arXiv subjects

Süha Tuna

Publications and source records attributed to Süha Tuna.

3 recordsLinked to original sources

arXiv2026

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

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.

cs.CV↗

arXiv2026

Efficient Spatial-Spectral Feature Extraction in Hyperspectral Images via Holistic Multivariance Decomposition

Tensor decomposition serves as a foundational tool for feature extraction in hyperspectral image classification, a domain classically dominated by the Tucker and Canonical Polyadic decompositions. Although widely adopted, these schemes often struggle to fully encapsulate the deeply coupled geometric and intrinsic structures inherent to multidimensional hyperspectral data. Their structural reliance on rigid low-rank approximations successfully captures independent mode variations but systematically neglects complex, cross-domain spatial and spectral interdependencies. To overcome this limitation, we introduce the Holistic Multivariance Decomposition framework to achieve highly discriminative hyperspectral feature extraction. The Holistic Multivariance Decomposition provides a novel, structurally flexible tensor algorithm that explicitly models isolated spatial and spectral behaviors, alongside intricate, higher dimensional cooperative interactions. Comprehensive experimental evaluations across four benchmark hyperspectral datasets demonstrate that the proposed Holistic Multivariance Decomposition approximants consistently yield superior classification accuracy compared to conventional Tucker and Canonical Polyadic decomposition methods across diverse supervised learning algorithms. By effectively preserving essential joint multivariance features even under severe subspace compression, these results establish the Holistic Multivariance Decomposition as a robust, high fidelity computational framework for resolving complex multidimensional data structures in hyperspectral analysis.

cs.CE↗

arXiv2026

Holistic Multivariance Decomposition: Adapting Mode Interrelations in Low-Rank Tensor Approximations

Low-rank tensor approximation is a foundational tool for multidimensional data analysis in scientific computing, classically dominated by Tucker and Canonical Polyadic (CP) decompositions. While widely adopted, these standard approximation schemes represent data as sums of rank-1 tensors formed via mode-wise outer products. This inherent mathematical structure captures the independent variations of individual modes but systematically neglects the mutual interactions and coupled dimensional interdependencies natively embedded within the tensor. To overcome this structural limitation, we introduce the Holistic Multivariance Decomposition (HMD) framework. HMD provides a novel tensor decomposition algorithm that explicitly models both isolated mode effects and higher order mutual relationships through specialized projection operators. Numerical evaluations focusing on three distinct benchmarks from various fields demonstrate that the proposed HMD framework consistently yields significantly lower reconstruction errors compared to both Tucker and CP decomposition. These results establish HMD as a robust, high fidelity computational method for resolving complex, deeply coupled multidimensional data structures in science and engineering applications.

cs.CE↗