_search_neighbors():
# Binary perplexity search approximation.
# Should be approximately equal to the slow method when we use
# all points as neighbors.
n_samples = 200
desired_perplexity = 25.0
random_state = check_random_state(0)
data = random_state.randn(n_samples, 2).astype(np.float32, copy=False)
distances = pairwise_distances(data)
P1 = _binary_search_perplexity(distances, desired_perplexity, verbose=0)
# Test that when we use all the neighbors the results are identical
n_neighbors = n_samples - 1
nn = NearestNeighbors().fit(data)
distance_graph = nn.kneighbors_graph(n_neighbors=n_neighbors,
mode='distance')
distances_nn = distance_graph.data.astype(np.float32, copy=False)
distances_nn = distances_nn.reshape(n_samples, n_neighbors)
P2 = _binary_search_perplexity(distances_nn, desired_perplexity, verbose=0)
indptr = distance_graph.indptr
P1_nn = np.array([P1[k, distance_graph.indices[indptr[k]:indptr[k + 1]]]
for k in range(n_samples)])
assert_array_almost_equal(P1_nn, P2, decimal=4)
# Test that the highest P_ij are the same when fewer neighbors are used
for k in np.linspace(150, n_samples - 1, 5):
k = int(k)
topn = k * 10 # check the top 10 * k entries out of k * k entries
distance_graph = nn.kneighbors_graph(n_neighbors=k, mode='distance')
distances_nn = distance_graph.data.astype(np.float32, copy=False)
distances_nn = distances_nn.reshape(n_samples, k)
P2k = _binary_search_perplexity(distances_nn, desired_perplexity,
verbose=0)
assert_array_almost_equal(P1_nn, P2, decimal=2)
idx = np.argsort(P1.ravel())[::-1]
P1top = P1.ravel()[idx][:topn]
idx = np.argsort(P2k.ravel())[::-1]
P2top = P2k.ravel()[idx][:topn]
assert_array_almost_equal(P1top, P2top, decimal=2)
def test_binary_perplexity_stability():
# Binary perplexity search should be stable.
# The binary_search_perplexity had a bug wherein the P array
# was uninitialized, leading to sporadically failing tests.
n_neighbors = 10
n_samples = 100
random_state = check_random_state(0)
data = random_state.randn(n_samples, 5)
nn = NearestNeighbors().fit(data)
distance_graph = nn.kneighbors_graph(n_neighbors=n_neighbors,
mode='distance')
distances = distance_graph.data.astype(np.float32, copy=False)
distances = distances.reshape(n_samples, n_neighbors)
last_P = None
desired_perplexity = 3
for _ in range(100):
P = _binary_search_perplexity(distances.copy(), desired_perplexity,
verbose=0)
P1 = _joint_probabilities_nn(distance_graph, desired_perplexity,
verbose=0)
# Convert the sparse matrix to a dense one for testing
P1 = P1.toarray()
if last_P is None:
last_P = P
last_P1 = P1
else:
assert_array_almost_equal(P, last_P, decimal=4)
assert_array_almost_equal(P1, last_P1, decimal=4)
def test_gradient():
# Test gradient of Kullback-Leibler divergence.
random_state = check_random_state(0)
n_samples = 50
n_features = 2
n_components = 2
alpha = 1.0
distances = random_state.randn(n_samples, n_features).astype(np.float32)
distances = np.abs(distances.dot(distances.T))
np.fill_diagonal(distances, 0.0)
X_embedded = random_state.randn(n_samples, n_components).astype(np.float32)
P = _joint_probabilities(distances, desired_perplexity=25.0,
verbose=0)
def fun(params):
return _kl_divergence(params, P, alpha, n_samples, n_components)[0]
def grad(params):
return _kl_divergence(params, P, alpha, n_samples, n_components)[1]
assert_almost_equal(check_grad(fun, grad, X_embedded.ravel()), 0.0,
decimal=5)
def test_trustworthiness():
