Adaptive Subspace Modeling With Functional Tucker Decomposition

• URL: http://arxiv.org/abs/2603.25530v1
• Date: Thu, 26 Mar 2026 15:06:14 GMT
• Title: Adaptive Subspace Modeling With Functional Tucker Decomposition
• Abstract summary: We introduce a functional Tucker decomposition (FTD) that embeds mode-wise continuity constraints directly into the decomposition.<n>The FTD employs reproducing kernel Hilbert spaces (RKHS) to model continuous modes without requiring an a-priori basis.<n>The value of this approach is demonstrated in domain-variant tensor classification.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Tensors provide a structured representation for multidimensional data, yet discretization can obscure important information when such data originates from continuous processes. We address this limitation by introducing a functional Tucker decomposition (FTD) that embeds mode-wise continuity constraints directly into the decomposition. The FTD employs reproducing kernel Hilbert spaces (RKHS) to model continuous modes without requiring an a-priori basis, while preserving the multi-linear subspace structure of the Tucker model. Through RKHS-driven representation, the model yields adaptive and expressive factor descriptions that enable targeted modeling of subspaces. The value of this approach is demonstrated in domain-variant tensor classification. In particular, we illustrate its effectiveness with classification tasks in hyperspectral imaging and multivariate time series analysis, highlighting the benefits of combining structural decomposition with functional adaptability.

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