# Generalized Least Squares Kernelized Tensor Factorization

arXiv: https://arxiv.org/abs/2412.07041 · HTML: https://mlsanity.com/paper/2412.07041/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 15 of its 46 references that are in the map.
- First posted on arXiv 9 Dec 2024.

## Builds on (most cited first, 15 of 15)

- [Tensor Decomposition for Signal Processing and Machine Learning](https://mlsanity.com/paper/1607.01668/) (2016)
- [Image Reconstruction: From Sparsity to Data-adaptive Methods and Machine Learning](https://mlsanity.com/paper/1904.02816/) (2019)
- [Tensor Methods in Computer Vision and Deep Learning](https://mlsanity.com/paper/2107.03436/) (2021)
- [Tensor Ring Decomposition with Rank Minimization on Latent Space: An Efficient Approach for Tensor Completion](https://mlsanity.com/paper/1809.02288/) (2018)
- [Low-Rank Autoregressive Tensor Completion for Spatiotemporal Traffic Data Imputation](https://mlsanity.com/paper/2104.14936/) (2021)
- [Smooth PARAFAC Decomposition for Tensor Completion](https://mlsanity.com/paper/1505.06611/) (2015)
- [Thoughts on Massively Scalable Gaussian Processes](https://mlsanity.com/paper/1511.01870/) (2015)
- [DuSK: A Dual Structure-preserving Kernel for Supervised Tensor Learning with Applications to Neuroimages](https://mlsanity.com/paper/1407.8289/) (2014)
- [Learning from Multiway Data: Simple and Efficient Tensor Regression](https://mlsanity.com/paper/1607.02535/) (2016)
- [Tensor Decompositions for Hyperspectral Data Processing in Remote Sensing: A Comprehensive Review](https://mlsanity.com/paper/2205.06407/) (2022)
- [Tensor Decomposition Meets RKHS: Efficient Algorithms for Smooth and Misaligned Data](https://mlsanity.com/paper/2408.05677/) (2024)
- [Scalable Spatiotemporally Varying Coefficient Modelling with Bayesian Kernelized Tensor Regression](https://mlsanity.com/paper/2109.00046/) (2021)
- [Functional Data Analysis by Matrix Completion](https://mlsanity.com/paper/1609.00834/) (2016)
- [Random Surface Covariance Estimation by Shifted Partial Tracing](https://mlsanity.com/paper/1912.12870/) (2019)
- [Bayesian Complementary Kernelized Learning for Multidimensional Spatiotemporal Data](https://mlsanity.com/paper/2208.09978/) (2022)

## Built on by (most cited first, 1 of 1)

- [Robust Tensor Completion via Gradient Tensor Nulclear L1-L2 Norm for Traffic Data Recovery](https://mlsanity.com/paper/2506.22732/) (2025)

## Abstract (arXiv)

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.