# Test trustworthiness score.
random_state = check_random_state(0)
# Affine transformation
X = random_state.randn(100, 2)
assert trustworthiness(X, 5.0 + X / 10.0) == 1.0
# Randomly shuffled
X = np.arange(100).reshape(-1, 1)
X_embedded = X.copy()
random_state.shuffle(X_embedded)
assert trustworthiness(X, X_embedded) < 0.6
# Completely different
X = np.arange(5).reshape(-1, 1)
X_embedded = np.array([[0], [2], [4], [1], [3]])
assert_almost_equal(trustworthiness(X, X_embedded, n_neighbors=1), 0.2)
@pytest.mark.parametrize("method", ['exact', 'barnes_hut'])
@pytest.mark.parametrize("init", ('random', 'pca'))
def test_preserve_trustworthiness_approximately(method, init):
# Nearest neighbors should be preserved approximately.
random_state = check_random_state(0)
n_components = 2
X = random_state.randn(50, n_components).astype(np.float32)
tsne = TSNE(n_components=n_components, init=init, random_state=0,
method=method, n_iter=700)
X_embedded = tsne.fit_transform(X)
t = trustworthiness(X, X_embedded, n_neighbors=1)
assert t > 0.85
def test_optimization_minimizes_kl_divergence():
"""t-SNE should give a lower KL divergence with more iterations."""
random_state = check_random_state(0)
X, _ = make_blobs(n_features=3, random_state=random_state)
kl_divergences = []
for n_iter in [250, 300, 350]:
tsne = TSNE(n_components=2, perplexity=10, learning_rate=100.0,
n_iter=n_iter, random_state=0)
tsne.fit_transform(X)
kl_divergences.append(tsne.kl_divergence_)
assert kl_divergences[1] <= kl_divergences[0]
assert kl_divergences[2] <= kl_divergences[1]
@pytest.mark.parametrize('method', ['exact', 'barnes_hut'])
def test_fit_csr_matrix(method):
# X can be a sparse matrix.
rng = check_random_state(0)
X = rng.randn(50, 2)
X[(rng.randint(0, 50, 25), rng.randint(0, 2, 25))] = 0.0
X_csr = sp.csr_matrix(X)
tsne = TSNE(n_components=2, perplexity=10, learning_rate=100.0,
random_state=0, method=method, n_iter=750)
X_embedded = tsne.fit_transform(X_csr)
assert_allclose(trustworthiness(X_csr, X_embedded, n_neighbors=1),
1.0, rtol=1.1e-1)
def test_preserve_trustworthiness_approximately_with_precomputed_distances():
# Nearest neighbors should be preserved approximately.
random_state = check_random_state(0)
for i in range(3):
X = random_state.randn(80, 2)
D = squareform(pdist(X), "sqeuclidean")
tsne = TSNE(n_components=2, perplexity=2, learning_rate=100.0,
early_exaggeration=2.0, metric="precomputed",
random_state=i, verbose=0, n_iter=500)
X_embedded = tsne.fit_transform(D)
t = trustworthiness(D, X_embedded, n_neighbors=1, metric="precomputed")
assert t > .95
def test_trustworthiness_not_euclidean_metric():
# Test trustworthiness with a metric different from 'euclidean' and
# 'precomputed'
random_state = check_random_state(0)
X = random_state.randn(100, 2)
assert (trustworthiness(X, X, metric='cosine') ==
trustworthiness(pairwise_distances(X, metric='cosine'), X,
metric='precomputed'))
def test_early_exaggeration_too_small():
# Early exaggeration factor must be >= 1.
tsne = TSNE(early_exaggeration=0.99)
with pytest.raises(ValueError, match="early_exaggeration .*"):
tsne.fit_transform(np.array([[0.0], [0.0]]))
def test_too_few_iterations():
# Number of gradient descent iterations must be at least 200.
tsne = TSNE(n_iter=199)
with pytest.raises(ValueError, match="n_iter .*"):
tsne.fit_transform(np.array([[0.0], [0.0]]))
@pytest.mark.parametrize('method, retype', [
('exact', np.asarray),
('barnes_hut', np.asarray),
('barnes_hut', sp.csr_matrix),
])
@pytest.mark.parametrize('D, message_regex', [
([[0.0], [1.0]], ".* square distance matrix"),
([[0., -1.], [1., 0.]], ".* positive.*"),
])
def test_bad_precomputed_distances(method, D, retype, message_regex):
tsne = TSNE(metric="precomputed", method=method)
with pytest.raises(ValueError, match=message_regex):
tsne.fit_transform(retype(D))
def test_exact_no_precomputed_sparse():
tsne = TSNE(metric='precomputed', method='exact')
with pytest.raises(TypeError, match='sparse'):
tsne.fit_transform(sp.csr_matrix([[0, 5], [5, 0]]))
def test_high_perplexity_precomputed_sparse_distances():
# Perplexity should be less than 50
dist = np.array([[1., 0., 0.], [0., 1., 0.], [1., 0., 0.]])
