Visual Analysis of Large Multivariate Scattered Data using Clustering and Probabilistic Summaries

TL;DR

This paper introduces a probabilistic clustering-based visualization method for large multivariate scattered data, enabling interactive analysis by efficiently representing high-dimensional distributions with low-dimensional Gaussian mixtures.

Contribution

It presents a novel compact probabilistic representation for large multivariate data that facilitates interactive visualization and analysis, including uncertainty and outlier visualization.

Findings

Scales effectively to large real-world datasets.

Enables interactive visual analysis of high-dimensional data.

Provides explicit uncertainty and outlier visualization.

Abstract

Rapidly growing data sizes of scientific simulations pose significant challenges for interactive visualization and analysis techniques. In this work, we propose a compact probabilistic representation to interactively visualize large scattered datasets. In contrast to previous approaches that represent blocks of volumetric data using probability distributions, we model clusters of arbitrarily structured multivariate data. In detail, we discuss how to efficiently represent and store a high-dimensional distribution for each cluster. We observe that it suffices to consider low-dimensional marginal distributions for two or three data dimensions at a time to employ common visual analysis techniques. Based on this observation, we represent high-dimensional distributions by combinations of low-dimensional Gaussian mixture models. We discuss the application of common interactive visual analysis techniques to this representation. In particular, we investigate several frequency-based views, such as density plots in 1D and 2D, density-based parallel coordinates, and a time histogram. We visualize the uncertainty introduced by the representation, discuss a level-of-detail mechanism, and explicitly visualize outliers. Furthermore, we propose a spatial visualization by splatting anisotropic 3D Gaussians for which we derive a closed-form solution. Lastly, we describe the application of brushing and linking to this clustered representation. Our evaluation on several large, real-world datasets demonstrates the scaling of our approach.