用于高效高光谱图像分类的无卷积整体多方差分解层：张量网络

中文摘要 AI 辅助

高光谱图像分类的特征提取通常采用刚性张量分解方法，这类方法无法捕捉复杂的空间-光谱相互依赖关系，或是采用参数规模庞大的卷积神经网络，计算成本高昂。为克服这些局限，本研究提出了整体多方差分解（Holistic Multivariance Decomposition, HMD）框架，作为一种新型端到端可微分神经网络层。该框架通过可学习的矩阵值支撑，将独立的单模变化与协作的高维交互显式分离，所提出的HMD-0、HMD-1和HMD-2近似模型可通过反向传播与下游分类器联合优化。在三个基准高光谱（HS）数据集上的全面评估显示，高阶HMD层相比Tucker、典型多面体分解（Canonical Polyadic）、张量列车（Tensor Train）等经典可学习张量基线，分类精度更优；此外，HMD-1和HMD-2的泛化能力与训练稳定性可与标准2D和3D卷积神经网络（CNN）媲美，同时所需的特征提取器参数显著更少。这些结果表明，HMD框架为多维高光谱图像分类中的传统卷积提供了结构鲁棒的替代方案，在优化过程中兼具高参数效率与稳定性。

英文摘要

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.

发表机构

• Istanbul Esenyurt University（伊斯坦布尔埃森耶尔特大学）
• Istanbul Technical University（伊斯坦布尔技术大学）

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