Circular Coordinates for Density-Robust Analysis

TL;DR

This paper introduces new circular coordinate methods in topological data analysis that produce density-robust, shape-preserving features for dimensionality reduction, improving stability across datasets.

Contribution

The authors develop novel circular coordinate techniques that are resistant to density variations, enhancing the robustness of topological data analysis for dimensionality reduction.

Findings

Methods effectively extract density-independent features

Demonstrated robustness on synthetic datasets

Validated on real-world datasets

Abstract

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.