bad_dist = sp.csr_matrix(dist)
tsne = TSNE(metric="precomputed")
msg = "3 neighbors per samples are required, but some samples have only 1"
with pytest.raises(ValueError, match=msg):
tsne.fit_transform(bad_dist)
@ignore_warnings(category=EfficiencyWarning)
def test_sparse_precomputed_distance():
"""Make sure that TSNE works identically for sparse and dense matrix"""
random_state = check_random_state(0)
X = random_state.randn(100, 2)
D_sparse = kneighbors_graph(X, n_neighbors=100, mode='distance',
include_self=True)
D = pairwise_distances(X)
assert sp.issparse(D_sparse)
assert_almost_equal(D_sparse.A, D)
tsne = TSNE(metric="precomputed", random_state=0)
Xt_dense = tsne.fit_transform(D)
for fmt in ['csr', 'lil']:
Xt_sparse = tsne.fit_transform(D_sparse.asformat(fmt))
assert_almost_equal(Xt_dense, Xt_sparse)
def test_non_positive_computed_distances():
# Computed distance matrices must be positive.
def metric(x, y):
return -1
tsne = TSNE(metric=metric, method='exact')
X = np.array([[0.0, 0.0], [1.0, 1.0]])
with pytest.raises(ValueError, match="All distances .*metric given.*"):
tsne.fit_transform(X)
def test_init_not_available():
# 'init' must be 'pca', 'random', or numpy array.
tsne = TSNE(init="not available")
m = "'init' must be 'pca', 'random', or a numpy array"
with pytest.raises(ValueError, match=m):
tsne.fit_transform(np.array([[0.0], [1.0]]))
def test_init_ndarray():
# Initialize TSNE with ndarray and test fit
tsne = TSNE(init=np.zeros((100, 2)))
X_embedded = tsne.fit_transform(np.ones((100, 5)))
assert_array_equal(np.zeros((100, 2)), X_embedded)
def test_init_ndarray_precomputed():
# Initialize TSNE with ndarray and metric 'precomputed'
# Make sure no FutureWarning is thrown from _fit
tsne = TSNE(init=np.zeros((100, 2)), metric="precomputed")
tsne.fit(np.zeros((100, 100)))
def test_distance_not_available():
# 'metric' must be valid.
tsne = TSNE(metric="not available", method='exact')
with pytest.raises(ValueError, match="Unknown metric not available.*"):
tsne.fit_transform(np.array([[0.0], [1.0]]))
tsne = TSNE(metric="not available", method='barnes_hut')
with pytest.raises(ValueError, match="Metric 'not available' not valid.*"):
tsne.fit_transform(np.array([[0.0], [1.0]]))
def test_method_not_available():
# 'nethod' must be 'barnes_hut' or 'exact'
tsne = TSNE(method='not available')
with pytest.raises(ValueError, match="'method' must be 'barnes_hut' or "):
tsne.fit_transform(np.array([[0.0], [1.0]]))
def test_angle_out_of_range_checks():
# check the angle parameter range
for angle in [-1, -1e-6, 1 + 1e-6, 2]:
tsne = TSNE(angle=angle)
with pytest.raises(ValueError, match="'angle' must be between "
"0.0 - 1.0"):
tsne.fit_transform(np.array([[0.0], [1.0]]))
def test_pca_initialization_not_compatible_with_precomputed_kernel():
