IsUMap: Manifold Learning and Data Visualization leveraging Vietoris-Rips filtrations
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arXiv
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| Autores principales: | , , , , , |
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| Formato: | Preprint |
| Publicado: |
2024
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| Acceso en línea: | |
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| _version_ | 1866912883182403584 |
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| author | Barth, Lukas Silvester Fatemeh Fahimi Joharinad, Parvaneh Jost, Jürgen Keck, Janis |
| author_facet | Barth, Lukas Silvester Fatemeh Fahimi Joharinad, Parvaneh Jost, Jürgen Keck, Janis |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_17835 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | IsUMap: Manifold Learning and Data Visualization leveraging Vietoris-Rips filtrations Barth, Lukas Silvester Fatemeh Fahimi Joharinad, Parvaneh Jost, Jürgen Keck, Janis Machine Learning Category Theory Differential Geometry Metric Geometry 51K05 (primary) 57-08, 53Z50, 55U10 (secondary) G.2.2; I.6.5 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. |
| title | IsUMap: Manifold Learning and Data Visualization leveraging Vietoris-Rips filtrations |
| topic | Machine Learning Category Theory Differential Geometry Metric Geometry 51K05 (primary) 57-08, 53Z50, 55U10 (secondary) G.2.2; I.6.5 |
| url | https://arxiv.org/abs/2407.17835 |