class CP_NN_HALS(rank, n_iter_max=100, tol=1e-08, init='svd', svd='numpy_svd', l2_reg=0, fixed_modes=None, normalize_factors=False, sparsity=None, exact=False, mask=None, svd_mask_repeats=5, return_errors=True, cvg_criterion='abs_rec_error', random_state=None, verbose=0)[source]

Non-Negative Candecomp-Parafac decomposition via Alternating-Least Square

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

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

Number of components.


Maximum number of iteration

init{‘svd’, ‘random’}, optional

Type of factor matrix initialization. See initialize_factors.

svdstr, default is ‘numpy_svd’

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

normalize_factorsif True, aggregate the weights of each factor in a 1D-tensor

of shape (rank, ), which will contain the norms of the factors

tolfloat, optional

(Default: 1e-6) Relative reconstruction error tolerance. The algorithm is considered to have found the global minimum when the reconstruction error is less than tol.

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

Level of verbosity

return_errorsbool, optional

Activate return of iteration errors


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). Allows for missing values [2]

cvg_criterion{‘abs_rec_error’, ‘rec_error’}, optional

Stopping criterion for ALS, works if tol is not None. If ‘rec_error’, ALS stops at current iteration if (previous rec_error - current rec_error) < tol. If ‘abs_rec_error’, ALS terminates when |previous rec_error - current rec_error| < tol.

sparsityfloat or int

If sparsity is not None, we approximate tensor as a sum of low_rank_component and sparse_component, where low_rank_component = cp_to_tensor((weights, factors)). sparsity denotes desired fraction or number of non-zero elements in the sparse_component of the tensor.

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.

svd_mask_repeats: int

If using a tensor with masked values, this initializes using SVD multiple times to remove the effect of these missing values on the initialization.

CPTensor(weight, factors)
  • weights1D array of shape (rank, )

    all ones if normalize_factors is False (default), weights of the (normalized) factors otherwise

  • factorsList of factors of the CP decomposition element i is of shape

    (tensor.shape[i], rank)

  • sparse_component : nD array of shape tensor.shape. Returns only if sparsity is not None.


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



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


Tomasi, Giorgio, and Rasmus Bro. “PARAFAC and missing values.” Chemometrics and Intelligent Laboratory Systems 75.2 (2005): 163-180.


R. Bro, “Multi-Way Analysis in the Food Industry: Models, Algorithms, and Applications”, PhD., University of Amsterdam, 1998


Decompose an input tensor

tensortensorly tensor

input tensor to decompose


decomposed tensor