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.

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