Analysis of the Stochastic Alternating Least Squares Method for the Decomposition of Random Tensors

2020/04/27 by Yanzhao Cao, Cao, Yanzhao, Somak Das +6
Computer Science · Engineering · Mathematics · #Matrix Theory and Algorithms #Sparse and Compressive Sensing Techniques #Tensor decomposition and applications #cs.NA #math.NA #math.OC #msc:15A69 #msc:65K10 #msc:68W20 #msc:90C15

paper · pdf · doi:10.48550/arxiv.2004.12530

22 pages

arxiv created 2020/04/27 · arxiv updated 2020/04/28

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.

Citations

• A Stochastic Approximation Method
• Analysis of Individual Differences in Multidimensional Scaling Via an N-way Generalization of “Eckart-Young” Decomposition
• Tensor Decompositions and Applications
• Most Tensor Problems Are NP-Hard
• Stochastic Majorization-Minimization Algorithms for Large-Scale Optimization
• Unfolding Latent Tree Structures using 4th Order Tensors

Cited by

• On calculation of canonical decomposition of Tensor via the grid of local discrepancies

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