##### https://github.com/tensorly/tensorly
Tip revision: 1bb217a
_tucker.py
``````import numpy as np
from ..base import unfold
from ..tenalg import multi_mode_dot, mode_dot, norm
from ..tenalg import partial_svd
from ..tucker import tucker_to_tensor
from ..random import check_random_state

# Author: Jean Kossaifi <jean.kossaifi+tensors@gmail.com>

def partial_tucker(tensor, modes, ranks=None, n_iter_max=100, init='svd', tol=10e-5,
random_state=None, verbose=False):
"""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 None:
ranks = [tensor.shape[mode] for mode in modes]

# SVD init
if init == 'svd':
factors = []
for index, mode in enumerate(modes):
eigenvecs, _, _ = partial_svd(unfold(tensor, mode), n_eigenvecs=ranks[index])
factors.append(eigenvecs)
else:
rng = check_random_state(random_state)
core = rng.random_sample(ranks)
factors = [rng.random_sample((tensor.shape[mode], ranks[index])) for (index, mode) in enumerate(modes)]

rec_errors = []
norm_tensor = 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, _, _ = partial_svd(unfold(core_approximation, mode), n_eigenvecs=ranks[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 = np.sqrt(abs(norm_tensor**2 - 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, 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(tensor.ndim))
return partial_tucker(tensor, modes, ranks=ranks, n_iter_max=n_iter_max, init=init,
tol=tol, random_state=random_state, verbose=verbose)

def non_negative_tucker(tensor, ranks, n_iter_max=10, init='svd', tol=10e-5,
random_state=None, verbose=False):
"""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
"""
epsilon = 10e-12

# Initialisation
if init == 'svd':
core, factors = tucker(tensor, ranks)
nn_factors = [np.abs(f) for f in factors]
nn_core = np.abs(core)
else:
rng = check_random_state(random_state)
core = rng.random_sample(ranks) + 0.01  # Check this
factors = [rng.random_sample(s) for s in zip(tensor.shape, ranks)]
nn_factors = [np.abs(f) for f in factors]
nn_core = np.abs(core)

n_factors = len(nn_factors)
norm_tensor = norm(tensor, 2)
rec_errors = []

for iteration in range(n_iter_max):
for mode in range(tensor.ndim):
B = tucker_to_tensor(nn_core, nn_factors, skip_factor=mode)
B = unfold(B, mode).T

numerator = np.dot(unfold(tensor, mode), B)
numerator = numerator.clip(min=epsilon)
denominator = np.dot(nn_factors[mode], B.T.dot(B))
denominator = denominator.clip(min=epsilon)
nn_factors[mode] *= numerator / denominator

numerator = tucker_to_tensor(tensor, nn_factors, transpose_factors=True)
numerator = numerator.clip(min=epsilon)
for i, f in enumerate(nn_factors):
if i:
denominator = mode_dot(denominator, f.T.dot(f), i)
else:
denominator = mode_dot(nn_core, f.T.dot(f), i)
denominator = denominator.clip(min=epsilon)
nn_core *= numerator / denominator

rec_error = 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
``````