Circular coordinates for density-robust analysis
Taejin Paik, Jaemin Park · Foundations of Data Science · 2025
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. These new coordinates depend only on the shape of the underlying manifold, not on the density. We demonstrate the effectiveness of our methods through extensive experiments on synthetic and real-world datasets.