aiqbench analysis
This paper introduces GLSKF, a novel framework for completing incomplete multidimensional tensor data by combining global smoothness constraints with local high-frequency variations via generalized least squares kernels. By exploiting the Kronecker and Toeplitz structures of covariance matrices within an alternating least squares algorithm, it achieves efficient reconstruction across diverse tasks such as traffic speed imputation, image completion, video recovery, and MRI data processing. The method demonstrates superior performance in capturing both long-range dependencies and localized anomalies compared to standard low-rank tensor factorization techniques.
Generalized Least Squares Kernelized Tensor Factorization
arXiv:2412.07041v4 Announce Type: replace-cross Abstract: Recovering incomplete multidimensional tensor-structured data is a fundamental task in many real-world applications. Smoothness-constrained low-rank tensor factorization effectively captures global and long-range correlations, but often struggles to characterize short-scale, high-frequency, or locally varying structures. We propose GLSKF, a complementary Generalized Least Squares Kernelized Tensor Factorization framework, for multidimensional spatiotemporal data completion. GLSKF additively integrates a covariance-regularized low-rank global component with an explicitly modeled locally correlated residual component under a GLS objective, enabling effective modeling of both global dependencies and localized variations. A covariance norm regularizer encodes spatiotemporal dependencies in both components: structured covariances are imposed on the latent factor columns to enforce smoothness in the global factorization, whereas compactly supported sparse kernels are used to model local correlations in the residual. We develop an alternating least squares algorithm with blockwise linear-system updates that exploit the Kronecker structure of the covariance matrices under missing data and facilitate fast conjugate gradient solves. Additional computational gains are obtained by exploiting the sparsity and Toeplitz structure of the local residual covariance matrices for efficient matrix-vector multiplications. We evaluate GLSKF on four real-world multidimensional data-completion tasks: traffic speed imputation, color image completion, digital video recovery, and MRI data reconstruction. Experimental results demonstrate that GLSKF achieves superior reconstruction performance and favorable scalability across a range of tensor completion tasks, supporting its broad applicability to multidimensional data completion.
Abstract:Recovering incomplete multidimensional tensor-structured data is a fundamental task in many real-world applications. Smoothness-constrained low-rank tensor factorization effectively captures global and long-range correlations, but often struggles to characterize short-scale, high-frequency, or locally varying structures. We propose GLSKF, a complementary Generalized Least Squares Kernelized Tensor Factorization framework, for multidimensional spatiotemporal data completion. GLSKF additively integrates a covariance-regularized low-rank global component with an explicitly modeled locally correlated residual component under a GLS objective, enabling effective modeling of both global dependencies and localized variations. A covariance norm regularizer encodes spatiotemporal dependencies in both components: structured covariances are imposed on the latent factor columns to enforce smoothness in the global factorization, whereas compactly supported sparse kernels are used to model local correlations in the residual. We develop an alternating least squares algorithm with blockwise linear-system updates that exploit the Kronecker structure of the covariance matrices under missing data and facilitate fast conjugate gradient solves. Additional computational gains are obtained by exploiting the sparsity and Toeplitz structure of the local residual covariance matrices for efficient matrix-vector multiplications. We evaluate GLSKF on four real-world multidimensional data-completion tasks: traffic speed imputation, color image completion, digital video recovery, and MRI data reconstruction. Experimental results demonstrate that GLSKF achieves superior reconstruction performance and favorable scalability across a range of tensor completion tasks, supporting its broad applicability to multidimensional data completion.
Machine Learning (stat.ML); Computer Vision and Pattern Recognition (cs.CV); Machine Learning (cs.LG)
arXiv:2412.07041 [stat.ML]
(or arXiv:2412.07041v4 [stat.ML] for this version)
https://doi.org/10.1016/j.patcog.2026.114342 DOI(s) linking to related resources
From: Lijun Sun Dr. [view email] [v1] Mon, 9 Dec 2024 23:01:04 UTC (3,729 KB) [v2] Wed, 11 Dec 2024 19:05:09 UTC (3,566 KB) [v3] Tue, 11 Feb 2025 14:57:40 UTC (4,316 KB) [v4] Tue, 21 Jul 2026 14:16:07 UTC (10,426 KB)
Full text under the publisher's open licence · 289 words
Related coverage
PIRAMID: Progress and Plans
LessWrong · Jul 27, 2026
Model Weight Profiles: Where Do the Parameters Go?
AMD · Sep 25, 2026
GEM Training: How Meta Doubled the Efficiency of Its LLM-Scale Ads Foundation Model
Meta Engineering · Aug 3, 2026
Attention Decode on AMD MI450 GPUs: A Gluon Kernel Optimization Guide
AMD · Jul 27, 2026