957 lines
36 KiB
Python
957 lines
36 KiB
Python
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import sys
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from io import StringIO
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import numpy as np
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from numpy.testing import assert_allclose
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import scipy.sparse as sp
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import pytest
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from sklearn.neighbors import NearestNeighbors
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from sklearn.neighbors import kneighbors_graph
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from sklearn.exceptions import EfficiencyWarning
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from sklearn.utils._testing import ignore_warnings
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from sklearn.utils._testing import assert_almost_equal
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from sklearn.utils._testing import assert_array_equal
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from sklearn.utils._testing import assert_array_almost_equal
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from sklearn.utils._testing import skip_if_32bit
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from sklearn.utils import check_random_state
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from sklearn.manifold._t_sne import _joint_probabilities
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from sklearn.manifold._t_sne import _joint_probabilities_nn
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from sklearn.manifold._t_sne import _kl_divergence
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from sklearn.manifold._t_sne import _kl_divergence_bh
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from sklearn.manifold._t_sne import _gradient_descent
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from sklearn.manifold._t_sne import trustworthiness
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from sklearn.manifold import TSNE
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# mypy error: Module 'sklearn.manifold' has no attribute '_barnes_hut_tsne'
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from sklearn.manifold import _barnes_hut_tsne # type: ignore
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from sklearn.manifold._utils import _binary_search_perplexity
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from sklearn.datasets import make_blobs
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from scipy.optimize import check_grad
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from scipy.spatial.distance import pdist
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from scipy.spatial.distance import squareform
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from sklearn.metrics.pairwise import pairwise_distances
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from sklearn.metrics.pairwise import manhattan_distances
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from sklearn.metrics.pairwise import cosine_distances
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x = np.linspace(0, 1, 10)
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xx, yy = np.meshgrid(x, x)
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X_2d_grid = np.hstack([
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xx.ravel().reshape(-1, 1),
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yy.ravel().reshape(-1, 1),
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])
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def test_gradient_descent_stops():
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# Test stopping conditions of gradient descent.
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class ObjectiveSmallGradient:
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def __init__(self):
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self.it = -1
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def __call__(self, _, compute_error=True):
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self.it += 1
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return (10 - self.it) / 10.0, np.array([1e-5])
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def flat_function(_, compute_error=True):
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return 0.0, np.ones(1)
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# Gradient norm
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old_stdout = sys.stdout
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sys.stdout = StringIO()
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try:
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_, error, it = _gradient_descent(
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ObjectiveSmallGradient(), np.zeros(1), 0, n_iter=100,
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n_iter_without_progress=100, momentum=0.0, learning_rate=0.0,
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min_gain=0.0, min_grad_norm=1e-5, verbose=2)
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finally:
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out = sys.stdout.getvalue()
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sys.stdout.close()
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sys.stdout = old_stdout
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assert error == 1.0
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assert it == 0
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assert("gradient norm" in out)
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# Maximum number of iterations without improvement
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old_stdout = sys.stdout
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sys.stdout = StringIO()
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try:
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_, error, it = _gradient_descent(
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flat_function, np.zeros(1), 0, n_iter=100,
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n_iter_without_progress=10, momentum=0.0, learning_rate=0.0,
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min_gain=0.0, min_grad_norm=0.0, verbose=2)
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finally:
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out = sys.stdout.getvalue()
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sys.stdout.close()
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sys.stdout = old_stdout
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assert error == 0.0
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assert it == 11
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assert("did not make any progress" in out)
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# Maximum number of iterations
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old_stdout = sys.stdout
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sys.stdout = StringIO()
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try:
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_, error, it = _gradient_descent(
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ObjectiveSmallGradient(), np.zeros(1), 0, n_iter=11,
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n_iter_without_progress=100, momentum=0.0, learning_rate=0.0,
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min_gain=0.0, min_grad_norm=0.0, verbose=2)
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finally:
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out = sys.stdout.getvalue()
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sys.stdout.close()
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sys.stdout = old_stdout
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assert error == 0.0
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assert it == 10
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assert("Iteration 10" in out)
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def test_binary_search():
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# Test if the binary search finds Gaussians with desired perplexity.
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random_state = check_random_state(0)
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data = random_state.randn(50, 5)
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distances = pairwise_distances(data).astype(np.float32)
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desired_perplexity = 25.0
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P = _binary_search_perplexity(distances, desired_perplexity, verbose=0)
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P = np.maximum(P, np.finfo(np.double).eps)
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mean_perplexity = np.mean([np.exp(-np.sum(P[i] * np.log(P[i])))
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for i in range(P.shape[0])])
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assert_almost_equal(mean_perplexity, desired_perplexity, decimal=3)
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def test_binary_search_neighbors():
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# Binary perplexity search approximation.
