This repository contains the source code and experiments for the paper titled "Circular Coordinates for Density-Robust Analysis". The paper proposes new circular coordinates for dimensionality reduction that are robust to variations in density. The methods generate a new coordinate system that depends on the shape of an underlying manifold, preserving topological structures.
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.
This repository includes examples in the form of Jupyter Notebook (.ipynb) files in the "experiments" folder. These examples demonstrate how to apply the proposed circular coordinates to various datasets.
Paik, T., & Park, J. (2023). Circular Coordinates for Density-Robust Analysis. arXiv preprint arXiv:2301.12742. https://arxiv.org/abs/2301.12742
@article{paik2023circular,
title={Circular Coordinates for Density-Robust Analysis},
author={Paik, Taejin and Park, Jaemin},
journal={arXiv preprint arXiv:2301.12742},
year={2023}
}This repository is licensed under the MIT License.