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arXiv Statistics ML

Adaptive Subspace Modeling With Functional Tucker Decomposition

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.

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Hugging Face Trending Papers
Jul 27

Structural Loss Metrics for Tensor Approximation via Matrix Low-Rank Approximation

Matricized low-rank approximation via SVD is a standard surrogate for tensor decompositions, but entry-wise reconstruction error fails to capture multiway geometric degradation. Under an orthogonal Tucker model, we characterize this degradation using two metrics: cross-mode Direction Loss, measuring geometric subspace deviation from rank truncation and noise rotation, and Interaction Loss, quantifying multilinear interaction distortion in the core tensor.

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arXiv Statistics ML
Sep 22

Tensor Completion using Subspace Information

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
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arXiv Statistics ML
Sep 4

Online Learning of Functional Principal Component Analysis for Multidimensional Functional Data

The paper introduces an online framework for functional principal component analysis (FPCA) tailored to multidimensional functional data streams. It models functional principal components with tensor product splines, enforcing smoothness and orthonormality via a penalized approach on a Stiefel manifold. The authors present efficient Riemannian stochastic gradient descent and AdaGrad algorithms, along with a dynamic smoothing parameter tuning strategy based on rolling block validation, and provide asymptotic normality results and confidence intervals for the estimators.

By Muye Nanshan, Nan Zhang, Jiguo Cao
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arXiv Machine Learning
Jun 4

Low-rank Distributional Matrix Completion

arXiv:2606. 04176v1 Announce Type: new Abstract: We study a distributional generalization of the matrix completion problem in which each entry of the target matrix is a probability distribution rather than a scalar.

By Jiayi Wang, Raymond K. W. Wong
rag
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arXiv Machine Learning
Jun 5

Anchor PCA

arXiv:2606. 06233v1 Announce Type: cross Abstract: Principal component analysis (PCA) is one of the most widely used unsupervised dimension reduction techniques.

By Benedikt Seiter, Anya Fries, Julius von K\"ugelgen, Jonas Peters
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arXiv Computer Vision
Sep 21

MultiHU-TD: Multifeature Hyperspectral Unmixing Based on Tensor Decomposition

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
multimodalsafety
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