`tensorly.decomposition`.ConstrainedCP

class ConstrainedCP(rank, n_iter_max=100, n_iter_max_inner=10, init='svd', svd='truncated_svd', tol_outer=1e-08, tol_inner=1e-06, random_state=None, verbose=0, return_errors=False, cvg_criterion='abs_rec_error', fixed_modes=None, non_negative=None, l1_reg=None, l2_reg=None, l2_square_reg=None, unimodality=None, normalize=None, simplex=None, normalized_sparsity=None, soft_sparsity=None, smoothness=None, monotonicity=None, hard_sparsity=None)[source]

CANDECOMP/PARAFAC decomposition via alternating optimization of alternating direction method of multipliers (AO-ADMM):

Computes a rank-rank decomposition of tensor [1] such that:

tensor = [|weights; factors[0], ..., factors[-1] |],

where factors are either penalized or constrained according to the user-defined constraint.

In order to compute the factors efficiently, the ADMM algorithm introduces an auxilliary factor which is called factor_aux in the function.

Parameters:

tensorndarray
rankint: Number of components.
n_iter_maxint: Maximum number of iteration for outer loop
n_iter_max_innerint: Number of iteration for inner loop
init{‘svd’, ‘random’, cptensor}, optional: Type of factor matrix initialization. See initialize_factors.
svdstr, default is ‘truncated_svd’: function to use to compute the SVD, acceptable values in tensorly.SVD_FUNS
tol_outerfloat, optional: (Default: 1e-8) Relative reconstruction error tolerance for outer loop. The algorithm is considered to have found a local minimum when the reconstruction error is less than tol_outer.
tol_innerfloat, optional: (Default: 1e-6) Absolute reconstruction error tolerance for factor update during inner loop, i.e. ADMM optimization.
random_state{None, int, np.random.RandomState}
verboseint, optional: Level of verbosity
return_errorsbool, optional: Activate return of iteration errors
non_negativebool or dictionary: This constraint is clipping negative values to ‘0’. If it is True, non-negative constraint is applied to all modes.
l1_regfloat or list or dictionary, optional: Penalizes the factor with the l1 norm using the input value as regularization parameter.
l2_regfloat or list or dictionary, optional: Penalizes the factor with the l2 norm using the input value as regularization parameter.
l2_square_regfloat or list or dictionary, optional: Penalizes the factor with the l2 square norm using the input value as regularization parameter.
unimodalitybool or dictionary, optional: If it is True, unimodality constraint is applied to all modes. Applied to each column seperately.
normalizebool or dictionary, optional: This constraint divides all the values by maximum value of the input array. If it is True, normalize constraint is applied to all modes.
simplexfloat or list or dictionary, optional: Projects on the simplex with the given parameter Applied to each column seperately.
normalized_sparsityfloat or list or dictionary, optional: Normalizes with the norm after hard thresholding
soft_sparsityfloat or list or dictionary, optional: Impose that the columns of factors have L1 norm bounded by a user-defined threshold.
smoothnessfloat or list or dictionary, optional: Optimizes the factors by solving a banded system
monotonicitybool or dictionary, optional: Projects columns to monotonically decreasing distrbution Applied to each column seperately. If it is True, monotonicity constraint is applied to all modes.
hard_sparsityfloat or list or dictionary, optional: Hard thresholding with the given threshold
cvg_criterion{‘abs_rec_error’, ‘rec_error’}, optional: Stopping criterion if tol is not None. If ‘rec_error’, algorithm stops at current iteration if (previous rec_error - current rec_error) < tol. If ‘abs_rec_error’, algorithm terminates when |previous rec_error - current rec_error| < tol.
fixed_modeslist, default is None: A list of modes for which the initial value is not modified. The last mode cannot be fixed due to error computation.

Returns:

CPTensor(weight, factors)

weights : 1D array of shape (rank, )
factors : List of factors of the CP decomposition element i is of shape (tensor.shape[i], rank)

errorslist

A list of reconstruction errors at each iteration of the algorithms.

References

[1]

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

[2]

Huang, Kejun, Nicholas D. Sidiropoulos, and Athanasios P. Liavas. “A flexible and efficient algorithmic framework for constrained matrix and tensor factorization.” IEEE Transactions on Signal Processing 64.19 (2016): 5052-5065.

fit_transform(tensor)[source]

Decompose an input tensor

Parameters:

tensortensorly tensor: input tensor to decompose

Returns:

CPTensor: decomposed tensor

tensorly.decomposition.ConstrainedCP

`tensorly.decomposition`.ConstrainedCP