PARAFAC2 AO-ADMM: Constraints in all modes
This work addresses the challenge of regularizing the evolving mode in PARAFAC2 for researchers and practitioners using tensor decompositions, offering a more flexible and efficient method.
The paper introduces an ADMM-based algorithm for the PARAFAC2 tensor decomposition model, enabling the application of various proximable regularisation penalties to the evolving mode. Numerical experiments show that this approach accurately recovers underlying components from simulated data, demonstrating computational efficiency and flexibility in imposing constraints.
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.