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 = 500
desired_perplexity = 25.0
random_state = check_random_state(0)
distances = random_state.randn(n_samples, 2).astype(np.float32)
# Distances shouldn't be negative
distances = np.abs(distances.dot(distances.T))
np.fill_diagonal(distances, 0.0)
P1 = _binary_search_perplexity(distances, None, desired_perplexity,
verbose=0)
# Test that when we use all the neighbors the results are identical
k = n_samples
neighbors_nn = np.argsort(distances, axis=1)[:, :k].astype(np.int64)
P2 = _binary_search_perplexity(distances, neighbors_nn,
desired_perplexity, verbose=0)
assert_array_almost_equal(P1, P2, decimal=4)
# Test that the highest P_ij are the same when few neighbors are used
for k in np.linspace(80, n_samples, 10):
k = int(k)
topn = k * 10 # check the top 10 *k entries out of k * k entries
neighbors_nn = np.argsort(distances, axis=1)[:, :k].astype(np.int64)
P2k = _binary_search_perplexity(distances, neighbors_nn,
desired_perplexity, verbose=0)
idx = np.argsort(P1.ravel())[::-1]
P1top = P1.ravel()[idx][:topn]
P2top = P2k.ravel()[idx][:topn]
assert_array_almost_equal(P1top, P2top, decimal=2)
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 = 500
desired_perplexity = 25.0
random_state = check_random_state(0)
distances = random_state.randn(n_samples, 2).astype(np.float32)
# Distances shouldn't be negative
distances = np.abs(distances.dot(distances.T))
np.fill_diagonal(distances, 0.0)
P1 = _binary_search_perplexity(distances, None, desired_perplexity,
verbose=0)
# Test that when we use all the neighbors the results are identical
k = n_samples
neighbors_nn = np.argsort(distances, axis=1)[:, :k].astype(np.int64)
P2 = _binary_search_perplexity(distances, neighbors_nn,
desired_perplexity, verbose=0)
assert_array_almost_equal(P1, P2, decimal=4)
# Test that the highest P_ij are the same when few neighbors are used
for k in np.linspace(80, n_samples, 10):
k = int(k)
topn = k * 10 # check the top 10 *k entries out of k * k entries
neighbors_nn = np.argsort(distances, axis=1)[:, :k].astype(np.int64)
P2k = _binary_search_perplexity(distances, neighbors_nn,
desired_perplexity, verbose=0)
idx = np.argsort(P1.ravel())[::-1]
P1top = P1.ravel()[idx][:topn]
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 _joint_probabilities(distances, desired_perplexity, verbose):
"""Compute joint probabilities p_ij from distances.
Parameters
----------
distances : array, shape (n_samples * (n_samples-1) / 2,)
Distances of samples are stored as condensed matrices, i.e.
we omit the diagonal and duplicate entries and store everything
in a one-dimensional array.
desired_perplexity : float
Desired perplexity of the joint probability distributions.
verbose : int
Verbosity level.
Returns
-------
P : array, shape (n_samples * (n_samples-1) / 2,)
Condensed joint probability matrix.
"""
# Compute conditional probabilities such that they approximately match
# the desired perplexity
distances = distances.astype(np.float32, copy=False)
conditional_P = _utils._binary_search_perplexity(
distances, None, desired_perplexity, verbose)
P = conditional_P + conditional_P.T
sum_P = np.maximum(np.sum(P), MACHINE_EPSILON)
P = np.maximum(squareform(P) / sum_P, MACHINE_EPSILON)
return P
def _joint_probabilities_nn(distances, neighbors, desired_perplexity, verbose):
"""Compute joint probabilities p_ij from distances using just nearest
neighbors.
This method is approximately equal to _joint_probabilities. The latter
is O(N), but limiting the joint probability to nearest neighbors improves
this substantially to O(uN).
Parameters
----------
distances : array, shape (n_samples * (n_samples-1) / 2,)
Distances of samples are stored as condensed matrices, i.e.
we omit the diagonal and duplicate entries and store everything
in a one-dimensional array.
desired_perplexity : float
Desired perplexity of the joint probability distributions.
verbose : int
Verbosity level.
