parafac2_to_slice(parafac2_tensor, slice_idx, validate=True)
Generate a single slice along the first mode from the PARAFAC2 tensor.
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.
- 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
Full tensor of shape [P[slice_idx].shape, C.shape], where P is the projection matrices and C is the last factor matrix of the Parafac2Tensor.