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, 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.
Example figure below shows how to reconstruct polar coordinates on the rectangular plane using cylindrical coordinates:
No further installation needed. Function files are directly runnable in Matlab. Work on any Matlab version with build-in functions for kmeans, dbscan, linkage.
Please put all .m files in the same folder to make sure the working path is matched. We separate the .m files into several folders here for organization purpose.
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functions for proposed algorithms: functions/
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how to implement functions and reproduce publication figures: figures/
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example data for phase entrainment: example_data/
Please see details of each function in .m file.
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Feature 1: Codes to reproduce all original figures are provided.
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Feature 2: Corresponding codes of all evaluated algorithms are provided.
(see kmeans_search, dbscan_search and hierarchical_search for details).
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Feature 3: Two example datasets are provided (phase entrainment and DNA sequence).
This project is licensed under the MIT License. Refer to the LICENSE file for more information.
Thanks to Chongkun Zhao for working with me to put the code materials together.
This work is currently under review at IEEE TCBB, preprint at arxiv is available here. Please cite our work if used.
This work is inspired by our branch's efforts within the closed-loop neuromodulation project (which focused on phase entrainment). For a more comprehensive background, I encourage you to check out our series of publications.
simultaneous fMRI-EEG-TMS: https://www.sciencedirect.com/science/article/pii/S1935861X23017746
phase-locked closed-loop EEG-rTMS: https://www.sciencedirect.com/science/article/pii/S1935861X22000365
Clinic outcomes: https://papers.ssrn.com/sol3/papers.cfm?abstract_id=4334289
For any inquiries or questions, you can reach me at [xiaoxiao.sun@columbia.edu]. Connect with me on LinkedIn for more updates and projects.