A rough-and-ready cluster-based approach for extracting finite-time coherent sets from sparse and incomplete trajectory data

TL;DR

This paper introduces a simple, fast clustering method to identify finite-time coherent regions in phase space from sparse, incomplete trajectory data, useful in real-world scenarios with limited observations.

Contribution

It proposes a novel cluster-based numerical approach that effectively detects coherent sets even with sparse and incomplete trajectory data, applicable in any dimension.

Findings

Works with few trajectories and data gaps

Easy to implement and fast

Applicable in any dimension

Abstract

We present a numerical method to identify regions of phase space that are approximately retained in a mobile compact neighbourhood over a finite time duration. Our approach is based on spatio-temporal clustering of trajectory data. The main advantages of the approach are the ability to produce useful results (i) when there are relatively few trajectories and (ii) when there are gaps in observation of the trajectories as can occur with real data. The method is easy to implement, works in any dimension, and is fast to run.