GRay: Ray Casting for Visualization and Interactive Data Exploration of Gaussian Mixture Models

Kai Lawonn, Monique Meuschke, Pepe Eulzer, Matthias Mitterreiter, Joachim Giesen, Tobias Günther

View presentation:2022-10-19T19:12:00ZGMT-0600Change your timezone on the schedule page
2022-10-19T19:12:00Z
Exemplar figure, described by caption below
We present an exploration framework for Gaussian Mixture Models that combines different visualization techniques. The top row shows raycasting-based visualizations that reveal cluster memberships (MIP view), spatial arrangement of Gaussians (hull view), and new modes (DVR view). To manage complexity, the bottom row contains overview visualizations that allow for the comparison of shapes (circle plot, line plot, PCA plot, and small multiples) and different choices of basis vectors (small multiples).

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Abstract

The Gaussian mixture model (GMM) describes the distribution of random variables from several different populations. GMMs have widespread applications in probability theory, statistics, machine learning for unsupervised cluster analysis and topic modeling, as well as in deep learning pipelines. So far, few efforts have been made to explore the underlying point distribution in combination with the GMMs, in particular when the data becomes high-dimensional and when the GMMs are composed of many Gaussians. We present an analysis tool comprising various GPU-based visualization techniques to explore such complex GMMs. To facilitate the exploration of high-dimensional data, we provide a novel navigation system to analyze the underlying data. Instead of projecting the data to 2D, we utilize interactive 3D views to better support users in understanding the spatial arrangements of the Gaussian distributions. The interactive system is composed of two parts: (1) raycasting-based views that visualize cluster memberships, spatial arrangements, and support the discovery of new modes. (2) overview visualizations that enable the comparison of Gaussians with each other, as well as small multiples of different choices of basis vectors. Users are supported in their exploration with customization tools and smooth camera navigations. Our tool was developed and assessed by five domain experts, and its usefulness was evaluated with 23 participants. To demonstrate the effectiveness, we identify interesting features in several data sets.