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

Brooke E Husic,John O Dabiri,Kristy L Schlueter-Kuck

doi:10.1371/journal.pone.0212442

Abstract

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.

Highlights

Modern science increasingly leverages machine learning on large datasets in the sciences, from electronic structure [1] to whole genome sequences [2] to distributed ocean sensor measurements [3]
We present a new method, simultaneous coherent structure coloring, which minimizes the assumptions required in an unsupervised clustering task. sCSC focuses solely on the efficient separation of the most dissimilar states in the system, resulting in a quantitative structure that automatically captures the clusters in the dataset and their interrelationships without a priori knowledge of the system
The present approach addresses the previously stated challenges with common clustering algorithms: it does not require a choice of cluster number or dendrogram cutting, it leverages the concept of dissimilarity in a computationally tractable way, and it maintains an interpretable hierarchical relationship among splittings

Summary

Introduction

Modern science increasingly leverages machine learning on large datasets in the sciences, from electronic structure [1] to whole genome sequences [2] to distributed ocean sensor measurements [3] Many of these datasets capture the dynamics of a system evolving in time, encoding trends with predictive power. [13], which utilizes the spectral gap in the graph Laplacian to determine the number of coherent structures. To avoid explicitly choosing the number of coherent structures, a spectral clustering method was introduced in Ref. It was subsequently shown in Ref. [14] that such a gap is only robust when the number of trajectories used exceeds 103

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Conclusion