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)
distances = random_state.randn(n_samples, n_features)
distances = distances.astype(np.float32)
distances = distances.dot(distances.T)
np.fill_diagonal(distances, 0.0)
params = random_state.randn(n_samples, n_components)
P = _joint_probabilities(distances, perplexity, False)
kl, gradex = _kl_divergence(params, P, degrees_of_freedom, n_samples,
n_components)
k = n_samples - 1
bt = BallTree(distances)
distances_nn, neighbors_nn = bt.query(distances, k=k + 1)
neighbors_nn = neighbors_nn[:, 1:]
Pbh = _joint_probabilities_nn(distances, neighbors_nn,
perplexity, False)
kl, gradbh = _kl_divergence_bh(params, Pbh, neighbors_nn,
degrees_of_freedom, n_samples,
n_components, angle=angle,
skip_num_points=0, verbose=False)
assert_array_almost_equal(Pbh, P, decimal=5)
assert_array_almost_equal(gradex, gradbh, decimal=5)
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)
distances = random_state.randn(n_samples, n_features)
distances = distances.astype(np.float32)
distances = distances.dot(distances.T)
np.fill_diagonal(distances, 0.0)
params = random_state.randn(n_samples, n_components)
P = _joint_probabilities(distances, perplexity, False)
kl, gradex = _kl_divergence(params, P, degrees_of_freedom, n_samples,
n_components)
k = n_samples - 1
bt = BallTree(distances)
distances_nn, neighbors_nn = bt.query(distances, k=k + 1)
neighbors_nn = neighbors_nn[:, 1:]
Pbh = _joint_probabilities_nn(distances, neighbors_nn,
perplexity, False)
kl, gradbh = _kl_divergence_bh(params, Pbh, neighbors_nn,
degrees_of_freedom, n_samples,
n_components, angle=angle,
skip_num_points=0, verbose=False)
assert_array_almost_equal(Pbh, P, decimal=5)
assert_array_almost_equal(gradex, gradbh, decimal=5)
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)
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 = distances.dot(distances.T)
np.fill_diagonal(distances, 0.0)
X_embedded = random_state.randn(n_samples, n_components)
P = _joint_probabilities(distances, desired_perplexity=25.0, verbose=0)
fun = lambda params: _kl_divergence(params, P, alpha, n_samples, n_components)[0]
grad = lambda params: _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_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 = distances.dot(distances.T)
np.fill_diagonal(distances, 0.0)
X_embedded = random_state.randn(n_samples, n_components)
P = _joint_probabilities(distances, desired_perplexity=25.0,
verbose=0)
fun = lambda params: _kl_divergence(params, P, alpha, n_samples,
n_components)[0]
grad = lambda params: _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_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)
distances = random_state.randn(n_samples, n_features)
distances = distances.astype(np.float32)
distances = abs(distances.dot(distances.T))
np.fill_diagonal(distances, 0.0)
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)
k = n_samples - 1
bt = BallTree(distances)
distances_nn, neighbors_nn = bt.query(distances, k=k + 1)
neighbors_nn = neighbors_nn[:, 1:]
distances_nn = np.array(
[distances[i, neighbors_nn[i]] for i in range(n_samples)])
assert np.all(distances[0, neighbors_nn[0]] == distances_nn[0]),\
abs(distances[0, neighbors_nn[0]] - distances_nn[0])
P_bh = _joint_probabilities_nn(distances_nn,
neighbors_nn,
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)
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)
distances = random_state.randn(n_samples, n_features)
distances = distances.astype(np.float32)
distances = abs(distances.dot(distances.T))
np.fill_diagonal(distances, 0.0)
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)
k = n_samples - 1
bt = BallTree(distances)
distances_nn, neighbors_nn = bt.query(distances, k=k + 1)
neighbors_nn = neighbors_nn[:, 1:]
distances_nn = np.array([distances[i, neighbors_nn[i]]
for i in range(n_samples)])
assert np.all(distances[0, neighbors_nn[0]] == distances_nn[0]),\
abs(distances[0, neighbors_nn[0]] - distances_nn[0])
P_bh = _joint_probabilities_nn(distances_nn, neighbors_nn,
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)
def grad(params):
return _kl_divergence(params, P, alpha, n_samples, n_components)[1]
#!/usr/bin/env python2
from sklearn.metrics import euclidean_distances
from sklearn.manifold import t_sne
import numpy as np
import _snack as snack
for i in xrange(10):
X = np.random.randn(1000, 2) * 10
params = X.ravel()
D = euclidean_distances(X)
probs1 = t_sne._joint_probabilities(D, 30, False)
probs2 = snack.my_joint_probabilities(D, 30, False)
c1,grad1 = t_sne._kl_divergence(params, probs1, 1.0, len(X), 2)
c2,grad2 = snack.my_kl_divergence(params, probs1, 1.0, len(X), 2.0)
print "Test", i
print "Difference norm:", np.linalg.norm(probs1 - probs2)
print "Difference norm:", np.linalg.norm(grad1 - grad2)
print "Difference norm:", c1-c2
assert np.allclose(probs1, probs2)
assert np.allclose(grad1, grad2)
assert np.allclose(c1, c2)
