Proximity Forests on Manifolds

NeurIPS 2025 Workshop NeurReps Submission153 Authors

Keywords: Machine Learning on Manifolds, Geometric AI, Learning on Graphs, Scalable Learning

TL;DR: We generalize the Proximity Forest model for manifold-valued data, showing that this distance-based classifier scales better than k-NN for large samples in high dimensions. This generalization also introduces GAP proximity graphs on manifolds.

Abstract: Recent work has focused on machine learning methods for manifold-valued data. Certain manifolds admit a notion of pairwise distance, allowing the $k$-nearest neighbors (KNN) classifier to be used with manifold-valued data. However, the computation of pairwise manifold distances is often computationally expensive, even with modern geometric machine learning software. In this work, we generalize the Proximity Forest (PF) model, originally designed as a time series distance-based classifier, to accommodate more general distance measures. We show that the PF model scales more favorably than KNN for large sample sizes in high dimensions. Given recent applications of the PF model, this also introduces supervised outlier detection and imputation for manifold-valued data. Additionally, we integrate the differential geometry software package for Maple to obtain a reduction in computational costs for certain pairwise manifold distances. We also introduce a method for estimating manifold distances on level sets.

Submission Number: 153