Dimensionality reduction for homological stability and global structure preservation

Abstract:We propose DiRe, a force-directed dimensionality reduction framework designed to preserve global structure and homological features while remaining practical on modern hardware. The method combines an initial embedding with a graph-based layout optimization and evaluates the resulting low-dimensional representation using local distortion, context preservation, and persistent homology measures. Across the benchmark suite considered here, DiRe provides a complementary tradeoff to UMAP and tSNE: it is designed less as a purely local visualization heuristic and more as a framework for embeddings whose large-scale geometry can be quantified through Betti curves and persistence diagrams.

Machine Learning (cs.LG); Artificial Intelligence (cs.AI); Mathematical Software (cs.MS)

arXiv:2503.03156 [cs.LG]

(or arXiv:2503.03156v4 [cs.LG] for this version)

https://doi.org/10.48550/arXiv.2503.03156 Focus to learn more arXiv-issued DOI via DataCite

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