_tucker.py
from .. import backend as T
from ..base import unfold
from ..tenalg import multi_mode_dot, mode_dot
from ..tucker_tensor import tucker_to_tensor
from ..random import check_random_state
from math import sqrt
import warnings
# Author: Jean Kossaifi <jean.kossaifi+tensors@gmail.com>
# License: BSD 3 clause
def partial_tucker(tensor, modes, rank=None, n_iter_max=100, init='svd', tol=10e-5,
random_state=None, verbose=False, ranks=None):
"""Partial tucker decomposition via Higher Order Orthogonal Iteration (HOI)
Decomposes `tensor` into a Tucker decomposition exclusively along the provided modes.
Parameters
----------
tensor : ndarray
modes : int list
list of the modes on which to perform the decomposition
ranks : None or int list
size of the core tensor, ``(len(ranks) == len(modes))``
n_iter_max : int
maximum number of iteration
init : {'svd', 'random'}, optional
tol : float, optional
tolerance: the algorithm stops when the variation in
the reconstruction error is less than the tolerance
random_state : {None, int, np.random.RandomState}
verbose : int, optional
level of verbosity
Returns
-------
core : ndarray
core tensor of the Tucker decomposition
factors : ndarray list
list of factors of the Tucker decomposition.
with ``core.shape[i] == (tensor.shape[i], ranks[i]) for i in modes``
"""
if ranks is not None:
message = "'ranks' is depreciated, please use 'rank' instead"
warnings.warn(message, DeprecationWarning)
rank = ranks
if rank is None:
rank = [T.shape(tensor)[mode] for mode in modes]
elif isinstance(rank, int):
message = "Given only one int for 'rank' intead of a list of {} modes. Using this rank for all modes.".format(len(modes))
warnings.warn(message, DeprecationWarning)
rank = [rank for _ in modes]
# SVD init
if init == 'svd':
factors = []
for index, mode in enumerate(modes):
eigenvecs, _, _ = T.partial_svd(unfold(tensor, mode), n_eigenvecs=rank[index])
factors.append(eigenvecs)
else:
rng = check_random_state(random_state)
core = T.tensor(rng.random_sample(rank), **T.context(tensor))
factors = [T.tensor(rng.random_sample((T.shape(tensor)[mode], rank[index])), **T.context(tensor)) for (index, mode) in enumerate(modes)]
rec_errors = []
norm_tensor = T.norm(tensor, 2)
for iteration in range(n_iter_max):
for index, mode in enumerate(modes):
core_approximation = multi_mode_dot(tensor, factors, modes=modes, skip=index, transpose=True)
eigenvecs, _, _ = T.partial_svd(unfold(core_approximation, mode), n_eigenvecs=rank[index])
factors[index] = eigenvecs
core = multi_mode_dot(tensor, factors, modes=modes, transpose=True)
# The factors are orthonormal and therefore do not affect the reconstructed tensor's norm
rec_error = sqrt(abs(norm_tensor**2 - T.norm(core, 2)**2)) / norm_tensor
rec_errors.append(rec_error)
if iteration > 1:
if verbose:
print('reconsturction error={}, variation={}.'.format(
rec_errors[-1], rec_errors[-2] - rec_errors[-1]))
if tol and abs(rec_errors[-2] - rec_errors[-1]) < tol:
if verbose:
print('converged in {} iterations.'.format(iteration))
break
return core, factors
def tucker(tensor, rank=None, ranks=None, n_iter_max=100, init='svd', tol=10e-5,
random_state=None, verbose=False):
"""Tucker decomposition via Higher Order Orthogonal Iteration (HOI)
Decomposes `tensor` into a Tucker decomposition:
``tensor = [| core; factors[0], ...factors[-1] |]`` [1]_
Parameters
----------
tensor : ndarray
ranks : None or int list
size of the core tensor, ``(len(ranks) == tensor.ndim)``
n_iter_max : int
maximum number of iteration
init : {'svd', 'random'}, optional
tol : float, optional
tolerance: the algorithm stops when the variation in
the reconstruction error is less than the tolerance
random_state : {None, int, np.random.RandomState}
verbose : int, optional
level of verbosity
Returns
-------
core : ndarray of size `ranks`
core tensor of the Tucker decomposition
factors : ndarray list
list of factors of the Tucker decomposition.
