Nonnegative PARAFAC2: a flexible coupling approach

TL;DR

This paper introduces a flexible PARAFAC2 tensor decomposition model that allows for nonnegativity constraints on the mode with variability, enhancing source separation capabilities.

Contribution

It proposes a relaxed PARAFAC2 model enabling nonnegativity constraints on the variable mode, along with an algorithm for its computation.

Findings

Effective on synthetic data for source separation

Improves modeling of variable data in chemometrics

Demonstrates flexibility over traditional PARAFAC2

Abstract

Modeling variability in tensor decomposition methods is one of the challenges of source separation. One possible solution to account for variations from one data set to another, jointly analysed, is to resort to the PARAFAC2 model. However, so far imposing constraints on the mode with variability has not been possible. In the following manuscript, a relaxation of the PARAFAC2 model is introduced, that allows for imposing nonnegativity constraints on the varying mode. An algorithm to compute the proposed flexible PARAFAC2 model is derived, and its performance is studied on both synthetic and chemometrics data.