tensorly.decomposition.tucker

tucker(tensor, rank, fixed_factors=None, n_iter_max=100, init='svd', return_errors=False, svd='truncated_svd', tol=0.0001, random_state=None, mask=None, verbose=False)[source]

Tucker decomposition via Higher Order Orthogonal Iteration (HOI)

Decomposes tensor into a Tucker decomposition: tensor = [| core; factors[0], ...factors[-1] |] [1]

Parameters:

tensorndarray

rankNone, int or int list

size of the core tensor, (len(ranks) == tensor.ndim) if int, the same rank is used for all modes

fixed_factorsint list or None, default is None

if not None, list of modes for which to keep the factors fixed. Only valid if a Tucker tensor is provided as init.

n_iter_maxint

maximum number of iteration

init{‘svd’, ‘random’}, optional

return_errorsboolean

Indicates whether the algorithm should return all reconstruction errors and computation time of each iteration or not Default: False

svdstr, default is ‘truncated_svd’

function to use to compute the SVD, acceptable values in tensorly.SVD_FUNS

tolfloat, optional

tolerance: the algorithm stops when the variation in the reconstruction error is less than the tolerance

random_state{None, int, np.random.RandomState}

maskndarray

array of booleans with the same shape as tensor should be 0 where the values are missing and 1 everywhere else. Note: if tensor is sparse, then mask should also be sparse with a fill value of 1 (or True).

verboseint, optional

level of verbosity

Returns:

corendarray of size ranks

core tensor of the Tucker decomposition

factorsndarray list

list of factors of the Tucker decomposition. Its i-th element is of shape (tensor.shape[i], ranks[i])

References

[1]

tl.G.Kolda and B.W.Bader, “Tensor Decompositions and Applications”, SIAM REVIEW, vol. 51, n. 3, pp. 455-500, 2009.