Its ``i``-th element is of shape ``(tensor.shape[i], ranks[i])``
References
----------
.. [1] T.G.Kolda and B.W.Bader, "Tensor Decompositions and Applications",
SIAM REVIEW, vol. 51, n. 3, pp. 455-500, 2009.
"""
modes = list(range(T.ndim(tensor)))
return partial_tucker(tensor, modes, rank=rank, ranks=ranks, n_iter_max=n_iter_max, init=init,
tol=tol, random_state=random_state, verbose=verbose)
def non_negative_tucker(tensor, rank, n_iter_max=10, init='svd', tol=10e-5,
random_state=None, verbose=False, ranks=None):
"""Non-negative Tucker decomposition
Iterative multiplicative update, see [2]_
Parameters
----------
tensor : ``ndarray``
rank : int
number of components
n_iter_max : int
maximum number of iteration
init : {'svd', 'random'}
random_state : {None, int, np.random.RandomState}
Returns
-------
core : ndarray
positive core of the Tucker decomposition
has shape `ranks`
factors : ndarray list
list of factors of the CP decomposition
element `i` is of shape ``(tensor.shape[i], rank)``
References
----------
.. [2] Yong-Deok Kim and Seungjin Choi,
"Nonnegative tucker decomposition",
IEEE Conference on Computer Vision and Pattern Recognition s(CVPR),
pp 1-8, 2007
"""
if ranks is not None:
message = "'ranks' is depreciated, please use 'rank' instead"
warnings.warn(message, DeprecationWarning)
rank = ranks
if rank is None:
rank = [T.shape(tensor)[mode] for mode in modes]
elif isinstance(rank, int):
message = "Given only one int for 'rank' intead of a list of {} modes. Using this rank for all modes.".format(len(modes))
warnings.warn(message, DeprecationWarning)
rank = [rank for _ in modes]
epsilon = 10e-12
# Initialisation
if init == 'svd':
core, factors = tucker(tensor, rank)
nn_factors = [T.abs(f) for f in factors]
nn_core = T.abs(core)
else:
rng = check_random_state(random_state)
core = T.tensor(rng.random_sample(rank) + 0.01, **T.context(tensor)) # Check this
factors = [T.tensor(rng.random_sample(s), **T.context(tensor)) for s in zip(T.shape(tensor), rank)]
nn_factors = [T.abs(f) for f in factors]
nn_core = T.abs(core)
n_factors = len(nn_factors)
norm_tensor = T.norm(tensor, 2)
rec_errors = []
for iteration in range(n_iter_max):
for mode in range(T.ndim(tensor)):
B = tucker_to_tensor(nn_core, nn_factors, skip_factor=mode)
B = T.transpose(unfold(B, mode))
numerator = T.dot(unfold(tensor, mode), B)
numerator = T.clip(numerator, a_min=epsilon, a_max=None)
denominator = T.dot(nn_factors[mode], T.dot(T.transpose(B), B))
denominator = T.clip(denominator, a_min=epsilon, a_max=None)
nn_factors[mode] *= numerator / denominator
numerator = tucker_to_tensor(tensor, nn_factors, transpose_factors=True)
numerator = T.clip(numerator, a_min=epsilon, a_max=None)
for i, f in enumerate(nn_factors):
if i:
denominator = mode_dot(denominator, T.dot(T.transpose(f), f), i)
else:
denominator = mode_dot(nn_core, T.dot(T.transpose(f), f), i)
denominator = T.clip(denominator, a_min=epsilon, a_max=None)
nn_core *= numerator / denominator
rec_error = T.norm(tensor - tucker_to_tensor(nn_core, nn_factors), 2) / norm_tensor
rec_errors.append(rec_error)
if iteration > 1 and verbose:
print('reconsturction error={}, variation={}.'.format(
rec_errors[-1], rec_errors[-2] - rec_errors[-1]))
if iteration > 1 and abs(rec_errors[-2] - rec_errors[-1]) < tol:
if verbose:
print('converged in {} iterations.'.format(iteration))
break
return nn_core, nn_factors
