# Generalized Nonnegative Structured Kruskal Tensor Regression

arXiv: https://arxiv.org/abs/2509.19900 · HTML: https://mlsanity.com/paper/2509.19900/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 12 of its 49 references that are in the map.
- First posted on arXiv 24 Sep 2025.

## Builds on (most cited first, 12 of 12)

- [Tensor Decomposition for Signal Processing and Machine Learning](https://mlsanity.com/paper/1607.01668/) (2016)
- [Learning to Optimize: A Primer and A Benchmark](https://mlsanity.com/paper/2103.12828/) (2021)
- [Tensor Regression Networks](https://mlsanity.com/paper/1707.08308/) (2017)
- [Guaranteed Tensor Recovery Fused Low-rankness and Smoothness](https://mlsanity.com/paper/2302.02155/) (2023)
- [A Flexible and Efficient Algorithmic Framework for Constrained Matrix and Tensor Factorization](https://mlsanity.com/paper/1506.04209/) (2015)
- [Tucker Tensor Regression and Neuroimaging Analysis](https://mlsanity.com/paper/1304.5637/) (2013)
- [Tensor-on-tensor regression](https://mlsanity.com/paper/1701.01037/) (2017)
- [Bayesian Tensor Regression](https://mlsanity.com/paper/1509.06490/) (2015)
- [Structured Point Cloud Data Analysis via Regularized Tensor Regression for Process Modeling and Optimization](https://mlsanity.com/paper/1807.10278/) (2018)
- [Supervised tensor decomposition with features on multiple modes](https://mlsanity.com/paper/1910.09499/) (2019)
- [Tensor Decomposition with Relational Constraints for Predicting Multiple Types of MicroRNA-disease Associations](https://mlsanity.com/paper/1911.05584/) (2019)
- [New penalized criteria for smooth non-negative tensor factorization with missing entries](https://mlsanity.com/paper/2203.11514/) (2022)

## Abstract (arXiv)

This paper introduces Generalized Nonnegative Structured Kruskal Tensor Regression (NS-KTR), a novel tensor regression framework that enhances interpretability and performance through mode-specific hybrid regularization and nonnegativity constraints. Our approach accommodates both linear and logistic regression formulations for diverse response variables while addressing the structural heterogeneity inherent in multidimensional tensor data. We integrate fused LASSO, total variation, and ridge regularizers, each tailored to specific tensor modes, and develop an efficient alternating direction method of multipliers (ADMM) based algorithm for parameter estimation. Comprehensive experiments on synthetic signals and real hyperspectral datasets demonstrate that NS-KTR consistently outperforms conventional tensor regression methods. The framework's ability to preserve distinct structural characteristics across tensor dimensions while ensuring physical interpretability makes it especially suitable for applications in signal processing and hyperspectral image analysis.