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arXiv · 1612.03839

Tensor Decompositions via Two-Mode Higher-Order SVD (HOSVD)

Miaoyan Wang·Yun S. Song
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Abstract

Tensor decompositions have rich applications in statistics and machine learning, and developing efficient, accurate algorithms for the problem has received much attention recently. Here, we present a new method built on Kruskal's uniqueness theorem to decompose symmetric, nearly orthogonally decomposable tensors. Unlike the classical higher-order singular value decomposition which unfolds a tensor along a single mode, we consider unfoldings along two modes and use rank-1 constraints to characterize the underlying components. This tensor decomposition method provably handles a greater level of noise compared to previous methods and achieves a high estimation accuracy. Numerical results demonstrate that our algorithm is robust to various noise distributions and that it performs especially favorably as the order increases.

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Miaoyan Wang, Yun S. Song. 2016-12-12. Tensor Decompositions via Two-Mode Higher-Order SVD (HOSVD). https://arxiv.org/abs/1612.03839

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