Analysis and Approximation of the Canonical Polyadic Tensor Decomposition

Details Analysis and Approximation of the Canonical Polyadic Tensor Decomposition Analysis and Approximation of the Canonical Polyadic Tensor Decomposition

2011-09-18

arxiv.org/abs/1109.3832v1

Mathematics

Numerical Analysis

Scientific paper

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.

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