Adaptive Subspace Modeling With Functional Tucker Decomposition
This work addresses tensor modeling for continuous data in domains like imaging and time series, representing an incremental advancement by combining structural decomposition with functional adaptability.
The paper tackles the limitation of tensor discretization obscuring information from continuous processes by introducing functional Tucker decomposition (FTD) that embeds continuity constraints, and demonstrates its effectiveness in domain-variant tensor classification tasks like hyperspectral imaging and multivariate time series analysis.
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.