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# Should be approximately equal to the slow method when we use
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# all points as neighbors.
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n_samples = 200
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desired_perplexity = 25.0
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random_state = check_random_state(0)
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data = random_state.randn(n_samples, 2).astype(np.float32, copy=False)
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distances = pairwise_distances(data)
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P1 = _binary_search_perplexity(distances, desired_perplexity, verbose=0)
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# Test that when we use all the neighbors the results are identical
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n_neighbors = n_samples - 1
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nn = NearestNeighbors().fit(data)
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distance_graph = nn.kneighbors_graph(n_neighbors=n_neighbors,
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mode='distance')
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distances_nn = distance_graph.data.astype(np.float32, copy=False)
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distances_nn = distances_nn.reshape(n_samples, n_neighbors)
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P2 = _binary_search_perplexity(distances_nn, desired_perplexity, verbose=0)
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indptr = distance_graph.indptr
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P1_nn = np.array([P1[k, distance_graph.indices[indptr[k]:indptr[k + 1]]]
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for k in range(n_samples)])
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assert_array_almost_equal(P1_nn, P2, decimal=4)
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# Test that the highest P_ij are the same when fewer neighbors are used
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for k in np.linspace(150, n_samples - 1, 5):
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k = int(k)
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topn = k * 10 # check the top 10 * k entries out of k * k entries
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distance_graph = nn.kneighbors_graph(n_neighbors=k, mode='distance')
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distances_nn = distance_graph.data.astype(np.float32, copy=False)
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distances_nn = distances_nn.reshape(n_samples, k)
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P2k = _binary_search_perplexity(distances_nn, desired_perplexity,
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verbose=0)
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assert_array_almost_equal(P1_nn, P2, decimal=2)
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idx = np.argsort(P1.ravel())[::-1]
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P1top = P1.ravel()[idx][:topn]
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idx = np.argsort(P2k.ravel())[::-1]
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P2top = P2k.ravel()[idx][:topn]
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assert_array_almost_equal(P1top, P2top, decimal=2)
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def test_binary_perplexity_stability():
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# Binary perplexity search should be stable.
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# The binary_search_perplexity had a bug wherein the P array
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# was uninitialized, leading to sporadically failing tests.
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n_neighbors = 10
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n_samples = 100
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random_state = check_random_state(0)
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data = random_state.randn(n_samples, 5)
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nn = NearestNeighbors().fit(data)
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distance_graph = nn.kneighbors_graph(n_neighbors=n_neighbors,
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mode='distance')
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distances = distance_graph.data.astype(np.float32, copy=False)
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distances = distances.reshape(n_samples, n_neighbors)
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last_P = None
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desired_perplexity = 3
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for _ in range(100):
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P = _binary_search_perplexity(distances.copy(), desired_perplexity,
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verbose=0)
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P1 = _joint_probabilities_nn(distance_graph, desired_perplexity,
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verbose=0)
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# Convert the sparse matrix to a dense one for testing
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P1 = P1.toarray()
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if last_P is None:
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last_P = P
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last_P1 = P1
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else:
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assert_array_almost_equal(P, last_P, decimal=4)
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assert_array_almost_equal(P1, last_P1, decimal=4)
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def test_gradient():
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# Test gradient of Kullback-Leibler divergence.
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random_state = check_random_state(0)
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n_samples = 50
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n_features = 2
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n_components = 2
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alpha = 1.0
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distances = random_state.randn(n_samples, n_features).astype(np.float32)
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distances = np.abs(distances.dot(distances.T))
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np.fill_diagonal(distances, 0.0)
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X_embedded = random_state.randn(n_samples, n_components).astype(np.float32)
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P = _joint_probabilities(distances, desired_perplexity=25.0,
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verbose=0)
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def fun(params):
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return _kl_divergence(params, P, alpha, n_samples, n_components)[0]
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def grad(params):
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return _kl_divergence(params, P, alpha, n_samples, n_components)[1]
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assert_almost_equal(check_grad(fun, grad, X_embedded.ravel()), 0.0,
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decimal=5)
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def test_trustworthiness():
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# Test trustworthiness score.
