arXiv:2603. 11308v3 Announce Type: replace Abstract: Principal Component Analysis (PCA) is a cornerstone of dimensionality reduction, yet its classical formulation relies critically on second-order moments and is therefore fragile in the presence of heavy-tailed data and impulsive noise.
By Mario Sayde, Christopher Khater, Jihad Fahs, Ibrahim Abou-Faycal
SuperPCA is a new algorithm for high‑dimensional principal component analysis that exploits an approximate eigenspace of the sample covariance matrix. The authors show that the subspace spanned by several leading eigenvectors contains useful signal information long before individual eigenvectors converge, and they derive posteriori bounds on the angle between this subspace and the true signal subspace. By using only a small number of subsampled coordinates, SuperPCA can achieve up to a ten‑fold improvement in accuracy over classical PCA while reducing data acquisition costs, especially when the signals are approximately sparse.
By Irina-Beatrice Haas, Maike Meier, Yuji Nakatsukasa, Taejun Park
arXiv:2607. 16638v1 Announce Type: cross Abstract: Principal component regression (PCR) regularizes high-dimensional prediction by choosing a spectral cutoff, but rank selection cannot correct systematic inflation of the retained empirical eigenvalues.
By Peng Zhao
arXiv:2609.05796v1 Announce Type: cross
Abstract: Principal component analysis (PCA) can rotate away from its population target when a covariance matrix is estimated from limited data. We introduce d...
By Qiang Sun
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
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