8 papers
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 Retrospective Benchmark of Spatiotemporal Covariates for Daily Active-Fire Detection in Cerrado Conservation Units
Juliano Eleno Silva Pádua, Alexandre Luis Magalhães Levada, Fredy João Valente
Wildfires threaten biodiversity, carbon stocks, and management capacity in the Brazilian Cerrado, where Conservation Units and their official buffer zones must allocate prevention…
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…
Adaptive -nearest neighbor classifier based on the local estimation of the shape operator
Alexandre Luís Magalhães Levada, Frank Nielsen, Michel Ferreira Cardia Haddad
The -nearest neighbor (-NN) algorithm is one of the most popular methods for nonparametric classification. However, a relevant limitation concerns the definition of the numbe…