Circular Clustering with Polar Coordinate Reconstruction

TL;DR

This paper introduces a novel framework for clustering circular data using cylindrical coordinate projections, improving accuracy and consistency over existing polar coordinate-based methods, applicable to diverse biological datasets.

Contribution

The paper presents a new analysis framework that utilizes cylindrical coordinate projections to enhance clustering accuracy for circular data, overcoming limitations of existing methods.

Findings

The method reliably finds correct clustering with sufficient data repetitions.

It outperforms standard clustering methods on synthetic and real datasets.

The approach is adaptable to most state-of-the-art clustering algorithms.

Abstract

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.