Convolution-Free Holistic Multivariance Decomposition Layer for Efficient Hyperspectral Image Classification Tensor Networks
2026-08-17 • Computer Vision and Pattern Recognition
Computer Vision and Pattern RecognitionMachine Learning
AI summaryⓘ
The authors introduced a new method called Holistic Multivariance Decomposition (HMD) to improve how hyperspectral images are classified. Their technique breaks down complex image features more effectively than traditional methods, and it works well with neural networks without needing many parameters. They tested different versions of HMD on standard datasets and found that their approach matches or beats existing methods in accuracy and stability while being more efficient to train. This suggests HMD could be a better way to handle complex image data compared to typical convolutional neural networks.
Hyperspectral image classificationTensor decompositionConvolutional neural networksHolistic Multivariance DecompositionBackpropagationTucker decompositionCanonical Polyadic decompositionTensor Train decompositionFeature extractionParameter efficiency
Authors
Süha Tuna, Ülker Başar
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.