Hierarchical Correlation Clustering in Multiple 2D Scalar Fields. (10th July 2018)

• Record Type: Journal Article
• Authors: Liebmann, Tom; Weber, Gunther H.; Scheuermann, Gerik
• Is Part Of: Computer graphics forum. Volume 37:Number 3(2018)
• Page Start: 1
• Page End: 12
• Publication Date: 2018-07-10
• Subjects: CCS Concepts -- Mathematics of computing → Cluster analysis -- Point‐set topology -- Human‐centered computing → Dendrograms; Computer graphics -- Periodicals; 006.605
• DOI: 10.1111/cgf.13396
• Languages: English
• ISSNs: 0167-7055

Abstract

Abstract: Sets of multiple scalar fields can be used to model many types of variation in data, such as uncertainty in measurements and simulations or time‐dependent behavior of scalar quantities. Many structural properties of such fields can be explained by dependencies between different points in the scalar field. Although these dependencies can be of arbitrary complexity, correlation, i.e., the linear dependency, already provides significant structural information. Existing methods for correlation analysis are usually limited to positive correlation, handle only local dependencies, or use combinatorial approximations to this continuous problem. We present a new approach for computing and visualizing correlated regions in sets of 2‐dimensional scalar fields. This paper describes the following three main contributions: (i) An algorithm for hierarchical correlation clustering resulting in a dendrogram, (ii) a generalization of topological landscapes for dendrogram visualization, and (iii) a new method for incorporating negative correlation values in the clustering and visualization. All steps are designed to preserve the special properties of correlation coefficients. The results are visualized in two linked views, one showing the cluster hierarchy as 2D landscape and the other providing a spatial context in the scalar field's domain. Different coloring and texturing schemes coupled with interactive selection support an exploratory data analysis.