  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.
