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)
pij_input = _joint_probabilities(*args)
pij_input = squareform(pij_input).astype(np.float32)
grad_bh = np.zeros(pos_output.shape, dtype=np.float32)
_barnes_hut_tsne.gradient(pij_input, pos_output, neighbors, grad_bh, 0.5, 2, 1, skip_num_points=0)
assert_array_almost_equal(grad_bh, grad_output, decimal=4)
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)
pij_input = _joint_probabilities(*args)
pij_input = squareform(pij_input).astype(np.float32)
grad_bh = np.zeros(pos_output.shape, dtype=np.float32)
_barnes_hut_tsne.gradient(pij_input, pos_output, neighbors,
grad_bh, 0.5, 2, 1, skip_num_points=0)
assert_array_almost_equal(grad_bh, grad_output, decimal=4)
def _kl_divergence_bh(params, P, neighbors, degrees_of_freedom, n_samples,
n_components, angle=0.5, skip_num_points=0,
verbose=False):
"""t-SNE objective function: KL divergence of p_ijs and q_ijs.
Uses Barnes-Hut tree methods to calculate the gradient that
runs in O(NlogN) instead of O(N^2)
Parameters
----------
params : array, shape (n_params,)
Unraveled embedding.
P : array, shape (n_samples * (n_samples-1) / 2,)
Condensed joint probability matrix.
neighbors: int64 array, shape (n_samples, K)
Array with element [i, j] giving the index for the jth
closest neighbor to point i.
degrees_of_freedom : float
Degrees of freedom of the Student's-t distribution.
n_samples : int
Number of samples.
n_components : int
Dimension of the embedded space.
angle : float (default: 0.5)
This is the trade-off between speed and accuracy for Barnes-Hut T-SNE.
'angle' is the angular size (referred to as theta in [3]) of a distant
node as measured from a point. If this size is below 'angle' then it is
used as a summary node of all points contained within it.
This method is not very sensitive to changes in this parameter
in the range of 0.2 - 0.8. Angle less than 0.2 has quickly increasing
computation time and angle greater 0.8 has quickly increasing error.
skip_num_points : int (optional, default:0)
This does not compute the gradient for points with indices below
`skip_num_points`. This is useful when computing transforms of new
data where you'd like to keep the old data fixed.
verbose : int
Verbosity level.
Returns
-------
kl_divergence : float
Kullback-Leibler divergence of p_ij and q_ij.
grad : array, shape (n_params,)
Unraveled gradient of the Kullback-Leibler divergence with respect to
the embedding.
"""
params = astype(params, np.float32, copy=False)
X_embedded = params.reshape(n_samples, n_components)
neighbors = astype(neighbors, np.int64, copy=False)
if len(P.shape) == 1:
sP = squareform(P).astype(np.float32)
else:
sP = P.astype(np.float32)
grad = np.zeros(X_embedded.shape, dtype=np.float32)
error = _barnes_hut_tsne.gradient(sP, X_embedded, neighbors,
grad, angle, n_components, verbose,
dof=degrees_of_freedom)
c = 2.0 * (degrees_of_freedom + 1.0) / degrees_of_freedom
grad = grad.ravel()
grad *= c
return error, grad
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 _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 KL_divergeance_BH(flat_X_LD, P, degrees_of_freedom, n_samples, n_components,
skip_num_points, compute_error,
angle=0.5, verbose=False, num_threads=1):
flat_X_LD = flat_X_LD.astype(np.float32, copy=False)
X_embedded = flat_X_LD.reshape(n_samples, n_components)
val_P = P.data.astype(np.float32, copy=False)
neighbors = P.indices.astype(np.int64, copy=False)
indptr = P.indptr.astype(np.int64, copy=False)
grad = np.zeros(X_embedded.shape, dtype=np.float32)
error = _barnes_hut_tsne.gradient(val_P, X_embedded, neighbors, indptr,
grad, angle, n_components, verbose,
dof=degrees_of_freedom,
compute_error=compute_error,
num_threads=num_threads)
c = 2.0 * (degrees_of_freedom + 1.0) / degrees_of_freedom
grad = grad.ravel()
grad *= c
return error, grad
def _kl_divergence_bh(params, P, degrees_of_freedom, n_samples, n_components,
angle=0.5, skip_num_points=0, verbose=False):
"""t-SNE objective function: KL divergence of p_ijs and q_ijs.
Uses Barnes-Hut tree methods to calculate the gradient that
runs in O(NlogN) instead of O(N^2)
Parameters
----------
params : array, shape (n_params,)
Unraveled embedding.
P : csr sparse matrix, shape (n_samples, n_sample)
Sparse approximate joint probability matrix, computed only for the
k nearest-neighbors and symmetrized.
degrees_of_freedom : float
Degrees of freedom of the Student's-t distribution.
n_samples : int
Number of samples.
n_components : int
Dimension of the embedded space.
angle : float (default: 0.5)
This is the trade-off between speed and accuracy for Barnes-Hut T-SNE.
'angle' is the angular size (referred to as theta in [3]) of a distant
node as measured from a point. If this size is below 'angle' then it is
used as a summary node of all points contained within it.
This method is not very sensitive to changes in this parameter
in the range of 0.2 - 0.8. Angle less than 0.2 has quickly increasing
computation time and angle greater 0.8 has quickly increasing error.
skip_num_points : int (optional, default:0)
This does not compute the gradient for points with indices below
`skip_num_points`. This is useful when computing transforms of new
data where you'd like to keep the old data fixed.
verbose : int
Verbosity level.
Returns
-------
kl_divergence : float
Kullback-Leibler divergence of p_ij and q_ij.
grad : array, shape (n_params,)
Unraveled gradient of the Kullback-Leibler divergence with respect to
the embedding.
"""
params = params.astype(np.float32, copy=False)
X_embedded = params.reshape(n_samples, n_components)
val_P = P.data.astype(np.float32, copy=False)
neighbors = P.indices.astype(np.int64, copy=False)
indptr = P.indptr.astype(np.int64, copy=False)
grad = np.zeros(X_embedded.shape, dtype=np.float32)
error = _barnes_hut_tsne.gradient(val_P, X_embedded, neighbors, indptr,
grad, angle, n_components, verbose,
dof=degrees_of_freedom)
c = 2.0 * (degrees_of_freedom + 1.0) / degrees_of_freedom
grad = grad.ravel()
grad *= c
return error, grad