Accelerating PARAFAC2 algorithms for non-negative complex tensor decomposition

Abstract

PARAFAC2 is a well-established method for specific type of tensor decomposition problems, for example when observations have different lengths or measured profiles slightly change position in the multi-way data. Most commonly used PARAFAC2-ALS algorithms are very slow. In this paper, we propose novel implementations of extrapolation-based PARAFAC2 algorithms. Next to the frequently implemented PARAFAC2-ALS, also Hierarchical ALS is investigated for PARAFAC2. We show that the newly proposed implementation of All-at-once Nesterov-like extrapolation PARAFAC2-ALS algorithm achieves the fastest convergence speed whilst maintaining a low fraction of local minima solutions. This new method is shown to be 13 times faster on average compared to a PARAFAC2-ALS algorithm without acceleration, whereas the commonly used N-way toolbox line search extrapolation PARAFAC2-ALS algorithm obtains only a 3 times speedup on the same simulated dataset. Furthermore, the proposed method is shown to outperform the latest extrapolation acceleration PARAFAC2 algorithms available in literature. A comprehensive investigation and comparison is performed of all the proposed extrapolation algorithms, using both simulated and real (GC-MS) data. To the best of our knowledge, this is the first paper that systematically investigates extrapolation acceleration PARAFAC2-ALS and PARAFAC2-HALS algorithms.