Returns
-------
P : array, shape (n_samples * (n_samples-1) / 2,)
Condensed joint probability matrix.
"""
# Compute conditional probabilities such that they approximately match
# the desired perplexity
distances = astype(distances, np.float32, copy=False)
neighbors = astype(neighbors, np.int64, copy=False)
conditional_P = _utils._binary_search_perplexity(distances, neighbors,
desired_perplexity,
verbose)
m = "All probabilities should be finite"
assert np.all(np.isfinite(conditional_P)), m
P = conditional_P + conditional_P.T
sum_P = np.maximum(np.sum(P), MACHINE_EPSILON)
P = np.maximum(squareform(P) / sum_P, MACHINE_EPSILON)
assert np.all(np.abs(P) <= 1.0)
return P
def _joint_probabilities_nn(distances, neighbors, desired_perplexity, verbose):
"""Compute joint probabilities p_ij from distances using just nearest
neighbors.
This method is approximately equal to _joint_probabilities. The latter
is O(N), but limiting the joint probability to nearest neighbors improves
this substantially to O(uN).
Parameters
----------
distances : array, shape (n_samples * (n_samples-1) / 2,)
Distances of samples are stored as condensed matrices, i.e.
we omit the diagonal and duplicate entries and store everything
in a one-dimensional array.
desired_perplexity : float
Desired perplexity of the joint probability distributions.
verbose : int
Verbosity level.
Returns
-------
P : array, shape (n_samples * (n_samples-1) / 2,)
Condensed joint probability matrix.
"""
# Compute conditional probabilities such that they approximately match
# the desired perplexity
distances = astype(distances, np.float32, copy=False)
neighbors = astype(neighbors, np.int64, copy=False)
conditional_P = _utils._binary_search_perplexity(
distances, neighbors, desired_perplexity, verbose)
m = "All probabilities should be finite"
assert np.all(np.isfinite(conditional_P)), m
P = conditional_P + conditional_P.T
sum_P = np.maximum(np.sum(P), MACHINE_EPSILON)
P = np.maximum(squareform(P) / sum_P, MACHINE_EPSILON)
assert np.all(np.abs(P) <= 1.0)
return P
def _joint_probabilities(distances, desired_perplexity, verbose):
"""Compute joint probabilities p_ij from distances.
Parameters
----------
distances : array, shape (n_samples * (n_samples-1) / 2,)
Distances of samples are stored as condensed matrices, i.e.
we omit the diagonal and duplicate entries and store everything
in a one-dimensional array.
desired_perplexity : float
Desired perplexity of the joint probability distributions.
verbose : int
Verbosity level.
Returns
-------
P : array, shape (n_samples * (n_samples-1) / 2,)
Condensed joint probability matrix.
"""
# Compute conditional probabilities such that they approximately match
# the desired perplexity
distances = astype(distances, np.float32, copy=False)
conditional_P = _utils._binary_search_perplexity(
distances, None, desired_perplexity, verbose)
P = conditional_P + conditional_P.T
sum_P = np.maximum(np.sum(P), MACHINE_EPSILON)
P = np.maximum(squareform(P) / sum_P, MACHINE_EPSILON)
return P
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.
k = 10
n_samples = 100
random_state = check_random_state(0)
distances = random_state.randn(n_samples, 2).astype(np.float32)
# Distances shouldn't be negative
distances = np.abs(distances.dot(distances.T))
np.fill_diagonal(distances, 0.0)
last_P = None
neighbors_nn = np.argsort(distances, axis=1)[:, :k].astype(np.int64)
for _ in range(100):
P = _binary_search_perplexity(distances.copy(), neighbors_nn.copy(),
3, verbose=0)
P1 = _joint_probabilities_nn(distances, neighbors_nn, 3, 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 _joint_probabilities(distances, desired_perplexity, verbose=0):
distances = distances.astype(np.float32, copy=True)
conditional_P = _binary_search_perplexity(distances, None,
desired_perplexity, verbose)
P = conditional_P + conditional_P.T
sum_P = np.maximum(np.sum(P), MACHINE_EPSILON_NP)
P = np.maximum(squareform(P) / sum_P, MACHINE_EPSILON_NP)
return P
def _joint_probabilities(distances, desired_perplexity, verbose):
# Compute conditional probabilities such that they approximately match
# the desired perplexity
distances = distances.astype(np.float32, copy=False)
conditional_P = _utils._binary_search_perplexity(distances, desired_perplexity, verbose)
P = conditional_P + conditional_P.T
sum_P = np.maximum(np.sum(P), MACHINE_EPSILON)
P = np.maximum(squareform(P) / sum_P, MACHINE_EPSILON)
return P
def test_binary_search_underflow():
