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Published March 13, 2019 | Submitted + Published + Supplemental Material
Journal Article Open

Simultaneous coherent structure coloring facilitates interpretable clustering of scientific data by amplifying dissimilarity


The clustering of data into physically meaningful subsets often requires assumptions regarding the number, size, or shape of the subgroups. Here, we present a new method, simultaneous coherent structure coloring (sCSC), which accomplishes the task of unsupervised clustering without a priori guidance regarding the underlying structure of the data. sCSC performs a sequence of binary splittings on the dataset such that the most dissimilar data points are required to be in separate clusters. To achieve this, we obtain a set of orthogonal coordinates along which dissimilarity in the dataset is maximized from a generalized eigenvalue problem based on the pairwise dissimilarity between the data points to be clustered. This sequence of bifurcations produces a binary tree representation of the system, from which the number of clusters in the data and their interrelationships naturally emerge. To illustrate the effectiveness of the method in the absence of a priori assumptions, we apply it to three exemplary problems in fluid dynamics. Then, we illustrate its capacity for interpretability using a high-dimensional protein folding simulation dataset. While we restrict our examples to dynamical physical systems in this work, we anticipate straightforward translation to other fields where existing analysis tools require ad hoc assumptions on the data structure, lack the interpretability of the present method, or in which the underlying processes are less accessible, such as genomics and neuroscience.

Additional Information

© 2019 Husic et al. This is an open access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. Received: September 3, 2018; Accepted: February 1, 2019; Published: March 13, 2019. The authors are grateful to Muneeb Sultan, Jared Dunnmon, Nicole Xu, and the referees for insightful manuscript feedback and to D. E. Shaw Research for providing the Protein G dataset. BEH and JOD received no specific funding for this work. KLS-K was supported by the U.S. National Science Foundation and by the Department of Defense (DoD) through the National Defense Science & Engineering Graduate Fellowship (NDSEG) Program. The funders had no role in study design, data collection and analysis, decision to publish, or preparation of the manuscript. Data Availability: The three fluid mechanics datasets and all adjacency matrices used to create the models in this work are available on github at https://github.com/brookehus/sCSC. This repository also contains example MATLAB and Python codes, including Jupyter notebook tutorials. The all-atom molecular dynamics simulations of Protein G were previously published in Ref. [51], and the trajectories are available at no cost for non-commercial use through contacting trajectories@deshawresearch.com. The authors have declared that no competing interests exist.

Attached Files

Published - journal.pone.0212442.pdf

Submitted - 1807.04427.pdf

Supplemental Material - pone.0212442.s001.tiff

Supplemental Material - pone.0212442.s002.pdf


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August 19, 2023
October 20, 2023