Paper ID: 2407.17835

IsUMap: Manifold Learning and Data Visualization leveraging Vietoris-Rips filtrations

Lukas Silvester Barth, Fatemeh, Fahimi, Parvaneh Joharinad, Jürgen Jost, Janis Keck

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.

Submitted: Jul 25, 2024