IsUMap: Manifold Learning and Data Visualization leveraging Vietoris-Rips filtrations
This addresses limitations in existing manifold learning methods for handling non-uniform data distributions and intricate local geometries, though it appears incremental as it builds on UMAP and Isomap.
The authors tackled the problem of manifold learning and data visualization by introducing IsUMap, which integrates UMAP and Isomap with Vietoris-Rips filtrations to better capture complex data structures. They demonstrated significant improvements in representation quality through experiments on geometric objects and real-world datasets.
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.