# Test if the binary search finds Gaussians with desired perplexity.
# A more challenging case than the one above, producing numeric
# underflow in float precision (see issue #19471 and PR #19472).
random_state = check_random_state(42)
data = random_state.randn(1, 90).astype(np.float32) + 100
desired_perplexity = 30.0
P = _binary_search_perplexity(data, desired_perplexity, verbose=0)
perplexity = 2 ** -np.nansum(P[0, 1:] * np.log2(P[0, 1:]))
assert_almost_equal(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 _joint_probabilities_nn(distances, neighbors, desired_perplexity, verbose):
"""Compute joint probabilities p_ij from distances using just nearest
neighbors.
This method is approximately equal to _joint_probabilities. The latter
is O(N), but limiting the joint probability to nearest neighbors improves
this substantially to O(uN).
Parameters
----------
distances : array, shape (n_samples, k)
Distances of samples to its k nearest neighbors.
neighbors : array, shape (n_samples, k)
Indices of the k nearest-neighbors for each samples.
desired_perplexity : float
Desired perplexity of the joint probability distributions.
verbose : int
Verbosity level.
Returns
-------
P : csr sparse matrix, shape (n_samples, n_samples)
Condensed joint probability matrix with only nearest neighbors.
"""
t0 = time()
# Compute conditional probabilities such that they approximately match
# the desired perplexity
n_samples, k = neighbors.shape
distances = distances.astype(np.float32, copy=False)
neighbors = neighbors.astype(np.int64, copy=False)
conditional_P = _utils._binary_search_perplexity(
distances, neighbors, desired_perplexity, verbose)
assert np.all(np.isfinite(conditional_P)), \
"All probabilities should be finite"
# Symmetrize the joint probability distribution using sparse operations
P = csr_matrix((conditional_P.ravel(), neighbors.ravel(),
range(0, n_samples * k + 1, k)),
shape=(n_samples, n_samples))
P = P + P.T
# Normalize the joint probability distribution
sum_P = np.maximum(P.sum(), MACHINE_EPSILON)
P /= sum_P
assert np.all(np.abs(P.data) <= 1.0)
if verbose >= 2:
duration = time() - t0
print("[t-SNE] Computed conditional probabilities in {:.3f}s"
.format(duration))
return P
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 _joint_probabilities_nn(distances, desired_perplexity, verbose):
"""Compute joint probabilities p_ij from distances using just nearest
neighbors.
This method is approximately equal to _joint_probabilities. The latter
is O(N), but limiting the joint probability to nearest neighbors improves
this substantially to O(uN).
Parameters
----------
distances : CSR sparse matrix, shape (n_samples, n_samples)
Distances of samples to its n_neighbors nearest neighbors. All other
distances are left to zero (and are not materialized in memory).
desired_perplexity : float
Desired perplexity of the joint probability distributions.
verbose : int
Verbosity level.
Returns
-------
P : csr sparse matrix, shape (n_samples, n_samples)
Condensed joint probability matrix with only nearest neighbors.
