Convolution-Free Holistic Multivariance Decomposition Layer for Efficient Hyperspectral Image Classification Tensor Networks

2026-08-17

AI Summary

This study addresses the limited representational capacity of tensor decomposition and parameter redundancy in CNNs for hyperspectral image classification by proposing a convolution-free, holistic multivariate decomposition (HMD) differentiable layer. Leveraging learnable matrices to disentangle unimodal variations from high-order interactions, HMD enables end-to-end joint optimization as a structured alternative to traditional convolutions. Experiments on three benchmark datasets demonstrate that HMD outperforms conventional tensor decomposition methods in accuracy while requiring significantly fewer parameters than CNNs. Furthermore, it achieves comparable generalization capability and training stability, effectively overcoming existing performance bottlenecks to realize efficient and robust feature extraction and classification.

Abstract

Feature extraction for hyperspectral image classification is conventionally addressed using rigid tensor decompositions that fail to capture complex spatio-spectral interdependencies, or heavily parameterized convolutional neural networks that are computationally expensive. To overcome these limitations, this work introduces the Holistic Multivariance Decomposition (HMD) framework as a novel, end-to-end differentiable neural network layer. By explicitly separating independent single mode variations from cooperative higher dimensional interactions via learnable, matrix valued supports, the proposed HMD-0, HMD-1 and HMD-2 approximants are optimized jointly with a downstream classifier via backpropagation. Comprehensive evaluations across three benchmark HS datasets demonstrate that the higher level HMD layers achieve superior classification accuracy compared to classical learnable tensor baselines, including Tucker, Canonical Polyadic, and Tensor Train decompositions. Furthermore, HMD-1 and HMD-2 achieve a generalization capacity and training stability comparable to standard 2D and 3D-CNNs while requiring significantly fewer feature extractor parameters. These results demonstrate that the HMD framework provides a structurally robust substitute for traditional convolution in multidimensional HS image classification, offering high parameter efficiency and stability throughout the optimization process.

Problem

• Hyperspectral Image Classification
• Feature Extraction
• Tensor Decomposition
• Parameter Efficiency

Innovation

• Holistic Multivariance Decomposition
• Convolution-Free
• Tensor Networks
• Hyperspectral Image Classification
• Parameter Efficiency