Simplified Algorithms for Canonical Polyadic Decomposition for Over-Complete Even Order Tensors (Ongoing Work)

Abstract

This paper considers canonical polyadic (CP) decomposition of symmetric even order tensors. In earlier work, we showed that decomposition of such tensors is equivalent to solving a system of quadratic equations. As part of ongoing work, we further show that for almost all tensors, singular value decomposition of a certain matrix can uniquely obtain the solution to the system of quadratic equations. Our proposed algorithm is able to find the CP-decomposition, even in the regime where the CP-rank exceeds the dimensions of the tensor (overcomplete tensors).