An NPDo Approach for Principal Joint SVD-type Block Diagonalization
For researchers in matrix factorization and signal processing, this work provides a convergent algorithm for a specific matrix decomposition problem, but it is incremental as it extends existing block diagonalization techniques.
This paper proposes an NPDo approach for partial joint SVD-type block diagonalization of multiple matrices, aiming to maximize the common dominant block-diagonal parts. The method combined with Gauss-Seidel-type updating is shown to be globally convergent with monotonic objective increase, and numerical experiments demonstrate its efficiency.
This paper is concerned with partial Joint SVD-type Block Diagonalization of several matrices so that the extracted diagonal parts collectively optimally assume part of the total mass of all given matrices. For that reason, it will be referred also as Principal Joint SVD-type Block Diagonalization. When each block-size is 1-by-1, it is about finding a dominant partial joint SVD decomposition for the matrices of interests. An NPDo approach is proposed for maximizing the common dominant block-diagonal parts collectively. It is shown that 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.