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

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.

33 pages, 5 figures

References in corpus (5)

• A Spectral Algorithm for Latent Dirichlet Allocation
• A statistical model for tensor PCA
• Tensor Factorization via Matrix Factorization
• Symmetric Orthogonal Tensor Decomposition is Trivial
• Operator Norm Inequalities between Tensor Unfoldings on the Partition Lattice

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