IsUMap: Manifold Learning and Data Visualization leveraging Vietoris-Rips filtrations
Machine Learning
2026-02-09 v1 Category Theory
Differential Geometry
Metric Geometry
Abstract
This work introduces IsUMap, a novel manifold learning technique that enhances data representation by integrating aspects of UMAP and Isomap with Vietoris-Rips filtrations. We present a systematic and detailed construction of a metric representation for locally distorted metric spaces that captures complex data structures more accurately than the previous schemes. Our approach addresses limitations in existing methods by accommodating non-uniform data distributions and intricate local geometries. We validate its performance through extensive experiments on examples of various geometric objects and benchmark real-world datasets, demonstrating significant improvements in representation quality.
Keywords
Cite
@article{arxiv.2407.17835,
title = {IsUMap: Manifold Learning and Data Visualization leveraging Vietoris-Rips filtrations},
author = {Lukas Silvester Barth and Fatemeh and Fahimi and Parvaneh Joharinad and Jürgen Jost and Janis Keck},
journal= {arXiv preprint arXiv:2407.17835},
year = {2026}
}