LRTuckerRep: Low-rank Tucker Representation Model for Multi-dimensional Data Completion

Fuente: arXiv
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Main Authors: Gong, Wenwu, Yang, Lili
Format: Preprint
Published: 2025
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author Gong, Wenwu
Yang, Lili
author_facet Gong, Wenwu
Yang, Lili
contents Multi-dimensional data completion is a critical problem in computational sciences, particularly in domains such as computer vision, signal processing, and scientific computing. Existing methods typically leverage either global low-rank approximations or local smoothness regularization, but each suffers from notable limitations: low-rank methods are computationally expensive and may disrupt intrinsic data structures, while smoothness-based approaches often require extensive manual parameter tuning and exhibit poor generalization. In this paper, we propose a novel Low-Rank Tucker Representation (LRTuckerRep) model that unifies global and local prior modeling within a Tucker decomposition. Specifically, LRTuckerRep encodes low rankness through a self-adaptive weighted nuclear norm on the factor matrices and a sparse Tucker core, while capturing smoothness via a parameter-free Laplacian-based regularization on the factor spaces. To efficiently solve the resulting nonconvex optimization problem, we develop two iterative algorithms with provable convergence guarantees. Extensive experiments on multi-dimensional image inpainting and traffic data imputation demonstrate that LRTuckerRep achieves superior completion accuracy and robustness under high missing rates compared to baselines.
format Preprint
id arxiv_https___arxiv_org_abs_2508_03755
institution arXiv
publishDate 2025
record_format arxiv
spellingShingle LRTuckerRep: Low-rank Tucker Representation Model for Multi-dimensional Data Completion
Gong, Wenwu
Yang, Lili
Machine Learning
Computer Vision and Pattern Recognition
Numerical Analysis
Multi-dimensional data completion is a critical problem in computational sciences, particularly in domains such as computer vision, signal processing, and scientific computing. Existing methods typically leverage either global low-rank approximations or local smoothness regularization, but each suffers from notable limitations: low-rank methods are computationally expensive and may disrupt intrinsic data structures, while smoothness-based approaches often require extensive manual parameter tuning and exhibit poor generalization. In this paper, we propose a novel Low-Rank Tucker Representation (LRTuckerRep) model that unifies global and local prior modeling within a Tucker decomposition. Specifically, LRTuckerRep encodes low rankness through a self-adaptive weighted nuclear norm on the factor matrices and a sparse Tucker core, while capturing smoothness via a parameter-free Laplacian-based regularization on the factor spaces. To efficiently solve the resulting nonconvex optimization problem, we develop two iterative algorithms with provable convergence guarantees. Extensive experiments on multi-dimensional image inpainting and traffic data imputation demonstrate that LRTuckerRep achieves superior completion accuracy and robustness under high missing rates compared to baselines.
title LRTuckerRep: Low-rank Tucker Representation Model for Multi-dimensional Data Completion
topic Machine Learning
Computer Vision and Pattern Recognition
Numerical Analysis
url https://arxiv.org/abs/2508.03755