Persistence Atlas for Critical Point Variability in Ensembles.

Area of Science:

• Data Visualization
• Scientific Computing
• Topological Data Analysis

Background:

• Analyzing spatial variability of features in ensemble data is challenging.
• Existing methods struggle with noise and identifying dominant patterns.
• Critical points are key features in many scientific datasets.

Purpose of the Study:

• To present a new framework, Persistence Atlas, for visualizing and analyzing spatial variability of critical points in ensemble data.
• To enable visualization of dominant spatial patterns and their statistical occurrence.
• To provide a robust method for identifying salient features and their trends.

Main Methods:

• Utilizes a novel Persistence Map to measure geometrical density of critical points, leveraging topological persistence for noise robustness.
• Employs spectral embedding to create low-dimensional representations of ensemble members, facilitating statistical analysis like clustering.
• Introduces the concept of mandatory critical points to define confidence regions for feature appearance within clusters.

Main Results:

• Persistence Atlas effectively visualizes dominant spatial patterns as confidence maps.
• The framework generates 2D layouts of ensembles, highlighting global trends.
• Quantitative evaluations demonstrate the accuracy of confidence regions compared to baseline methods.
• Successful application to real-life datasets reveals clear feature layout trends.

Conclusions:

• Persistence Atlas offers a powerful and robust approach for analyzing spatial variability in ensemble data.
• The method enhances understanding of feature patterns and their statistical significance.
• The framework is parallelizable and includes an open-source implementation for reproducibility.