arXiv:2510. 15141v5 Announce Type: replace-cross Abstract: Most existing manifold dimension estimators rely on the assumption that the underlying manifold is locally flat within the neighborhoods under consideration.
Summary generated by The Flow from the publisher's feed. The full article lives at arXiv Machine Learning.
arXiv:2510. 02308v2 Announce Type: replace Abstract: Estimating the tangent spaces of a data manifold is a fundamental problem in geometric data analysis.
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.
arXiv:2606. 06233v1 Announce Type: cross Abstract: Principal component analysis (PCA) is one of the most widely used unsupervised dimension reduction techniques.
arXiv:2601. 19179v2 Announce Type: replace Abstract: Autoencoders have long been considered a nonlinear extension of Principal Component Analysis (PCA).
arXiv:2607. 07034v1 Announce Type: cross Abstract: We introduce Intrinsic Green's Learning (IGL), a framework that models a target function on a manifold as the solution to a linear PDE whose source term is learned from data.
arXiv:2607. 25295v2 Announce Type: replace Abstract: Tensorial multi-view clustering (TMC) has achieved strong performance due to its ability to capture high-order correlations across multiple views.