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
arXiv:2607. 05229v1 Announce Type: cross Abstract: We present msPCA: an open-source R package for sparse principal component analysis with multiple components.
By Ryan Cory-Wright, Jean Pauphilet
arXiv:2606. 03553v1 Announce Type: cross Abstract: While principal component analysis (PCA) is a fundamental tool for dimensionality reduction, its dense representations make it ill-suited for high-dimensional data.
By David V\"avinggren, Francis Bach, Andr\'e M. H. Teixeira, Dave Zachariah, Ant\^onio H. Ribeiro
arXiv:2609.10490v2 Announce Type: replace
Abstract: This feature article provides an overview of the theoretical foundations for coVariance neural networks (VNNs), i.e., graph neural networks (GNNs)...
By Saurabh Sihag, Andrea Cavallo, Elvin Isufi, Gonzalo Mateos, Alejandro Ribeiro
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
The paper introduces Sparse Separable Factor Analysis (SSFA), a latent factor model designed for complex-valued arrays that preserves amplitude and phase information. SSFA models each mode’s covariance with a low‑rank Hermitian factor structure plus a diagonal residual, applying element‑wise lasso penalties to achieve interpretable, phase‑preserving loadings via complex soft‑thresholding. The method is validated through simulations showing improved covariance estimation over vectorization approaches and applied to local field potential data from mice to compare separability across brain region, frequency, and time, as well as to impute missing recordings due to electrode misplacement.
By Ian Hultman, Kirtikanth Kalapatapu, Yassine Filali, Rainbo Hultman, Sanvesh Srivastava
arXiv:2606. 05488v1 Announce Type: cross Abstract: Identifying subtypes of complex conditions, such as Inflammatory Bowel Disease (IBD), often requires capturing latent patterns in longitudinal omics data.
By Yue Zhao, Thierry Chekouo, Sandra Safo
arXiv:2505. 19925v2 Announce Type: replace-cross Abstract: The sample covariance matrix is a cornerstone of multivariate statistics, but it is highly sensitive to outliers.
By Fabio Centofanti, Mia Hubert, Peter J. Rousseeuw
arXiv:2601. 19179v2 Announce Type: replace Abstract: Autoencoders have long been considered a nonlinear extension of Principal Component Analysis (PCA).
By Qipeng Zhan, Zhuoping Zhou, Zexuan Wang, Li Shen
arXiv:2608.30418v1 Announce Type: cross
Abstract: Resting-state functional magnetic resonance imaging (rs-fMRI) functional connectivity (FC) matrices are widely used for individual-level prediction,...
By Ce Ju, Antoine Collas, Florent Bouchard, Bertrand Thirion
arXiv:2608. 15121v1 Announce Type: cross Abstract: Sufficient dimension reduction (SDR) seeks the minimal subspace of the predictors that captures the full conditional distribution of the response, which is known as the central subspace (CS).
By Ye Tian
arXiv:2608. 15313v1 Announce Type: cross Abstract: In this paper, we propose SHOPCA (Shape Operator-based Principal Component Analysis), a novel method for unsupervised metric learning and dimensionality reduction that incorporates differential geometric information into the covariance structure of classical PCA.
By Alexandre L. M. Levada