arXiv:2510. 02308v2 Announce Type: replace Abstract: Estimating the tangent spaces of a data manifold is a fundamental problem in geometric data analysis.
By Dhruv Kohli, Sawyer J. Robertson, Gal Mishne, Alexander Cloninger
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
The paper introduces a geometry‑aware graph construction method that adaptively selects Gaussian kernel bandwidths per node to align the kernel’s spectral complexity with the intrinsic dimensionality of the underlying manifold. By matching the kernel’s effective rank to a local intrinsic dimension estimate derived from a minimum spanning tree, the method operates within a manifold‑consistent log‑log scaling regime. Experiments on CIFAR‑100 demonstrate that this adaptive bandwidth approach consistently improves leave‑one‑out classification and label propagation accuracy compared to fixed‑bandwidth and other adaptive techniques.
By Ecem Bozkurt, Antonio Ortega
arXiv:2601.20173v3 Announce Type: replace
Abstract: We present a new nonlinear dimensionality reduction method, MAPLE, that enhances UMAP by improving manifold modeling. MAPLE employs a self-supervis...
By Zeyang Huang, Takanori Fujiwara, Angelos Chatzimparmpas, Wandrille Duchemin, Andreas Kerren
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: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