Tensor Decomposition via Joint Matrix Schur Decomposition

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Nicolo Colombo, Nikos Vlassis ;
Proceedings of The 33rd International Conference on Machine Learning, PMLR 48:2820-2828, 2016.

Abstract

We describe an approach to tensor decomposition that involves extracting a set of observable matrices from the tensor and applying an approximate joint Schur decomposition on those matrices, and we establish the corresponding first-order perturbation bounds. We develop a novel iterative Gauss-Newton algorithm for joint matrix Schur decomposition, which minimizes a nonconvex objective over the manifold of orthogonal matrices, and which is guaranteed to converge to a global optimum under certain conditions. We empirically demonstrate that our algorithm is faster and at least as accurate and robust than state-of-the-art algorithms for this problem.

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