An inexactly accelerated algorithm for nonnegative tensor CP decomposition with the column unit constraints

Zihao Wang and Minru Bai ()
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Zihao Wang: Hunan University
Minru Bai: Hunan University

Computational Optimization and Applications, 2024, vol. 88, issue 3, No 8, 923-962

Abstract: Abstract The component separation problem in complex chemical systems is very important and challenging in chemometrics. In this paper, we study a third-order nonnegative CANDECOMP/PARAFAC decomposition model with the column unit constraints (NCPD_CU) motivated by the component separation problem. To solve the NCPD_CU model, we first explore rapid computational methods for a generalized class of three-block optimization problems, which may exhibit nonconvexity and nonsmoothness. To this end, we propose the accelerated inexact block coordinate descent (AIBCD) algorithm, where each subproblem is inexactly solved through a finite number of inner-iterations employing the alternating proximal gradient method. Additionally, the algorithm incorporates extrapolation during the outer-iterations to enhance overall efficiency. We prove that the iterative sequence generated by the algorithm converges to a stationary point under mild conditions. Subsequently, we apply this methodology to the NCPD_CU model that satisfies the specified conditions. Finally, we present numerical results using both synthetic and real-world data, showcasing the remarkable efficiency of our proposed method.

Keywords: Accelerated block coordinate descent; Inexact algorithm; Nonnegative CANDECOMP/PARAFAC decomposition; Column unit constraint; Component separation (search for similar items in EconPapers)
Date: 2024
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DOI: 10.1007/s10589-024-00574-8

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