Statistical Parameter Selection for Clustering Persistence Diagrams

TL;DR

This paper introduces a statistical method for selecting the optimal number of clusters in persistence diagrams derived from ensemble simulation data, aiding in identifying distinct outcome scenarios.

Contribution

It proposes a new approach combining statistical score functions with a clustering algorithm for persistence diagrams, including a prototype implementation and experimental validation.

Findings

Effective determination of the number of clusters in real-world data

Improved identification of distinct outcome scenarios

Validation through experimental studies

Abstract

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.