The paper introduces a functional Tucker decomposition (FTD) that incorporates a mode-wise continuity constraint into tensor factorization, modeling continuous modes as functions in a reproducing kernel Hilbert space (RKHS) without requiring a predefined basis. It preserves the multilinear subspace structure of the Tucker model and provides a reconstruction error bound for continuous modes, quantifying approximation quality when a subspace estimated on one domain is reused on another. The authors demonstrate the practical value of this subspace transfer on cross-domain classification tasks in hyperspectral imaging and multivariate time-series analysis.
By Noah Steidle, Joppe De Jonghe, Mariya Ishteva
The paper introduces MultiHU‑TD, an interpretable framework for multifeature hyperspectral unmixing that employs tensor decomposition and incorporates the abundance sum‑to‑one constraint via an ADMM algorithm. It extends previous models by adding mathematical morphology and neighborhood patch analysis, and provides detailed mathematical, physical, and graphical interpretations linked to the extended linear mixing model. Experiments on real hyperspectral images demonstrate the model’s interpretability and effectiveness, with code released on GitHub.
By Mohamad Jouni, Mauro Dalla Mura, Lucas Drumetz, Pierre Comon
The paper introduces a new semi‑tensor product for third‑order tensors that relaxes the dimensional constraints of the standard t‑product while preserving the closed‑form nature of T‑SVD. It builds a multi‑term semi‑tensor product singular value decomposition (MSTP‑SVD) that improves low‑rank approximation accuracy, and further accelerates it with randomized projection and power iteration to create the MRSTP‑SVD algorithm. Experiments on image and video compression and completion show that this method balances reconstruction accuracy and computational efficiency.
By Xingchen Xiao (School of Mathematics and Statistics, Southwest University, Chongqing, China), Feng Zhang (School of Mathematics and Statistics, Southwest University, Chongqing, China), Wenjin Qin (School of Mathematics and Statistics, Southwest University, Chongqing, China), Jianjun Wang (School of Mathematics and Statistics, Southwest University, Chongqing, China)
arXiv:2609.24679v1 Announce Type: new
Abstract: We consider the recovery of low-multilinear-rank tensors from linear measurements and propose an adaptive block-weighted modewise Riemannian gradient d...
By Yushi Zhou, Feng Zhang
Tensor Completion using Subspace Information (TCSI) is an algorithm that leverages side information by estimating a subspace and reformulating tensor completion as a matrix regression problem. Theoretical analysis shows that accurate subspace information reduces sample complexity to nearly linear in the uncoupled ambient dimensions and relaxes signal-to-noise ratio requirements compared to existing guarantees. Numerical simulations and an application to reconstructing global Total Electron Content (TEC) maps demonstrate lower reconstruction errors than competing methods.
By Jingyang Li, Michael K. Ng
arXiv:2609.14307v1 Announce Type: new
Abstract: Low-rank tensor factorization provides a flexible framework for completing multidimensional data from incomplete and corrupted observations. However, u...
By Binghao Wang, Feng Zhang, Wendong Wang, Jianjun Wang