"""
t0 = time()
# Compute conditional probabilities such that they approximately match
# the desired perplexity
distances.sort_indices()
n_samples = distances.shape[0]
distances_data = distances.data.reshape(n_samples, -1)
distances_data = distances_data.astype(np.float32, copy=False)
conditional_P = _utils._binary_search_perplexity(
distances_data, desired_perplexity, verbose)
assert np.all(np.isfinite(conditional_P)), \
"All probabilities should be finite"
# Symmetrize the joint probability distribution using sparse operations
P = csr_matrix((conditional_P.ravel(), distances.indices,
distances.indptr),
shape=(n_samples, n_samples))
P = P + P.T
# Normalize the joint probability distribution
sum_P = np.maximum(P.sum(), MACHINE_EPSILON)
P /= sum_P
assert np.all(np.abs(P.data) <= 1.0)
if verbose >= 2:
duration = time() - t0
print("[t-SNE] Computed conditional probabilities in {:.3f}s"
.format(duration))
return P
def test_binary_search():
"""Test if the binary search finds Gaussians with desired perplexity."""
random_state = check_random_state(0)
distances = random_state.randn(50, 2)
distances = distances.dot(distances.T)
np.fill_diagonal(distances, 0.0)
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():
"""Test if the binary search finds Gaussians with desired perplexity."""
random_state = check_random_state(0)
distances = random_state.randn(50, 2)
distances = distances.dot(distances.T)
np.fill_diagonal(distances, 0.0)
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 joint_probabilities_nn(D, target_PP):
from sklearn.manifold._utils import _binary_search_perplexity
from scipy.sparse import csr_matrix
D.sort_indices()
N = D.shape[0]
D_data = D.data.reshape(N, -1)
D_data = D_data.astype(np.float32, copy=False)
conditional_P = _binary_search_perplexity(D_data, target_PP, 0)
assert np.all(np.isfinite(conditional_P))
P = csr_matrix((conditional_P.ravel(), D.indices, D.indptr), shape=(N, N))
P = P + P.T
sum_P = np.maximum(P.sum(), np.finfo(np.double).eps)
P /= sum_P
assert np.all(np.abs(P.data) <= 1.0)
return P
def sample_weights_tsne_symmetric(data, perplexity, symmetric):
"""
Calculates p-values between samples using the procedure
from tSNE
As this version uses symmetric p-values, it must calculate
the p-values for every sample vs every other sample
data: pandas.DataFrame
data matrix with samples as columns
perplexity: float
binary search perplexity target
symmetric: boolean
whether or not to symmetrize the weights
"""
columns = data.columns
data = data.values
# Calculate affinities (distance-squared) between samples
sumData2 = np.sum(data**2, axis=0, keepdims=True)
aff = -2 * np.dot(data.T, data)
aff += sumData2
aff = aff.T
aff += sumData2
np.fill_diagonal(aff, 0)
aff = aff.astype('float32')
# Run the tsne perplexity procedure
pvals = _binary_search_perplexity(aff, perplexity, 0)
# Symmetrize the pvals
if symmetric:
pvals += pvals.T
pvals /= 2
# Make the rows sum to 1
pvals /= pvals.sum(axis=1, keepdims=True)
pvals = pd.DataFrame(pvals, index=columns, columns=columns)
return pvals
method = 'barnes_hut'
angle = 0.5
n_samples = X.shape[0]
neighbors_nn = None
k = min(n_samples - 1, int(3. * perplexity + 1))
knn = NearestNeighbors(algorithm='auto', n_neighbors=k, metric=metric)
knn.fit(X)
distances_nn, neighbors_nn = knn.kneighbors(None, n_neighbors=k)
del knn
distances_nn **= 2
# in the function _joint_probabilities_nn ----from here
distances = distances_nn.astype(np.float32, copy=True)
neighbors = neighbors_nn.astype(np.int64, copy=True)
conditional_P = _utils._binary_search_perplexity(distances, neighbors,
perplexity, verbose)
P = csr_matrix(
(conditional_P.ravel(), neighbors.ravel(), range(0, n_samples * k + 1, k)),
shape=(n_samples, n_samples))
P = P + P.T
MACHINE_EPSILON = np.finfo(np.double).eps
sum_P = np.maximum(P.sum(), MACHINE_EPSILON)
P /= sum_P
# in the function _joint_probabilities_nn ----till here
# simplified _binary_search_perplexity() from github ---- from here
# https://github.com/scikit-learn/scikit-learn/blob/master/sklearn/manifold/_utils.pyx
sqdistances = distances
desired_entropy = np.log(perplexity)
PERPLEXITY_TOLEARANCE = 1e-5
Pi = np.zeros(sqdistances.shape)
