# Circular Coordinates for Density-Robust Analysis

arXiv: https://arxiv.org/abs/2301.12742 · HTML: https://mlsanity.com/paper/2301.12742/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 30 Jan 2023.

## Built on by (most cited first, 2 of 2)

- [Point-Level Topological Representation Learning on Point Clouds](https://mlsanity.com/paper/2406.02300/) (2024)
- [Selecting Interpretable Circular Coordinates from Data](https://mlsanity.com/paper/2607.08230/) (2026)

## Abstract (arXiv)

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.