# Adaptive Subspace Modeling With Functional Tucker Decomposition

arXiv: https://arxiv.org/abs/2603.25530 · HTML: https://mlsanity.com/paper/2603.25530/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 5 of its 25 references that are in the map.
- First posted on arXiv 26 Mar 2026.

## Builds on (most cited first, 5 of 5)

- [Measuring the Ripeness of Fruit with Hyperspectral Imaging and Deep Learning](https://mlsanity.com/paper/2104.09808/) (2021)
- [Guaranteed Functional Tensor Singular Value Decomposition](https://mlsanity.com/paper/2108.04201/) (2021)
- [Tensor Decomposition Meets RKHS: Efficient Algorithms for Smooth and Misaligned Data](https://mlsanity.com/paper/2408.05677/) (2024)
- [Tensor Decomposition with Unaligned Observations](https://mlsanity.com/paper/2410.14046/) (2024)
- [Smooth tensor decomposition with application to ambulatory blood pressure monitoring data](https://mlsanity.com/paper/2507.11723/) (2025)

## Abstract (arXiv)

Tensors provide a structured representation for multidimensional data, yet discretization discards the underlying continuous structure when the data originate from continuous processes. We address this limitation by introducing a functional Tucker decomposition (FTD) that embeds a mode-wise continuity constraint directly into the factorization. The FTD models the continuous mode as a function in a reproducing kernel Hilbert space (RKHS), avoiding a prespecified basis while preserving the multilinear subspace structure of the Tucker model. We derive a reconstruction error bound for the continuous mode that quantifies the approximation quality when a subspace estimated on one domain is reused on another. This bound provides theoretical justification for subspace transfer, whose practical value we demonstrate on cross-domain classification tasks in hyperspectral imaging and multivariate time-series analysis.