IsUMap: Manifold Learning and Data Visualization leveraging Vietoris-Rips filtrations
<|reference_start|>IsUMap: Manifold Learning and Data Visualization leveraging Vietoris-Rips filtrations: 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.<|reference_end|>
@article{barth2024isumap:,
    title={IsUMap: Manifold Learning and Data Visualization leveraging
  Vietoris-Rips filtrations},
    author={Lukas Silvester Barth, Fatemeh (Hannaneh) Fahimi, Parvaneh Joharinad,
  J"urgen Jost, Janis Keck},
    journal={arXiv preprint arXiv:2407.17835},
    year={2024},
    archivePrefix={arXiv},
    eprint={2407.17835},
    primaryClass={cs.LG math.CT math.DG math.MG}
}