Adaptive Subspace Modeling With Functional Tucker Decomposition

TL;DR

This paper introduces a functional Tucker decomposition that embeds continuity constraints into tensor models using RKHS, enabling adaptive, expressive, and domain-variant analysis of multidimensional data.

Contribution

It presents a novel functional Tucker decomposition method that incorporates mode-wise continuity via RKHS, enhancing tensor modeling for continuous data without predefined bases.

Findings

Effective in hyperspectral image classification

Improves multivariate time series analysis

Demonstrates adaptability to domain variations

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.