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Tensor decompositions have rich applications in statistics and machinelearning, and developing efficient, accurate algorithms for the problem hasreceived much attention recently. Here, we present a new method built onKruskal's uniqueness theorem to decompose symmetric, nearly orthogonallydecomposable tensors. Unlike the classical higher-order singular valuedecomposition which unfolds a tensor along a single mode, we considerunfoldings along two modes and use rank-1 constraints to characterize theunderlying components. This tensor decomposition method provably handles agreater level of noise compared to previous methods and achieves a highestimation accuracy. Numerical results demonstrate that our algorithm is robustto various noise distributions and that it performs especially favorably as theorder increases.

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