Exploiting Commutativity Condition For Cp Decomposition Via Approximate Simultaneous Diagonalization

In this paper, we propose a novel strategy which utilizes an inherent algebraic property of simultaneously diagonalizable matrix tuples, i.e., commutativity, for both (i) reducing approximate CP decomposition of a higher-order tensor to Approximate Simultaneous Diagonalization (ASD) and (ii) solving the ASD. By using a commutativity criterion, we design a matrix tuple with matrix slices of a given tensor. Then, for the ASD of the designed tuple, we use the Approximate-Then-Diagonalize-Simultaneously (ATDS) algorithm which utilizes commutativity to solve ASD. Numerical experiments show that the proposed strategy achieves better performance than conventional ones particularly when matrices to be estimated has almost collinear columns.