Accelerated Stochastic Gradient for Nonnegative Tensor Completion and Parallel Implementation

TL;DR

This paper introduces an accelerated stochastic gradient method for nonnegative tensor completion, demonstrating its efficiency and scalability through parallel implementation and extensive testing on real and synthetic datasets.

Contribution

It proposes a novel stochastic accelerated gradient algorithm for nonnegative tensor completion and provides a parallel implementation that significantly improves computational speed.

Findings

Effective on real-world and synthetic data

Achieves significant speedup with multi-threaded implementation

Competitive for large-scale tensor completion problems

Abstract

We consider the problem of nonnegative tensor completion. We adopt the alternating optimization framework and solve each nonnegative matrix completion problem via a stochastic variation of the accelerated gradient algorithm. We experimentally test the effectiveness and the efficiency of our algorithm using both real-world and synthetic data. We develop a shared-memory implementation of our algorithm using the multi-threaded API OpenMP, which attains significant speedup. We believe that our approach is a very competitive candidate for the solution of very large nonnegative tensor completion problems.