# Precomputed distance matrices must be square matrices.
tsne = TSNE(metric="precomputed", init="pca")
with pytest.raises(ValueError, match="The parameter init=\"pca\" cannot"
" be used with"
" metric=\"precomputed\"."):
tsne.fit_transform(np.array([[0.0], [1.0]]))
def test_n_components_range():
# barnes_hut method should only be used with n_components <= 3
tsne = TSNE(n_components=4, method="barnes_hut")
with pytest.raises(ValueError, match="'n_components' should be .*"):
tsne.fit_transform(np.array([[0.0], [1.0]]))
def test_early_exaggeration_used():
# check that the ``early_exaggeration`` parameter has an effect
random_state = check_random_state(0)
n_components = 2
methods = ['exact', 'barnes_hut']
X = random_state.randn(25, n_components).astype(np.float32)
for method in methods:
tsne = TSNE(n_components=n_components, perplexity=1,
learning_rate=100.0, init="pca", random_state=0,
method=method, early_exaggeration=1.0, n_iter=250)
X_embedded1 = tsne.fit_transform(X)
tsne = TSNE(n_components=n_components, perplexity=1,
learning_rate=100.0, init="pca", random_state=0,
method=method, early_exaggeration=10.0, n_iter=250)
X_embedded2 = tsne.fit_transform(X)
assert not np.allclose(X_embedded1, X_embedded2)
def test_n_iter_used():
# check that the ``n_iter`` parameter has an effect
random_state = check_random_state(0)
n_components = 2
methods = ['exact', 'barnes_hut']
X = random_state.randn(25, n_components).astype(np.float32)
for method in methods:
for n_iter in [251, 500]:
tsne = TSNE(n_components=n_components, perplexity=1,
learning_rate=0.5, init="random", random_state=0,
method=method, early_exaggeration=1.0, n_iter=n_iter)
tsne.fit_transform(X)
assert tsne.n_iter_ == n_iter - 1
def test_answer_gradient_two_points():
# Test the tree with only a single set of children.
#
# These tests & answers have been checked against the reference
# implementation by LvdM.
pos_input = np.array([[1.0, 0.0], [0.0, 1.0]])
pos_output = np.array([[-4.961291e-05, -1.072243e-04],
[9.259460e-05, 2.702024e-04]])
neighbors = np.array([[1],
[0]])
grad_output = np.array([[-2.37012478e-05, -6.29044398e-05],
[2.37012478e-05, 6.29044398e-05]])
_run_answer_test(pos_input, pos_output, neighbors, grad_output)
def test_answer_gradient_four_points():
# Four points tests the tree with multiple levels of children.
#
# These tests & answers have been checked against the reference
# implementation by LvdM.
pos_input = np.array([[1.0, 0.0], [0.0, 1.0],
[5.0, 2.0], [7.3, 2.2]])
pos_output = np.array([[6.080564e-05, -7.120823e-05],
[-1.718945e-04, -4.000536e-05],
[-2.271720e-04, 8.663310e-05],
[-1.032577e-04, -3.582033e-05]])
neighbors = np.array([[1, 2, 3],
[0, 2, 3],
[1, 0, 3],
[1, 2, 0]])
grad_output = np.array([[5.81128448e-05, -7.78033454e-06],
[-5.81526851e-05, 7.80976444e-06],
[4.24275173e-08, -3.69569698e-08],
[-2.58720939e-09, 7.52706374e-09]])
_run_answer_test(pos_input, pos_output, neighbors, grad_output)
def test_skip_num_points_gradient():
# Test the kwargs option skip_num_points.
#
# Skip num points should make it such that the Barnes_hut gradient
# is not calculated for indices below skip_num_point.
# Aside from skip_num_points=2 and the first two gradient rows
# being set to zero, these data points are the same as in
# test_answer_gradient_four_points()
pos_input = np.array([[1.0, 0.0], [0.0, 1.0],
[5.0, 2.0], [7.3, 2.2]])
pos_output = np.array([[6.080564e-05, -7.120823e-05],
[-1.718945e-04, -4.000536e-05],
[-2.271720e-04, 8.663310e-05],
[-1.032577e-04, -3.582033e-05]])
neighbors = np.array([[1, 2, 3],
[0, 2, 3],
[1, 0, 3],
[1, 2, 0]])
grad_output = np.array([[0.0, 0.0],
[0.0, 0.0],
[4.24275173e-08, -3.69569698e-08],
[-2.58720939e-09, 7.52706374e-09]])
_run_answer_test(pos_input, pos_output, neighbors, grad_output,
False, 0.1, 2)
def _run_answer_test(pos_input, pos_output, neighbors, grad_output,
verbose=False, perplexity=0.1, skip_num_points=0):
distances = pairwise_distances(pos_input).astype(np.float32)
args = distances, perplexity, verbose
pos_output = pos_output.astype(np.float32)
neighbors = neighbors.astype(np.int64, copy=False)
pij_input = _joint_probabilities(*args)
pij_input = squareform(pij_input).astype(np.float32)
grad_bh = np.zeros(pos_output.shape, dtype=np.float32)
from scipy.sparse import csr_matrix
P = csr_matrix(pij_input)
neighbors = P.indices.astype(np.int64)
indptr = P.indptr.astype(np.int64)
_barnes_hut_tsne.gradient(P.data, pos_output, neighbors, indptr,
grad_bh, 0.5, 2, 1, skip_num_points=0)
assert_array_almost_equal(grad_bh, grad_output, decimal=4)
def test_verbose():
