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.

翻译：近年来，表征生物系统中循环数据的兴趣日益增长。此类数据范围广泛且形式多样，从神经记录中的信号相位到环形基因组中的核苷酸序列均属此类。传统聚类算法因难以区分周期分量的差异而常存在不足。现行基于极坐标系的聚类方案存在局限性，例如仅聚焦于角度特征或缺乏通用性。为克服这些限制，我们提出一种新分析框架，通过投影至柱坐标系来更优地表征极坐标系中的对象。利用循环数据的数学性质，我们证明在数据具有足够周期重复次数的条件下，该方法总能从重构数据集中获得正确的聚类结果。该框架具有通用性和可适配性，可整合至大多数现有聚类算法中。在合成数据与真实数据上的实验表明，相较于标准方法，本方法能生成更合理且一致的聚类结果。综上所述，我们提出的分析框架克服了现有极坐标聚类方法的局限，为循环数据聚类提供了更准确高效的途径。