TY - JOUR
T1 - Optimization methods for tensor decomposition
T2 - A comparison of new algorithms for fitting the CP(CANDECOMP/PARAFAC) model
AU - Yu, Huiwen
AU - Larsen, Kasper Green
AU - Christiansen, Ove
N1 - Publisher Copyright:
© 2024
PY - 2025/2
Y1 - 2025/2
N2 - Tensor decomposition is widely used for multi-way data analysis and computations in chemical science. CP decomposition is one of the most useful tensor decomposition models for capturing the essential information in massive multi-way chemical data and for efficiently performing computations with such tensors. However, efficiently and accurately computing the tensor decomposition itself is a nontrivial problem that sometimes limits the advantage of tensor decomposition methods. In this work we propose and test three new decomposition algorithms, that are defined from extrapolation ideas applied to the alternating least square (ALS) algorithm for CP tensor decomposition. The performance of the proposed algorithms are validated on both a variety of simulated datasets and real experimental datasets including fluorescence spectroscopy data, hyperspectral data and electroencephalogram (EEG) data. The results show that the proposed algorithms significantly accelerate the standard CP-ALS decomposition while maintaining favorable accuracy. One of the proposed methods, denoted direct inversion of the iterative subspace-like extrapolated ALS(CP-AD), is inspired from widely used extrapolation procedures used in the context of solving non-linear equations in quantum chemistry, and shows a particular attractive combination of a much reduced number of iterations needed for convergence, and modest computational cost. For example, CP-AD provided resulting tensors of similar accuracy but significantly lower computational cost than the standard CP-ALS algorithm and the widely used line-search based CP-ALS extrapolation procedure. The proposed methodology may thereby boost the application of tensor decomposition modeling in both experimental and computational chemistry.
AB - Tensor decomposition is widely used for multi-way data analysis and computations in chemical science. CP decomposition is one of the most useful tensor decomposition models for capturing the essential information in massive multi-way chemical data and for efficiently performing computations with such tensors. However, efficiently and accurately computing the tensor decomposition itself is a nontrivial problem that sometimes limits the advantage of tensor decomposition methods. In this work we propose and test three new decomposition algorithms, that are defined from extrapolation ideas applied to the alternating least square (ALS) algorithm for CP tensor decomposition. The performance of the proposed algorithms are validated on both a variety of simulated datasets and real experimental datasets including fluorescence spectroscopy data, hyperspectral data and electroencephalogram (EEG) data. The results show that the proposed algorithms significantly accelerate the standard CP-ALS decomposition while maintaining favorable accuracy. One of the proposed methods, denoted direct inversion of the iterative subspace-like extrapolated ALS(CP-AD), is inspired from widely used extrapolation procedures used in the context of solving non-linear equations in quantum chemistry, and shows a particular attractive combination of a much reduced number of iterations needed for convergence, and modest computational cost. For example, CP-AD provided resulting tensors of similar accuracy but significantly lower computational cost than the standard CP-ALS algorithm and the widely used line-search based CP-ALS extrapolation procedure. The proposed methodology may thereby boost the application of tensor decomposition modeling in both experimental and computational chemistry.
KW - Algorithms
KW - Alternating least square
KW - Computations
KW - Optimization
KW - Tensor decomposition
UR - http://www.scopus.com/inward/record.url?scp=85213266563&partnerID=8YFLogxK
U2 - 10.1016/j.chemolab.2024.105290
DO - 10.1016/j.chemolab.2024.105290
M3 - Journal article
AN - SCOPUS:85213266563
SN - 0169-7439
VL - 257
JO - Chemometrics and Intelligent Laboratory Systems
JF - Chemometrics and Intelligent Laboratory Systems
M1 - 105290
ER -