Octree and Clustering Based Hierarchical Ensemble Visualization

Interest in ensembles of simulations has increased rapidly in recent years as scientists from various domains use them to assist in their research. An ensemble is a set of results collected from a series of runs of a simulation or an experiment. Each run forms an ensemble member. Ensembles are normally temporal, spatial and contain multiple attribute values at each sample location, making them difficult to analyze or visualize. Techniques have been proposed to provide better insight for a small number of ensemble members, or to present an overview of the entire ensemble but without maintaining fine-grained details. In this paper, we design and implement a system to combine these two directions of ensemble analysis, providing a scalable approach to facilitate analytics of large ensembles and pattern discovery in both the space and the time dimensions.;We begin with a static ensemble analysis and visualization system that focuses on ensemble data at a specific point in time. The static system supports: (1) an octree comparison and clustering techniques to provide a hierarchical overview of inter-member shape and data similarity; (2) a glyph-based rendering to create an effective visual representation---a visualization---for a static ensemble member; and (3) a cluster visualization to display similarities and dissimilarities in shape and data value distributions between members.;We then extend the techniques to support analysis and visualization of a temporal ensemble, each member encoding data collected from a number of time-steps. The extended system supports two approaches of temporal ensemble analysis.;The first approach provides segment based temporal ensemble analysis, using: (1) member segmentation to combine similar shapes adjacent in a local region in time, thereby improving shape clustering efficiency in large ensembles; (2) segment clustering to combine similar member segments and discover similar shapes in all members across all time-steps; (3) segment cluster abstraction to transform a time-series member into a sequence of clusters of member segments; (4) closed contiguous item sequential pattern mining (CISP) over the member cluster participation sequences to identify frequent contiguous changes in shape over time; (5) dynamic time warping (DTW) and time-series member clustering to generate a hierarchical overview of relationships between time-series members, respecting changes in shape over time that include possible shifting and distorting in the time dimension; and (6) animation-based extensions to visualize changes in shape over time.;The second approach provides time-step based temporal ensemble analysis, which is more applicable to short ensembles with members that are exactly aligned in the time dimension. This approach is an extension of the static ensemble analysis, using: (1) hierarchical clustering to combine similar shapes at every time-step; (2) time-step shape cluster abstraction to transform a time-series member into a sequence of time-step shape clusters; (3) CISP in the time-step shape cluster participation sequences to discover common shape changes in the ensemble; (4) Manhattan distance member comparison and time-series member clustering to provide a hierarchical overview of inter-member relationships; and (5) the same animation technique to visualize a time-series member cluster or a pattern.;We implemented a stand-alone system, integrating the proposed techniques to support interactive and scalable ensemble analysis and visualization. We exemplified our techniques using a relativistic heavy ion collision (RHIC) ensemble, collected by our physics collaborators at Duke University. Member segmentation captures important shape transition time-steps in the RHIC simulations. The resulting segments simplify analysis and visualization of the RHIC ensemble in the time dimension by reducing the length of each time-series member. The CISPs discover important time regions where shape changes are similar across multiple simulations. The time-series member cluster tree combines similar simulation results according to changes in shape over time. Our ensemble analysis system enables scientists to interactively balance studying inter-member relationships against visualizing fine-grained details in each member dataset. It provides a computationally efficient method to generate an overview of inter-member relationships prior to performing detailed comparison, thus enabling scientists to quickly choose a subset of members for a full visual comparison. Our system also supports concise visual representations for multiple members, allowing it to scale to large ensembles with hundreds or thousands of members.