arXiv Machine Learning
A Functional SVD Framework for Regularized Multivariate Functional PCA with Dual Penalization
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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.
arXiv Machine Learning
Jul 7
msPCA: An R Package for Sparse PCA with Multiple Components
arXiv:2607. 05229v1 Announce Type: cross Abstract: We present msPCA: an open-source R package for sparse principal component analysis with multiple components.
arXiv Machine Learning
Jun 3
A Robust Optimization Approach to Sparse Principal Component Analysis
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.
arXiv Machine Learning
3d ago
Learning with Covariance Matrices: Principal Component Analysis Meets Learning with Graphs
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)...
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.
arXiv Statistics ML
Aug 25
Sparse Separable Factor Analysis in the Complex Domain with an Application to Local Field Potential Data
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.