Before revision:  Application of the method to empirical measurements of vortex formation leads to the discovery of a well defined region in which vortex ring entrainment occurs, with potential implications ranging from flow control to cardiovascular diagnostics. Finally, the protein folding example demonstrates a data-rich application governed by equilibrium dynamics, where the technique in this manuscript automatically discovers the hierarchy of distinct processes that govern protein folding and clusters protein configurations accordingly. We anticipate straightforward translation to many other fields where existing analysis tools , such as k-means and traditional hierarchical clustering, require ad hoc assumptions on the data structure or lack the interpretability of the present method .
After revision:  Application of the method in the absence of a priori assumptions we apply it to two 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 many other fields where existing analysis tools , such as k-means and traditional hierarchical clustering, require ad hoc assumptions on the data structure or lack the interpretability of the present method .