##### https://github.com/tensorly/tensorly
Tip revision: 1e94ea4
_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 ..utils import check_random_state

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

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] |]``

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])``
"""
if ranks is None:
ranks = [s for s in tensor.shape]

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

rec_errors = []
norm_tensor = norm(tensor, 2)

for iteration in range(n_iter_max):
for mode in range(tensor.ndim):
core_approximation = tucker_to_tensor(tensor, factors, skip_factor=mode, transpose_factors=True)
eigenvecs, _, _ = partial_svd(unfold(core_approximation, mode), n_eigenvecs=ranks[mode])
factors[mode] = eigenvecs

core = tucker_to_tensor(tensor, factors, transpose_factors=True)

rec_error = np.sqrt(norm_tensor**2 - norm(core, 2)**2) / norm_tensor
#rec_error = norm(tensor - tucker_to_tensor(core, factors), 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 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 [1]_, [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
----------
.. [1] G. Zhou, A. Cichocki, Q. Zhao and S. Xie,
"Nonnegative Matrix and Tensor Factorizations : An algorithmic perspective,"
in IEEE Signal Processing Magazine, vol. 31, no. 3, pp. 54-65, May 2014.

.. [2] DD Lee and HS Seung,
"Algorithms for non-negative matrix factorization",
in Advances in neural information processing systems (NIPS), 2001
"""
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
``````