Adaptive Subspace Modeling With Functional Tucker Decomposition
Fuente:
arXiv
Saved in:
| Main Authors: | , , |
|---|---|
| Format: | Preprint |
| Published: |
2026
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866914425272795136 |
|---|---|
| author | Steidle, Noah De Jonghe, Joppe Ishteva, Mariya |
| author_facet | Steidle, Noah De Jonghe, Joppe Ishteva, Mariya |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_25530 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Adaptive Subspace Modeling With Functional Tucker Decomposition Steidle, Noah De Jonghe, Joppe Ishteva, Mariya Machine Learning Numerical Analysis 15A69, 41A63, 62H30, 65D15 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. |
| title | Adaptive Subspace Modeling With Functional Tucker Decomposition |
| topic | Machine Learning Numerical Analysis 15A69, 41A63, 62H30, 65D15 |
| url | https://arxiv.org/abs/2603.25530 |