Alternating minimization algorithms for graph regularized tensor completion
From MaRDI portal
Publication:6347955
arXiv2008.12876MaRDI QIDQ6347955
Bin Gao, Shuyu Dong, Yu Guan, François Glineur, P. -A. Absil
Publication date: 28 August 2020
Abstract: We consider a low-rank tensor completion (LRTC) problem which aims to recover a tensor from incomplete observations. LRTC plays an important role in many applications such as signal processing, computer vision, machine learning, and neuroscience. A widely used approach is to combine the tensor completion data fitting term with a regularizer based on a convex relaxation of the multilinear ranks of the tensor. For the data fitting function, we model the tensor variable by using the Canonical Polyadic (CP) decomposition and for the low-rank promoting regularization function, we consider a graph Laplacian-based function which exploits correlations between the rows of the matrix unfoldings. For solving our LRTC model, we propose an efficient alternating minimization algorithm. Furthermore, based on the Kurdyka-{L}ojasiewicz property, we show that the sequence generated by the proposed algorithm globally converges to a critical point of the objective function. Besides, an alternating direction method of multipliers algorithm is also developed for the LRTC model. Extensive numerical experiments on synthetic and real data indicate that the proposed algorithms are effective and efficient.
Has companion code repository: https://gitlab.com/ricky7guanyu/tensor-completion-with-regularization-term
Nonconvex programming, global optimization (90C26) Nonlinear programming (90C30) Extrapolation to the limit, deferred corrections (65B05) Multilinear algebra, tensor calculus (15A69) Numerical methods of relaxation type (49M20) Methods of reduced gradient type (90C52)
This page was built for publication: Alternating minimization algorithms for graph regularized tensor completion
Report a bug (only for logged in users!)Click here to report a bug for this page (MaRDI item Q6347955)
