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
The paper investigates Partial Least Squares (PLS) in high-dimensional settings, focusing on a model where two data matrices share a low-rank latent structure plus individual-specific components. By analyzing the singular vectors of the cross‑covariance matrix with random matrix theory, the authors derive asymptotic characterizations of how well the estimated latent directions align with the true ones. They show that the PLS variant based on Singular Value Decomposition (PLS‑SVD) outperforms separate principal component analysis in detecting the common latent subspace, while also identifying regimes where PLS‑SVD behaves counter‑intuitively or reaches fundamental limits.
By Victor L\'eger, Florent Chatelain
Kernel Singular Value Decomposition (KSVD) learns singular vectors for an asymmetric kernel matrix derived from two data sources. The paper extends KSVD to multiple data sources, introducing eKSVD, which jointly learns nonlinear feature mappings and captures maximal information across all sources while incorporating pair‑wise couplings. The authors derive a dual optimization framework, a covariance‑based approach, and demonstrate the effectiveness of eKSVD and neural‑network‑based feature mappings through numerical experiments.
By Xinjie Zeng, Qinghua Tao, Johan Suykens
The paper introduces robust multi-task procedures for principal component analysis that leverage similarity across tasks to enhance eigenspace estimation while remaining resilient to outlier tasks. It establishes non-asymptotic convergence rates and demonstrates that the methods achieve minimax optimal performance across various regimes. One procedure, based on matrix-depth, attains optimal error dependence on the proportion of outlier tasks, addressing a key challenge in robust multi-task learning.
By Dali Liu, Haolei Weng
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
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
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:2610.07284v1 Announce Type: cross
Abstract: Spectral methods are central to high-dimensional statistics and machine learning, underlying procedures for covariance estimation, matrix denoising,...
By Lorenzo Mauri
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