TY - JOUR

T1 - Accelerating PARAFAC2 algorithms for non-negative complex tensor decomposition

AU - Yu, Huiwen

AU - Augustijn, Dillen

AU - Bro, Rasmus

PY - 2021

Y1 - 2021

N2 - 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.

AB - 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.

U2 - 10.1016/j.chemolab.2021.104312

DO - 10.1016/j.chemolab.2021.104312

M3 - Journal article

VL - 214

JO - Chemometrics and Intelligent Laboratory Systems

JF - Chemometrics and Intelligent Laboratory Systems

SN - 0169-7439

M1 - 104312

ER -