Symmetric Orthogonal Tensor Decomposition is Trivial

Understand

We consider the problem of decomposing a real-valued symmetric tensor as the sum of outer products of real-valued, pairwise orthogonal vectors.

• Such decompositions do not generally exist, but we show that some symmetric tensor decomposition problems can be converted to orthogonal problems following the whitening procedure proposed by Anandkumar et al.
• (2012).
• If an orthogonal decomposition of an $m$-way $n$-dimensional symmetric tensor exists, we propose a novel method to compute it that reduces to an $n \times n$ symmetric matrix eigenproblem.