Apply functional constraints to CPD

Background: The paper develops the Functional Tucker Decomposition (FTD) based on the Tucker decomposition structure.

Question / Future Work: Future work could involve investigating the application of the continuity constraint and functional modeling approach used in the Functional Tucker Decomposition (FTD) to the Canonical Polyadic Decomposition (CPD), which emphasizes individual mode interpretability rather than the shared subspace structure of the Tucker model. This shift in perspective might offer benefits when explicit mode interpretation is paramount.

Why It Matters: Exploring functional constraints within the CPD would extend the RKHS modeling to decompositions where individual factor interpretation is the primary objective, contrasting with the FTD’s focus on subspace structure.

Evidence: The proposed approach joins recent advances in functional tensor mode modeling. However, the FTD builds on the Tucker decomposition (TD) instead of the Canonical Polyadic decomposition (CPD). This choice inherently shifts emphasis toward subspace structure rather than explicit interpretation of individual modes.