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

• URL: http://arxiv.org/abs/2407.17835v1
• Date: Thu, 25 Jul 2024 07:46:30 GMT
• Title: IsUMap: Manifold Learning and Data Visualization leveraging Vietoris-Rips filtrations
• Authors: Lukas Silvester Barth, Fatemeh, Fahimi, Parvaneh Joharinad, Jürgen Jost, Janis Keck,
• Abstract summary: We present a systematic and detailed construction of a metric representation for locally distorted metric spaces. Our approach addresses limitations in existing methods by accommodating non-uniform data distributions and intricate local geometries.
• Score: 0.08796261172196743
• License: http://creativecommons.org/licenses/by-nc-nd/4.0/
• Abstract: 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.

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