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.

翻译：降维是数据分析中的关键技术，它能够高效地实现高维数据集的可视化与理解。环形坐标作为拓扑数据分析中与降维相关的方法之一，却可能对密度变化较为敏感。为解决这一问题，我们提出了一种新型环形坐标，用于提取鲁棒且密度无关的特征。该方法生成了一套新的坐标系，该坐标系依赖于底层流形的形状，并能够保持拓扑结构。通过在合成数据集和真实数据集上的大量实验，我们验证了所提方法的有效性。