arXiv AI August 18, 2026 By Alexandre L. M. Levada

Shape Operator PCA: Curvature-Aware Projections for Geometric Machine Learning

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.

Summary generated by The Flow from the publisher's feed. The full article lives at arXiv AI.

arXiv Machine Learning

Jun 5

Efficient Mean Curvature Computation on High-Dimensional Data Manifolds

arXiv:2606. 06329v1 Announce Type: new Abstract: Estimating local mean curvature at each point of a high-dimensional dataset is a key ingredient of geometry-aware machine learning algorithms, such as the Mean Curvature Boundary Points (MCBP) method.

By Alexandre L. M. Levada

arXiv Machine Learning

Jul 24

Regularized Optimization on Grassmann Manifold: Theory, Algorithm and Applications

arXiv:2607. 21039v1 Announce Type: new Abstract: Spectral methods are among the most widely used techniques for community detection, clustering, and graph learning.

By Zhuan Liang, Zheng Zhai

arXiv Machine Learning

Jun 30

Robust Tangent Space Estimation via Laplacian Eigenvector Gradient Orthogonalization

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 Machine Learning

Jul 20

Manifold Dimension Estimation via Local Graph Structure

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.

By Zelong Bi, Pierre Lafaye de Micheaux

rag benchmarks

arXiv Machine Learning

Jun 5

Monte Carlo Steklov Operators for Large-Scale Geometry Processing in the Wild

arXiv:2606. 05581v1 Announce Type: cross Abstract: Intrinsic methods fill the default toolbox for geometry processing on meshes.

By Arman Maesumi, Tanish Makadia, Aruna Anderson, Oras Phongpanangam, Justin Solomon, Daniel Ritchie

arXiv AI

Jul 7

CuBAS: Information Geometric Curvature-Based Adaptive Sampling for Supervised Classification

arXiv:2607. 03145v1 Announce Type: cross Abstract: The informativeness of a training set is as consequential as its size, yet most sampling strategies remain agnostic to the intrinsic geometry of the data distribution.

By Alexandre L. M. Levada

benchmarks

Related stories

Efficient Mean Curvature Computation on High-Dimensional Data Manifolds

Regularized Optimization on Grassmann Manifold: Theory, Algorithm and Applications

Robust Tangent Space Estimation via Laplacian Eigenvector Gradient Orthogonalization

Manifold Dimension Estimation via Local Graph Structure

Monte Carlo Steklov Operators for Large-Scale Geometry Processing in the Wild

CuBAS: Information Geometric Curvature-Based Adaptive Sampling for Supervised Classification