标题： 基于极坐标重建的圆形聚类 显示英文标题

标题： Circular Clustering with Polar Coordinate Reconstruction

摘要： 对生物系统中发现的圆形数据进行表征的兴趣正在增长。 此类数据范围广泛且多样，从神经记录中的信号相位到环形基因组中的核苷酸序列。 由于传统聚类算法在区分周期分量差异方面的能力有限，因此通常不够充分。 目前在极坐标系中工作的聚类方案存在局限性，例如仅关注角度或缺乏普遍性。 为了克服这些限制，我们提出了一种新的分析框架，该框架利用投影到圆柱坐标系以更好地表示极坐标系中的对象。 利用圆形数据的数学特性，我们表明，在数据有足够的周期重复的情况下，我们的方法总能在重构的数据集中找到正确的聚类结果。 我们的方法具有普遍适用性和适应性，可以融入大多数最先进的聚类算法中。 我们在合成数据和真实数据上进行了演示，结果表明，与标准方法相比，我们的方法生成了更合适且一致的聚类结果。 总之，我们提出的分析框架克服了现有基于极坐标聚类方法的局限性，并提供了一种更准确、高效的聚类圆形数据的方法。 显示英文摘要

摘要： There is a growing interest in characterizing circular data found in biological systems. Such data are wide ranging and varied, from signal phase in neural recordings to nucleotide sequences in round genomes. Traditional clustering algorithms are often inadequate due to their limited ability to distinguish differences in the periodic component. Current clustering schemes that work in a polar coordinate system have limitations, such as being only angle-focused or lacking generality. To overcome these limitations, we propose a new analysis framework that utilizes projections onto a cylindrical coordinate system to better represent objects in a polar coordinate system. Using the mathematical properties of circular data, we show our approach always finds the correct clustering result within the reconstructed dataset, given sufficient periodic repetitions of the data. Our approach is generally applicable and adaptable and can be incorporated into most state-of-the-art clustering algorithms. We demonstrate on synthetic and real data that our method generates more appropriate and consistent clustering results compared to standard methods. In summary, our proposed analysis framework overcomes the limitations of existing polar coordinate-based clustering methods and provides a more accurate and efficient way to cluster circular data.