# Verbose options write to stdout.
random_state = check_random_state(0)
tsne = TSNE(verbose=2)
X = random_state.randn(5, 2)
old_stdout = sys.stdout
sys.stdout = StringIO()
try:
tsne.fit_transform(X)
finally:
out = sys.stdout.getvalue()
sys.stdout.close()
sys.stdout = old_stdout
assert("[t-SNE]" in out)
assert("nearest neighbors..." in out)
assert("Computed conditional probabilities" in out)
assert("Mean sigma" in out)
assert("early exaggeration" in out)
def test_chebyshev_metric():
# t-SNE should allow metrics that cannot be squared (issue #3526).
random_state = check_random_state(0)
tsne = TSNE(metric="chebyshev")
X = random_state.randn(5, 2)
tsne.fit_transform(X)
def test_reduction_to_one_component():
# t-SNE should allow reduction to one component (issue #4154).
random_state = check_random_state(0)
tsne = TSNE(n_components=1)
X = random_state.randn(5, 2)
X_embedded = tsne.fit(X).embedding_
assert(np.all(np.isfinite(X_embedded)))
@pytest.mark.parametrize('method', ['barnes_hut', 'exact'])
@pytest.mark.parametrize('dt', [np.float32, np.float64])
def test_64bit(method, dt):
# Ensure 64bit arrays are handled correctly.
random_state = check_random_state(0)
X = random_state.randn(10, 2).astype(dt, copy=False)
tsne = TSNE(n_components=2, perplexity=2, learning_rate=100.0,
random_state=0, method=method, verbose=0,
n_iter=300)
X_embedded = tsne.fit_transform(X)
effective_type = X_embedded.dtype
# tsne cython code is only single precision, so the output will
# always be single precision, irrespectively of the input dtype
assert effective_type == np.float32
@pytest.mark.parametrize('method', ['barnes_hut', 'exact'])
def test_kl_divergence_not_nan(method):
# Ensure kl_divergence_ is computed at last iteration
# even though n_iter % n_iter_check != 0, i.e. 1003 % 50 != 0
random_state = check_random_state(0)
X = random_state.randn(50, 2)
tsne = TSNE(n_components=2, perplexity=2, learning_rate=100.0,
random_state=0, method=method, verbose=0, n_iter=503)
tsne.fit_transform(X)
assert not np.isnan(tsne.kl_divergence_)
def test_barnes_hut_angle():
