tensorly.parafac2_tensor.parafac2_to_slice

parafac2_to_slice(parafac2_tensor, slice_idx, validate=True)[source]

Generate a single slice along the first mode from the PARAFAC2 tensor.

The decomposition is on the form $(A[B_i]C)$ such that the i-th frontal slice, $X_i$, of $X$ is given by

$$X_i=B_{i}diag(a_i)C^T,$$

where $diag(a_i)$ is the diagonal matrix whose nonzero entries are equal to the $i$-th row of the $I\times R$ factor matrix $A$, $B_i$ is a $J_i\times R$ factor matrix such that the cross product matrix $B_{i_1}^T{B}_{i_1}$ is constant for all $i$, and $C$ is a $K\times R$ factor matrix. To compute this decomposition, we reformulate the expression for $B_i$ such that

$$B_i=P_{i}B,$$

where $P_i$ is a $J_i\times R$ orthogonal matrix and $B$ is a $R\times R$ matrix.

An alternative formulation of the PARAFAC2 decomposition is that the tensor element $X_{ijk}$ is given by

$$X_{ijk}=\sum _{r=1}^R{A}_{ir}{B}_{ijr}{C}_{kr},$$

with the same constraints hold for $B_i$ 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 $A$, $B$ and $C$ described above

• projection_matricesList of projection matrices used to create evolving

  factors.

Returns:

ndarray

Full tensor of shape [P[slice_idx].shape[1], C.shape[1]], where P is the projection matrices and C is the last factor matrix of the Parafac2Tensor.