tensorly.parafac2_tensor
.parafac2_to_vec
-
parafac2_to_vec
(parafac2_tensor)[source] Construct a vectorized tensor from a PARAFAC2 decomposition. Uneven slices are padded by zeros.
The decomposition is on the form
such that the i-th frontal slice,
, of
is given by
where
is the diagonal matrix whose nonzero entries are equal to the
-th row of the
factor matrix
,
is a
factor matrix such that the cross product matrix
is constant for all
, and
is a
factor matrix. To compute this decomposition, we reformulate the expression for
such that
where
is a
orthogonal matrix and
is a
matrix.
An alternative formulation of the PARAFAC2 decomposition is that the tensor element
is given by
with the same constraints hold for
as above.
Parameters: - parafac2_tensorParafac2Tensor - (weight, factors, projection_matrices)
- weights1D array of shape (rank, )
- weights of the factors
- factorsList of factors of the PARAFAC2 decomposition
- Contains the matrices
,
and
described above
- projection_matricesList of projection matrices used to create evolving
- factors.
Returns: - ndarray
Full constructed tensor. Uneven slices are padded with zeros.