# When Barnes-Hut's angle=0 this corresponds to the exact method.
angle = 0.0
perplexity = 10
n_samples = 100
for n_components in [2, 3]:
n_features = 5
degrees_of_freedom = float(n_components - 1.0)
random_state = check_random_state(0)
data = random_state.randn(n_samples, n_features)
distances = pairwise_distances(data)
params = random_state.randn(n_samples, n_components)
P = _joint_probabilities(distances, perplexity, verbose=0)
kl_exact, grad_exact = _kl_divergence(params, P, degrees_of_freedom,
n_samples, n_components)
n_neighbors = n_samples - 1
distances_csr = NearestNeighbors().fit(data).kneighbors_graph(
n_neighbors=n_neighbors, mode='distance')
P_bh = _joint_probabilities_nn(distances_csr, perplexity, verbose=0)
kl_bh, grad_bh = _kl_divergence_bh(params, P_bh, degrees_of_freedom,
n_samples, n_components,
angle=angle, skip_num_points=0,
verbose=0)
P = squareform(P)
P_bh = P_bh.toarray()
assert_array_almost_equal(P_bh, P, decimal=5)
assert_almost_equal(kl_exact, kl_bh, decimal=3)
@skip_if_32bit
def test_n_iter_without_progress():
# Use a dummy negative n_iter_without_progress and check output on stdout
random_state = check_random_state(0)
X = random_state.randn(100, 10)
for method in ["barnes_hut", "exact"]:
tsne = TSNE(n_iter_without_progress=-1, verbose=2, learning_rate=1e8,
random_state=0, method=method, n_iter=351, init="random")
tsne._N_ITER_CHECK = 1
tsne._EXPLORATION_N_ITER = 0
old_stdout = sys.stdout
sys.stdout = StringIO()
try:
tsne.fit_transform(X)
finally:
out = sys.stdout.getvalue()
sys.stdout.close()
sys.stdout = old_stdout
# The output needs to contain the value of n_iter_without_progress
assert ("did not make any progress during the "
"last -1 episodes. Finished." in out)
def test_min_grad_norm():
# Make sure that the parameter min_grad_norm is used correctly
random_state = check_random_state(0)
X = random_state.randn(100, 2)
min_grad_norm = 0.002
tsne = TSNE(min_grad_norm=min_grad_norm, verbose=2,
random_state=0, method='exact')
old_stdout = sys.stdout
sys.stdout = StringIO()
try:
tsne.fit_transform(X)
finally:
out = sys.stdout.getvalue()
sys.stdout.close()
sys.stdout = old_stdout
lines_out = out.split('\n')
# extract the gradient norm from the verbose output
gradient_norm_values = []
for line in lines_out:
# When the computation is Finished just an old gradient norm value
# is repeated that we do not need to store
if 'Finished' in line:
break
start_grad_norm = line.find('gradient norm')
if start_grad_norm >= 0:
line = line[start_grad_norm:]
line = line.replace('gradient norm = ', '').split(' ')[0]
gradient_norm_values.append(float(line))
# Compute how often the gradient norm is smaller than min_grad_norm
gradient_norm_values = np.array(gradient_norm_values)
n_smaller_gradient_norms = \
len(gradient_norm_values[gradient_norm_values <= min_grad_norm])
# The gradient norm can be smaller than min_grad_norm at most once,
# because in the moment it becomes smaller the optimization stops
assert n_smaller_gradient_norms <= 1
def test_accessible_kl_divergence():
# Ensures that the accessible kl_divergence matches the computed value
random_state = check_random_state(0)
X = random_state.randn(50, 2)
tsne = TSNE(n_iter_without_progress=2, verbose=2,
random_state=0, method='exact',
n_iter=500)
old_stdout = sys.stdout
sys.stdout = StringIO()
try:
tsne.fit_transform(X)
finally:
out = sys.stdout.getvalue()
sys.stdout.close()
sys.stdout = old_stdout
# The output needs to contain the accessible kl_divergence as the error at
# the last iteration
for line in out.split('\n')[::-1]:
if 'Iteration' in line:
_, _, error = line.partition('error = ')
if error:
error, _, _ = error.partition(',')
break
assert_almost_equal(tsne.kl_divergence_, float(error), decimal=5)
@pytest.mark.parametrize('method', ['barnes_hut', 'exact'])
def test_uniform_grid(method):
"""Make sure that TSNE can approximately recover a uniform 2D grid
Due to ties in distances between point in X_2d_grid, this test is platform
dependent for ``method='barnes_hut'`` due to numerical imprecision.
Also, t-SNE is not assured to converge to the right solution because bad
initialization can lead to convergence to bad local minimum (the
optimization problem is non-convex). To avoid breaking the test too often,
we re-run t-SNE from the final point when the convergence is not good
enough.
