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Circular Coordinates for Density-Robust Analysis

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arxiv 2301.12742 v1 pith:FUGDAUNO submitted 2023-01-30 math.AT cs.CG

Taejin Paik , Jaemin Park This is my paper · ORCID
classification math.ATcs.CG
keywords analysiscircularcoordinatecoordinatesdatadatasetsdimensionalitymethods
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Dimensionality reduction is a crucial technique in data analysis, as it allows for the efficient visualization and understanding of high-dimensional datasets. The circular coordinate is one of the topological data analysis techniques associated with dimensionality reduction but can be sensitive to variations in density. To address this issue, we propose new circular coordinates to extract robust and density-independent features. Our new methods generate a new coordinate system that depends on a shape of an underlying manifold preserving topological structures. We demonstrate the effectiveness of our methods through extensive experiments on synthetic and real-world datasets.

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Cited by 3 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Selecting Interpretable Circular Coordinates from Data

    math.AT 2026-07 conditional novelty 7.0 of 10

    CIRCOL selects a minimum-energy dictionary basis spanning detected H1 classes via a density-corrected cochain inner product proven consistent for fixed smooth 1-forms under non-uniform sampling.

  2. Density-Robust Spherical Coordinates from Persistent Cohomology

    math.AT 2026-07 conditional novelty 6.0 of 10

    Density-robust S² coordinates are obtained by rejection-sampling uniform subsamples, computing classical spherical coordinates on each, and aligning them via a spherical Procrustes problem with a proven Euclidean relaxation.

  3. Subsampling, aligning, and averaging to find circular coordinates in recurrent time series

    stat.ML 2024-12 conditional novelty 6.0 of 10

    A subsample-and-average pipeline with rejection sampling and Procrustes alignment yields density-robust circular coordinates from persistent cohomology, validated on synthetic and C. elegans data.

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