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random_state = check_random_state(0)
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# Affine transformation
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X = random_state.randn(100, 2)
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assert trustworthiness(X, 5.0 + X / 10.0) == 1.0
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# Randomly shuffled
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X = np.arange(100).reshape(-1, 1)
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X_embedded = X.copy()
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random_state.shuffle(X_embedded)
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assert trustworthiness(X, X_embedded) < 0.6
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# Completely different
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X = np.arange(5).reshape(-1, 1)
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X_embedded = np.array([[0], [2], [4], [1], [3]])
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assert_almost_equal(trustworthiness(X, X_embedded, n_neighbors=1), 0.2)
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@pytest.mark.parametrize("method", ['exact', 'barnes_hut'])
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@pytest.mark.parametrize("init", ('random', 'pca'))
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def test_preserve_trustworthiness_approximately(method, init):
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# Nearest neighbors should be preserved approximately.
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random_state = check_random_state(0)
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n_components = 2
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X = random_state.randn(50, n_components).astype(np.float32)
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tsne = TSNE(n_components=n_components, init=init, random_state=0,
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method=method, n_iter=700)
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X_embedded = tsne.fit_transform(X)
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t = trustworthiness(X, X_embedded, n_neighbors=1)
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assert t > 0.85
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def test_optimization_minimizes_kl_divergence():
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"""t-SNE should give a lower KL divergence with more iterations."""
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random_state = check_random_state(0)
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X, _ = make_blobs(n_features=3, random_state=random_state)
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kl_divergences = []
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for n_iter in [250, 300, 350]:
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tsne = TSNE(n_components=2, perplexity=10, learning_rate=100.0,
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n_iter=n_iter, random_state=0)
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tsne.fit_transform(X)
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kl_divergences.append(tsne.kl_divergence_)
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assert kl_divergences[1] <= kl_divergences[0]
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assert kl_divergences[2] <= kl_divergences[1]
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@pytest.mark.parametrize('method', ['exact', 'barnes_hut'])
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def test_fit_csr_matrix(method):
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# X can be a sparse matrix.
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rng = check_random_state(0)
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X = rng.randn(50, 2)
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X[(rng.randint(0, 50, 25), rng.randint(0, 2, 25))] = 0.0
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X_csr = sp.csr_matrix(X)
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tsne = TSNE(n_components=2, perplexity=10, learning_rate=100.0,
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random_state=0, method=method, n_iter=750)
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X_embedded = tsne.fit_transform(X_csr)
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assert_allclose(trustworthiness(X_csr, X_embedded, n_neighbors=1),
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1.0, rtol=1.1e-1)
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def test_preserve_trustworthiness_approximately_with_precomputed_distances():
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# Nearest neighbors should be preserved approximately.
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random_state = check_random_state(0)
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for i in range(3):
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X = random_state.randn(80, 2)
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D = squareform(pdist(X), "sqeuclidean")
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tsne = TSNE(n_components=2, perplexity=2, learning_rate=100.0,
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early_exaggeration=2.0, metric="precomputed",
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random_state=i, verbose=0, n_iter=500,
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square_distances=True)
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X_embedded = tsne.fit_transform(D)
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t = trustworthiness(D, X_embedded, n_neighbors=1, metric="precomputed")
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assert t > .95
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def test_trustworthiness_not_euclidean_metric():
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# Test trustworthiness with a metric different from 'euclidean' and
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# 'precomputed'
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random_state = check_random_state(0)
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X = random_state.randn(100, 2)
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assert (trustworthiness(X, X, metric='cosine') ==
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trustworthiness(pairwise_distances(X, metric='cosine'), X,
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metric='precomputed'))
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def test_early_exaggeration_too_small():
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# Early exaggeration factor must be >= 1.
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tsne = TSNE(early_exaggeration=0.99)
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with pytest.raises(ValueError, match="early_exaggeration .*"):
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tsne.fit_transform(np.array([[0.0], [0.0]]))
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def test_too_few_iterations():
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# Number of gradient descent iterations must be at least 200.
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tsne = TSNE(n_iter=199)
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with pytest.raises(ValueError, match="n_iter .*"):
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tsne.fit_transform(np.array([[0.0], [0.0]]))
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@pytest.mark.parametrize('method, retype', [
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('exact', np.asarray),
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('barnes_hut', np.asarray),
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('barnes_hut', sp.csr_matrix),
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])
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@pytest.mark.parametrize('D, message_regex', [
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([[0.0], [1.0]], ".* square distance matrix"),
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([[0., -1.], [1., 0.]], ".* positive.*"),
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])
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def test_bad_precomputed_distances(method, D, retype, message_regex):
|
||
|
|
tsne = TSNE(metric="precomputed", method=method,
|
||
|
|
square_distances=True)
|
||
|
|
with pytest.raises(ValueError, match=message_regex):
|
||
|
|
tsne.fit_transform(retype(D))
|
||
|
|
|
||
|
|
|
||
|
|
def test_exact_no_precomputed_sparse():
|
||
|
|
tsne = TSNE(metric='precomputed', method='exact', square_distances=True)
|
||
|
|
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", square_distances=True)
|
||
|
|
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, square_distances=True)
|
||
|
|
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
|
||
|
|
|
||
|
|
# Negative computed distances should be caught even if result is squared
|
||
|
|
tsne = TSNE(metric=metric, method='exact', square_distances=True)
|
||
|
|
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",
|
||
|
|
square_distances=True)
|
||
|
|
tsne.fit(np.zeros((100, 100)))
|
||
|
|
|
||
|
|
|
||
|
|
def test_distance_not_available():