"""
seeds = range(3)
n_iter = 500
for seed in seeds:
tsne = TSNE(n_components=2, init='random', random_state=seed,
perplexity=50, n_iter=n_iter, method=method)
Y = tsne.fit_transform(X_2d_grid)
try_name = "{}_{}".format(method, seed)
try:
assert_uniform_grid(Y, try_name)
except AssertionError:
# If the test fails a first time, re-run with init=Y to see if
# this was caused by a bad initialization. Note that this will
# also run an early_exaggeration step.
try_name += ":rerun"
tsne.init = Y
Y = tsne.fit_transform(X_2d_grid)
assert_uniform_grid(Y, try_name)
def assert_uniform_grid(Y, try_name=None):
# Ensure that the resulting embedding leads to approximately
# uniformly spaced points: the distance to the closest neighbors
# should be non-zero and approximately constant.
nn = NearestNeighbors(n_neighbors=1).fit(Y)
dist_to_nn = nn.kneighbors(return_distance=True)[0].ravel()
assert dist_to_nn.min() > 0.1
smallest_to_mean = dist_to_nn.min() / np.mean(dist_to_nn)
largest_to_mean = dist_to_nn.max() / np.mean(dist_to_nn)
assert smallest_to_mean > .5, try_name
assert largest_to_mean < 2, try_name
def test_bh_match_exact():
# check that the ``barnes_hut`` method match the exact one when
# ``angle = 0`` and ``perplexity > n_samples / 3``
random_state = check_random_state(0)
n_features = 10
X = random_state.randn(30, n_features).astype(np.float32)
X_embeddeds = {}
n_iter = {}
for method in ['exact', 'barnes_hut']:
tsne = TSNE(n_components=2, method=method, learning_rate=1.0,
init="random", random_state=0, n_iter=251,
perplexity=30.0, angle=0)
# Kill the early_exaggeration
tsne._EXPLORATION_N_ITER = 0
X_embeddeds[method] = tsne.fit_transform(X)
n_iter[method] = tsne.n_iter_
assert n_iter['exact'] == n_iter['barnes_hut']
assert_allclose(X_embeddeds['exact'], X_embeddeds['barnes_hut'], rtol=1e-4)
def test_gradient_bh_multithread_match_sequential():
# check that the bh gradient with different num_threads gives the same
# results
n_features = 10
n_samples = 30
n_components = 2
degrees_of_freedom = 1
angle = 3
perplexity = 5
random_state = check_random_state(0)
data = random_state.randn(n_samples, n_features).astype(np.float32)
params = random_state.randn(n_samples, n_components)
n_neighbors = n_samples - 1
distances_csr = NearestNeighbors().fit(data).kneighbors_graph(
n_neighbors=n_neighbors, mode='distance')
P_bh = _joint_probabilities_nn(distances_csr, perplexity, verbose=0)
kl_sequential, grad_sequential = _kl_divergence_bh(
params, P_bh, degrees_of_freedom, n_samples, n_components,
angle=angle, skip_num_points=0, verbose=0, num_threads=1)
for num_threads in [2, 4]:
kl_multithread, grad_multithread = _kl_divergence_bh(
params, P_bh, degrees_of_freedom, n_samples, n_components,
angle=angle, skip_num_points=0, verbose=0, num_threads=num_threads)
assert_allclose(kl_multithread, kl_sequential, rtol=1e-6)
assert_allclose(grad_multithread, grad_multithread)
def test_tsne_with_different_distance_metrics():
"""Make sure that TSNE works for different distance metrics"""
random_state = check_random_state(0)
n_components_original = 3
n_components_embedding = 2
X = random_state.randn(50, n_components_original).astype(np.float32)
metrics = ['manhattan', 'cosine']
dist_funcs = [manhattan_distances, cosine_distances]
for metric, dist_func in zip(metrics, dist_funcs):
X_transformed_tsne = TSNE(
metric=metric, n_components=n_components_embedding,
random_state=0, n_iter=300).fit_transform(X)
X_transformed_tsne_precomputed = TSNE(
metric='precomputed', n_components=n_components_embedding,
random_state=0, n_iter=300).fit_transform(dist_func(X))
assert_array_equal(X_transformed_tsne, X_transformed_tsne_precomputed)
@pytest.mark.parametrize('method', ['exact', 'barnes_hut'])
def test_tsne_n_jobs(method):
"""Make sure that the n_jobs parameter doesn't impact the output"""
random_state = check_random_state(0)
n_features = 10
X = random_state.randn(30, n_features)
X_tr_ref = TSNE(n_components=2, method=method, perplexity=30.0,
angle=0, n_jobs=1, random_state=0).fit_transform(X)
X_tr = TSNE(n_components=2, method=method, perplexity=30.0,
angle=0, n_jobs=2, random_state=0).fit_transform(X)
assert_allclose(X_tr_ref, X_tr)