The average number of critical rank-one approximations to a tensor

Abstract

\u3cp\u3eMotivated by the many potential applications of low-rank multi-way tensor approximations, we set out to count the rank-one tensors that are critical points of the distance function to a general tensor v. As this count depends on v, we average over v drawn from a Gaussian distribution, and find a formula that relates this average to problems in random matrix theory.\u3c/p\u3