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：减少尺寸是数据分析中的关键技术,因为它可以使高维数据集具有高效率的可视化和理解性,循环协调是与减少维度有关的地形数据分析技术之一,但能敏感地注意密度的变化。为了解决这个问题,我们提议新的循环协调,以提取稳健和密度独立的特征。我们的新方法产生了一个新的协调系统,它取决于一个保存高维的多元结构的形状。我们通过对合成和真实世界数据集的广泛实验,展示了我们方法的有效性。