Statistical Parameter Selection for Clustering Persistence Diagrams
This work addresses the need for automated scenario analysis in urgent decision-making applications, though it appears incremental as it builds on existing clustering algorithms and statistical methods.
The paper tackles the problem of determining the number of significantly different outcome scenarios from ensemble simulations by clustering persistence diagrams, using statistical score functions to select the optimal number of clusters and providing a proof-of-concept implementation tested on real-world data.
In urgent decision making applications, ensemble simulations are an important way to determine different outcome scenarios based on currently available data. In this paper, we will analyze the output of ensemble simulations by considering so-called persistence diagrams, which are reduced representations of the original data, motivated by the extraction of topological features. Based on a recently published progressive algorithm for the clustering of persistence diagrams, we determine the optimal number of clusters, and therefore the number of significantly different outcome scenarios, by the minimization of established statistical score functions. Furthermore, we present a proof-of-concept prototype implementation of the statistical selection of the number of clusters and provide the results of an experimental study, where this implementation has been applied to real-world ensemble data sets.