  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.
