Statistics for Spatial Data.

Massive simulations and arrays of sensing devices, in combination with increasing computing resources, have generated large, complex, high-dimensional datasets used to study phenomena across numerous fields of study. Visualization plays an important role in exploring such datasets. We provide a comprehensive survey of advances in high-dimensional data visualization that focuses on the past decade. We aim at providing guidance for data practitioners to navigate through a modular view of the recent advances, inspiring the creation of new visualizations along the enriched visualization pipeline, and identifying future opportunities for visualization research.

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Visualizing High-Dimensional Data: Advances in the Past Decade

Visualizing High-Dimensional Data: Advances in the Past Decade.

A Dictionary of Statistics

Supporting comparison is a common and diverse challenge in visualization. Such support is difficult to design because solutions must address both the specifics of their scenario as well as the general issues of comparison. This paper aids designers by providing a strategy for considering those general issues. It presents four considerations that abstract comparison. These considerations identify issues and categorize solutions in a domain independent manner. The first considers how the common elements of comparison—a target set of items that are related and an action the user wants to perform on that relationship—are present in an analysis problem. The second considers why these elements lead to challenges because of their scale, in number of items, complexity of items, or complexity of relationship. The third considers what strategies address the identified scaling challenges, grouping solutions into three broad categories. The fourth considers which visual designs map to these strategies to provide solutions for a comparison analysis problem. In sequence, these considerations provide a process for developers to consider support for comparison in the design of visualization tools. Case studies show how these considerations can help in the design and evaluation of visualization solutions for comparison problems.

Considerations for Visualizing Comparison

A comparative visualization of multiple volume data sets is challenging due to the inherent occlusion effects, yet it is important to effectively reveal uncertainties, correlations and reliable trends in 3D ensemble fields. In this paper we present bidirectional linking of multi-charts and volume visualization as a means to analyze visually 3D scalar ensemble fields at the data level. Multi-charts are an extension of conventional bar and line charts: They linearize the 3D data points along a space-filling curve and draw them as multiple charts in the same plot area. The bar charts encode statistical information on ensemble members, such as histograms and probability densities, and line charts are overlayed to allow comparing members against the ensemble. Alternative linearizations based on histogram similarities or ensemble variation allow clustering of spatial locations depending on data distribution. Multi-charts organize the data at multiple scales to quickly provide overviews and enable users to select regions exhibiting interesting behavior interactively. They are further put into a spatial context by allowing the user to brush or query value intervals and specific distributions, and to simultaneously visualize the corresponding spatial points via volume rendering. By providing a picking mechanism in 3D and instantly highlighting the corresponding data points in the chart, the user can go back and forth between the abstract and the 3D view to focus the analysis.

Multi-Charts for Comparative 3D Ensemble Visualization.

We present a new visual analysis approach to support the comparative exploration of 2D vector-valued ensemble fields. Our approach enables the user to quickly identify the most similar groups of ensemble members, as well as the locations where the variation among the members is high. We further provide means to visualize the main features of the potentially multimodal directional distributions at user-selected locations. For this purpose, directional data is modelled using mixtures of probability density functions (pdfs), which allows us to characterize and classify complex distributions with relatively few parameters. The resulting mixture models are used to determine the degree of similarity between ensemble members, and to construct glyphs showing the direction, spread, and strength of the principal modes of the directional distributions. We also propose several similarity measures, based on which we compute pairwise member similarities in the spatial domain and form clusters of similar members. The hierarchical clustering is shown using dendrograms and similarity matrices, which can be used to select particular members and visualize their variations. A user interface providing multiple linked views enables the simultaneous visualization of aggregated global and detailed local variations, as well as the selection of members for a detailed comparison.

Comparative visual analysis of vector field ensembles

Visualizing sets of isosurfaces from 3D scalar ensemble fields is a difficult task due to inherent occlusion effects, yet it is often required to analyze the uncertainty represented by such an ensemble. In this paper, we present a novel visualization technique for ensembles of isosurfaces based on screen-space silhouettes. By using silhouettes, the displayed information is reduced to avoid occlusions, yet the major shape of the surfaces can be maintained. Our approach preserves spatial coherence and does not make any assumption about the underlying surface distribution. By providing additional mechanisms, i.e., picking, clustering, cutting and animation, we enable the user to explore an ensemble of surfaces interactively.

Screen-space silhouettes for visualizing ensembles of 3D isosurfaces

We propose a new approach for analyzing the central tendency (centrality) of an ensemble of shapes in 2D or 3D space. Our approach provides means to determine the most central shape from a given set of shapes, to quantify the region-wise centrality of the shapes, and to compute a locally most representative shape. Unlike previous approaches, which build upon binary functions or signed distance fields to locate domain points with respect to orientable shapes, we introduce a closest point representation for the analysis of ensembles of shapes. By using this representation, our approach can handle arbitrary non-parametric shapes regardless of dimension and orientability. Shapes are first converted into an implicit representation based on vectors to closest surface points, and the resulting directional distributions are then used to perform region-wise classifications. Shapes are either analyzed separately by evaluating the classifications over the shape, or additional fields are derived from these classifications, in which specific shapes like the locally best mean are given as level-sets. We demonstrate the effectiveness of our approach on synthetic and weather forecast ensembles in 2D and 3D.

Visualizing the central tendency of ensembles of shapes

In this paper we present a technique which allows us to perform high quality and progressive response surface prediction from multidimensional input samples in an efficient manner. We utilize kriging interpolation to estimate a response surface which minimizes the expectation value and variance of the prediction error. High computational efficiency is achieved by employing parallel matrix and vector operations on the GPU. Our approach differs from previous kriging approaches in that it uses a novel progressive updating scheme for new samples based on blockwise matrix inversion. In this way we can handle very large sample sets to which new samples are continually added. Furthermore, we can monitor the incremental evolution of the surface, providing a means to early terminate the computation when no significant changes have occurred. When the generation of input samples is fast enough, our technique enables steering this generation process interactively to find relevant dependency relations.

Ismail Demir

Papers

Multi-Charts for Comparative 3D Ensemble Visualization.

Comparative visual analysis of vector field ensembles

Screen-space silhouettes for visualizing ensembles of 3D isosurfaces

Visualizing the central tendency of ensembles of shapes

Progressive high-quality response surfaces for visually guided sensitivity analysis