PARAFAC2 AO-ADMM: Constraints in all modes

TL;DR

This paper introduces an ADMM-based algorithm for PARAFAC2 tensor decomposition, enabling flexible regularisation of the evolving mode, improving accuracy and efficiency over traditional methods.

Contribution

The paper presents a novel ADMM-based method for fitting PARAFAC2, allowing for arbitrary proximable regularisation penalties on the evolving mode.

Findings

Accurately recovers underlying components from simulated data

Demonstrates computational efficiency

Allows flexible regularisation constraints

Abstract

The PARAFAC2 model provides a flexible alternative to the popular CANDECOMP/PARAFAC (CP) model for tensor decompositions. Unlike CP, PARAFAC2 allows factor matrices in one mode (i.e., evolving mode) to change across tensor slices, which has proven useful for applications in different domains such as chemometrics, and neuroscience. However, the evolving mode of the PARAFAC2 model is traditionally modelled implicitly, which makes it challenging to regularise it. Currently, the only way to apply regularisation on that mode is with a flexible coupling approach, which finds the solution through regularised least-squares subproblems. In this work, we instead propose an alternating direction method of multipliers (ADMM)-based algorithm for fitting PARAFAC2 and widen the possible regularisation penalties to any proximable function. Our numerical experiments demonstrate that the proposed ADMM-based approach for PARAFAC2 can accurately recover the underlying components from simulated data while being both computationally efficient and flexible in terms of imposing constraints.