Parallel Algorithms for Constrained Tensor Factorization via the Alternating Direction Method of Multipliers

TL;DR

This paper introduces a parallel, distributed framework for constrained tensor factorization using ADMoM, enabling scalable, constraint-aware tensor analysis suitable for big data applications.

Contribution

It develops a novel ADMoM-based tensor factorization method that simplifies computations and supports distributed implementation with constraints like nonnegativity.

Findings

High potential for nonnegative tensor factorization as an alternative to existing methods

Enables parallel and distributed computation for large-scale tensor data

Framework can incorporate various constraints beyond nonnegativity

Abstract

Tensor factorization has proven useful in a wide range of applications, from sensor array processing to communications, speech and audio signal processing, and machine learning. With few recent exceptions, all tensor factorization algorithms were originally developed for centralized, in-memory computation on a single machine; and the few that break away from this mold do not easily incorporate practically important constraints, such as nonnegativity. A new constrained tensor factorization framework is proposed in this paper, building upon the Alternating Direction method of Multipliers (ADMoM). It is shown that this simplifies computations, bypassing the need to solve constrained optimization problems in each iteration; and it naturally leads to distributed algorithms suitable for parallel implementation on regular high-performance computing (e.g., mesh) architectures. This opens the door for many emerging big data-enabled applications. The methodology is exemplified using nonnegativity as a baseline constraint, but the proposed framework can more-or-less readily incorporate many other types of constraints. Numerical experiments are very encouraging, indicating that the ADMoM-based nonnegative tensor factorization (NTF) has high potential as an alternative to state-of-the-art approaches.