Generalized Nonnegative Structured Kruskal Tensor Regression

2025-09-24

AI Summary

To address insufficient interpretability and modeling performance caused by structural heterogeneity in multidimensional tensor data, this paper proposes a modality-adaptive tensor regression framework. Methodologically, it integrates modality-specific regularizers—LASSO for sparsity, total variation for smoothness, and ridge for stability—coupled with nonnegative Kruskal decomposition to ensure physical interpretability. An efficient ADMM-based optimization algorithm unifies support for both linear and logistic regression. Our key contribution is the first synergistic integration of hybrid modality-aware regularization with nonnegative tensor decomposition, explicitly capturing heterogeneous structures across tensor modes. Extensive experiments on synthetic data and real-world hyperspectral image tasks demonstrate significant improvements over state-of-the-art tensor regression methods, validating the framework’s effectiveness and generalizability in signal processing and remote sensing image analysis.

Technology Category

• Machine Learning: Multimodal Learning
• Computer Vision: Multi-modal Vision
• Intelligent Robots: Multimodal Perception & Sensor Fusion

Application Category

• Search and Retrieval-Augmented AI: Retrieval-Augmented Generation (RAG) and multi-modal RAG
• Graph Algorithms and Modeling for the Web: Algorithms and analysis for heterogeneous, signed, attributed, multi-relational, temporal, higher-order, and annotated Web-related graphs
• User Modeling, Personalization and Recommendation: Explainable and interpretable methods for personalization

Abstract

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.

Problem

• Addresses structural heterogeneity in multidimensional tensor data
• Enhances interpretability through hybrid regularization and nonnegativity constraints
• Improves performance for signal processing and hyperspectral image analysis

Innovation

• Nonnegative structured Kruskal tensor regression framework
• Mode-specific hybrid regularization with fused LASSO
• Efficient ADMM algorithm for parameter estimation