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The clustering of data into physically meaningful subsets often requiresassumptions regarding the number, size, or shape of the subgroups. Here, wepresent a new method, simultaneous coherent structure coloring (sCSC), whichaccomplishes the task of unsupervised clustering without a priori guidanceregarding the underlying structure of the data. sCSC performs a sequence ofbinary splittings on the dataset such that the most dissimilar data points arerequired to be in separate clusters. To achieve this, we obtain a set oforthogonal coordinates along which dissimilarity in the dataset is maximizedfrom a generalized eigenvalue problem based on the pairwise dissimilaritybetween the data points to be clustered. This sequence of bifurcations producesa binary tree representation of the system, from which the number of clustersin the data and their interrelationships naturally emerge. To illustrate theeffectiveness of the method in the absence of a priori assumptions, we apply itto three exemplary problems in fluid dynamics. Then, we illustrate its capacityfor interpretability using a high-dimensional protein folding simulationdataset. While we restrict our examples to dynamical physical systems in thiswork, we anticipate straightforward translation to other fields where existinganalysis tools require ad hoc assumptions on the data structure, lack theinterpretability of the present method, or in which the underlying processesare less accessible, such as genomics and neuroscience.

Simultaneous Coherent Structure Coloring facilitates interpretable clustering of scientific data by amplifying dissimilarity