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
arXiv:2608.19021v2 Announce Type: replace
Abstract: Global Covariance Pooling (GCP) improves deep networks by capturing second-order feature statistics, and is especially effective for fine-grained r...
By Md Rifat Ur Rahman, Md Raihan Khan, Md Sakib Hossain Shovon, Pietro Li\`o, Mohammad Ali Moni
Curvature-Aware Radius Shrinkage for Adaptive Nearest Neighbor Classification (CARSANN) is a geometry-driven framework that adapts the spatial support of each neighborhood based on local geometric complexity. It estimates intrinsic dimensionality with TwoNN, builds an intrinsic representation via PCA, and uses a shape-operator-based estimate of local mean curvature to shrink the radius in highly curved regions while keeping a broader support in flatter areas. Experiments on over 70 OpenML datasets show that CARSANN consistently outperforms standard k‑NN and rivals other adaptive nearest‑neighbor methods, achieving a mean balanced accuracy increase from 0.6506 to 0.7528 and statistically significant improvements on most datasets.
By Alexandre L. M. Levada
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:2606. 23867v1 Announce Type: new Abstract: The exact computation of the Normalized Maximum Likelihood (NML) codelength for regular non-smooth estimators (e.
By Trenton Lau, Gary P. T. Choi
The paper proposes using eigenvalue decomposition (or PCA) to denoise noisy cost observations for shortest‑path problems, instead of the traditional predict‑then‑optimize approach. By projecting new cost vectors onto the top‑k eigenvectors of the training covariance matrix before running Dijkstra’s algorithm, the method can recover the true underlying costs. Experiments on a 5×5 grid benchmark show that choosing k equal to the true latent feature dimension (k=5) yields the best performance, outperforming the SPO+ method especially under high model misspecification.
By Henry Aldridge-Krawciw, Irene Aldridge