Analysis and Approximation of the Canonical Polyadic Tensor Decomposition
Abstract
We study the least-squares (LS) functional of the canonical polyadic (CP) tensor decomposition. Our approach is based on the elimination of one factor matrix which results in a reduced functional. The reduced functional is reformulated into a projection framework and into a Rayleigh quotient. An analysis of this functional leads to several conclusions: new sufficient conditions for the existence of minimizers of the LS functional, the existence of a critical point in the rank-one case, a heuristic explanation of "swamping" and computable bounds on the minimal value of the LS functional. The latter result leads to a simple algorithm -- the Centroid Projection algorithm -- to compute suboptimal solutions of tensor decompositions. These suboptimal solutions are applied to iterative CP algorithms as initial guesses, yielding a method called centroid projection for canonical polyadic (CPCP) decomposition which provides a significant speedup in our numerical experiments compared to the standard methods.
Cite
@article{arxiv.1109.3832,
title = {Analysis and Approximation of the Canonical Polyadic Tensor Decomposition},
author = {Stefan Kindermann and Carmeliza Navasca},
journal= {arXiv preprint arXiv:1109.3832},
year = {2011}
}