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Stochastic optimization on tensor factorization and completion

Siaminou Ioanna

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Year 2021
Type of Item Master Thesis
Bibliographic Citation Ioanna Siaminou, "Stochastic optimization on tensor factorization and completion", Master Thesis, School of Electrical and Computer Engineering, Technical University of Crete, Chania, Greece, 2021
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We consider the problem of structured canonical polyadic decomposition (CPD). If the size of the problem is very big, then stochastic optimization approaches are viable alternatives to classical methods, such as Alternating Optimization (AO) and All-At-Once (AAO) optimization. We extend a recent stochastic gradient approach by employing an acceleration step (Nesterov momentum) in each iteration. We compare our approach with state-of-the-art alternatives, using both synthetic and real-world data, and find it to be very competitive. Furthermore, we examine the drawbacks of a parallel implementation of our accelerated stochastic algorithm and describe an alternative method that deals with these limitations. Finally, we propose an accelerated stochastic algorithm for the Nonnegative Tensor Completion problem and its parallel implementation via the shared–memory API OpenMP. Through numerical experiments, we test its efficiency in very large problems.

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