An NPDo Approach for Tensor Block-Diagonalization
For researchers in tensor decomposition, this work provides a novel method for block-diagonalizing tensors, though it is incremental as it extends existing concepts.
This paper proposes Principal Tensor Block-Diagonalization (PTBD), which generalizes Tucker decomposition and dominant tensor SVD, and develops an NPDo approach with Gauss-Seidel-type updating that globally converges to a stationary point. Numerical experiments demonstrate efficiency.
This paper is concerned with Partial Tensor Block-Diagonalization of a multiway tensor by orthonormal matrices so that the extracted block-diagonal part optimally represents the tensor. The basic idea is to maximize the block-diagonal part via the tensor's mode-multiplications by orthonormal matrices. For that reason, it will be referred to Principal Tensor Block-Diagonalization (PTBD), which contains the Tucker decomposition (TD) of a tensor as a special case with just one block. Also as a special case is the approximate dominant tensor SVD in which each block-size is 1-by-1. An NPDo approach is proposed to optimize the block-diagonal part for computing \ptbd. It is shown the NPDo approach combined with Gauss-Seidel-type updating is globally convergent to a stationary point while the objective increases monotonically. Numerical experiments are presented to illustrate the efficiency of the NPDo approach.