Generic order-4 symmetric tensors of rank up to 2n+1 are efficiently decomposable via moment matrix extension, with a conjectured extension to O(n^2) rank.
Analysis of the Stochastic Alternating Least Squares Method for the Decomposition of Random Tensors
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abstract
Stochastic Alternating Least Squares (SALS) is a method that approximates the canonical decomposition of averages of sampled random tensors. Its simplicity and efficient memory usage make SALS an ideal tool for decomposing tensors in an online setting. We show, under mild regularization and readily verifiable assumptions on the boundedness of the data, that the SALS algorithm is globally convergent. Numerical experiments validate our theoretical findings and demonstrate the algorithm's performance and complexity.
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Efficient Tensor Decomposition via Moment Matrix Extension
Generic order-4 symmetric tensors of rank up to 2n+1 are efficiently decomposable via moment matrix extension, with a conjectured extension to O(n^2) rank.