An Accelerated Stochastic Gradient for Canonical Polyadic Decomposition

TL;DR

This paper introduces an accelerated stochastic gradient method with Nesterov momentum for large-scale canonical polyadic decomposition, demonstrating competitive performance against existing methods on synthetic and real data.

Contribution

It extends existing stochastic gradient approaches by incorporating acceleration, improving efficiency for large-scale structured tensor decompositions.

Findings

The accelerated method outperforms traditional stochastic approaches.

It is effective on both synthetic and real-world datasets.

The approach is computationally competitive with state-of-the-art methods.

Abstract

We consider the problem of structured canonical polyadic decomposition. If the size of the problem is very big, then stochastic gradient approaches are viable alternatives to classical methods, such as Alternating Optimization and All-At-Once 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.