|
||
|
|
# 'metric' must be valid.
|
||
|
|
tsne = TSNE(metric="not available", method='exact', square_distances=True)
|
||
|
|
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',
|
||
|
|
square_distances=True)
|
||
|
|
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_square_distances_not_available():
|
||
|
|
# square_distances must be True or 'legacy'.
|
||
|
|
tsne = TSNE(square_distances="not_available")
|
||
|
|
with pytest.raises(ValueError, match="'square_distances' must be True 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", square_distances=True)
|
||
|
|
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", square_distances=True)
|
||
|
|
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, square_distances=True).fit_transform(X)
|
||
|
|
X_transformed_tsne_precomputed = TSNE(
|
||
|
|
metric='precomputed', n_components=n_components_embedding,
|
||
|
|
random_state=0, n_iter=300,
|
||
|
|
square_distances=True).fit_transform(dist_func(X))
|
||
|
|
assert_array_equal(X_transformed_tsne, X_transformed_tsne_precomputed)
|
||
|
|
|
||
|
|
|
||
|
|
@pytest.mark.parametrize('method', ['exact', 'barnes_hut'])
|
||
|
|
@pytest.mark.parametrize('metric', ['euclidean', 'manhattan'])
|
||
|
|
@pytest.mark.parametrize('square_distances', [True, 'legacy'])
|
||
|
|
@ignore_warnings(category=FutureWarning)
|
||
|
|
def test_tsne_different_square_distances(method, metric, square_distances):
|
||
|
|
# Make sure that TSNE works for different square_distances settings
|
||
|
|
# FIXME remove test when square_distances=True becomes the default in 1.1
|
||
|
|
random_state = check_random_state(0)
|
||
|
|
n_components_original = 3
|
||
|
|
n_components_embedding = 2
|
||
|
|
|
||
|
|
# Used to create data with structure; this avoids unstable behavior in TSNE
|
||
|
|
X, _ = make_blobs(n_features=n_components_original,
|
||
|
|
random_state=random_state)
|
||
|
|
X_precomputed = pairwise_distances(X, metric=metric)
|
||
|
|
|
||
|
|
if metric == 'euclidean' and square_distances == 'legacy':
|
||
|
|
X_precomputed **= 2
|
||
|
|
|
||
|
|
X_transformed_tsne = TSNE(
|
||
|
|
metric=metric, n_components=n_components_embedding,
|
||
|
|
square_distances=square_distances, method=method,
|
||
|
|
random_state=0).fit_transform(X)
|
||
|
|
X_transformed_tsne_precomputed = TSNE(
|
||
|
|
metric='precomputed', n_components=n_components_embedding,
|
||
|
|
square_distances=square_distances, method=method,
|
||
|
|
random_state=0).fit_transform(X_precomputed)
|
||
|
|
|
||
|
|
assert_allclose(X_transformed_tsne, X_transformed_tsne_precomputed)
|
||
|
|
|
||
|
|
|
||
|
|
@pytest.mark.parametrize('metric', ['euclidean', 'manhattan'])
|
||
|
|
@pytest.mark.parametrize('square_distances', [True, 'legacy'])
|
||
|
|
def test_tsne_square_distances_futurewarning(metric, square_distances):
|
||
|
|
# Make sure that a FutureWarning is only raised when a non-Euclidean
|
||
|
|
# metric is specified and square_distances is not set to True.
|
||
|
|
random_state = check_random_state(0)
|
||
|
|
|
||
|
|
X = random_state.randn(5, 2)
|
||
|
|
tsne = TSNE(metric=metric, square_distances=square_distances)
|
||
|
|
|
||
|
|
if metric != 'euclidean' and square_distances is not True:
|
||
|
|
with pytest.warns(FutureWarning, match="'square_distances'.*"):
|
||
|
|
tsne.fit_transform(X)
|
||
|
|
else:
|
||
|
|
with pytest.warns(None) as record:
|
||
|
|
tsne.fit_transform(X)
|
||
|
|
assert not record
|
||
|
|
|
||
|
|
|
||
|
|
@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)
|