7 papers · 1 filter
Curvature-Aware Radius Shrinkage for Adaptive Nearest Neighbor Classification
Alexandre L. M. Levada
Nearest neighbor classification relies fundamentally on how locality is defined, yet conventional -NN imposes the same neighborhood cardinality throughout the feature space. Thi…
Shape Operator PCA: Curvature-Aware Projections for Geometric Machine Learning
Alexandre L. M. Levada
In this paper, we propose SHOPCA (Shape Operator-based Principal Component Analysis), a novel method for unsupervised metric learning and dimensionality reduction that incorporates…
CuBAS: Information Geometric Curvature-Based Adaptive Sampling for Supervised Classification
Alexandre L. M. Levada
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. We introduce…
Efficient Mean Curvature Computation on High-Dimensional Data Manifolds
Alexandre L. M. Levada
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 P…
A Mean Curvature Approach to Boundary Detection: Geometric Insights for Unsupervised Learning
Alexandre L. M. Levada
Accurate boundary detection in high-dimensional data remains a central challenge in unsupervised learning, particularly in the presence of non-linear structures and heterogeneous d…
Curvature-Aware PCA with Geodesic Tangent Space Aggregation for Semi-Supervised Learning
Alexandre L. M. Levada
Principal Component Analysis (PCA) is a fundamental tool for representation learning, but its global linear formulation fails to capture the structure of data supported on curved m…