arXiv:2607. 01993v1 Announce Type: cross Abstract: The silhouette is one of the most widely used measures to assess the quality of a $k$-clustering of a dataset of $n$ elements.
By Ilie Sarpe, Federico Altieri, Andrea Pietracaprina, Geppino Pucci, Fabio Vandin
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
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:2607. 09490v1 Announce Type: cross Abstract: Terminal embeddings have emerged as a powerful tool for dimension reduction.
By Alexander Munteanu, Matteo Russo, David Saulpic, Chris Schwiegelshohn
arXiv:2502. 00168v5 Announce Type: replace-cross Abstract: Supervised dimensionality reduction maps labeled data into a low-dimensional feature space while preserving class separation.
By Daniel Herrera-Esposito, Johannes Burge
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