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

TL;DR

LRTuckerRep introduces a unified low-rank Tucker model for multi-dimensional data completion, combining global low-rank and local smoothness priors, with efficient algorithms and superior empirical performance.

Contribution

It proposes a novel Low-Rank Tucker Representation model that unifies global and local priors in a single framework with adaptive regularization and provable algorithms.

Findings

Achieves higher accuracy in image inpainting and traffic data imputation.

Demonstrates robustness under high missing data rates.

Outperforms baseline methods in empirical tests.

Abstract

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.