Efficient Constrained Tensor Factorization by Alternating Optimization with Primal-Dual Splitting

TL;DR

This paper introduces an efficient and flexible tensor factorization algorithm that uses alternating optimization combined with primal-dual splitting, overcoming limitations of existing methods in handling constraints and regularizations.

Contribution

The proposed method replaces matrix inversion with primal-dual splitting in alternating optimization, enabling better handling of constraints and regularizations in tensor factorization.

Findings

Outperforms AO-ADMM in regularized nonnegative tensor factorization

Avoids matrix inversion, increasing computational efficiency

Handles structured regularizations more effectively

Abstract

Tensor factorization with hard and/or soft constraints has played an important role in signal processing and data analysis. However, existing algorithms for constrained tensor factorization have two drawbacks: (i) they require matrix-inversion; and (ii) they cannot (or at least is very difficult to) handle structured regularizations. We propose a new tensor factorization algorithm that circumvents these drawbacks. The proposed method is built upon alternating optimization, and each subproblem is solved by a primal-dual splitting algorithm, yielding an efficient and flexible algorithmic framework to constrained tensor factorization. The advantages of the proposed method over a state-of-the-art constrained tensor factorization algorithm, called AO-ADMM, are demonstrated on regularized nonnegative tensor factorization.