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

This thesis provides substantial contributions to the research domain of visualizing and analyzing uncertain multidimensional data. We propose several approaches predicated on displaying visual abstractions derived from given data sets. In particular, we provide means to explore higher dimensional scalar fields and ensembles of shapes and scalar fields in two or three dimensions. By utilizing GPU acceleration, our methods are computationally efficient and allow the user to discover data sets interactively.

Visual Abstractions for Analyzing Uncertain Multidimensional Data

GPU voxel-based surface ray-casting has positioned as an interesting alternative to rasterization-based rendering approaches, because it allows using many processing units simultaneously, can effectively exploit thread level parallelism, and enables fine-granularity occlusion culling on the pixel level. Yet voxel-based techniques face the problem that an extremely high resolution is necessary to avoid block artifacts at high zoom levels. In this work, we propose a novel improvement of voxel-based ray-casting to overcome this limitation. By using a hierarchical Vector-to-Closest-Point (VCP) representation, we can inherit the advantages of a voxel-based approach at a much smoother approximation of the surface. We demonstrate that, although the VCP grid consumes more memory per cell, it requires less memory overall, because it builds upon a significantly shallower tree hierarchy. In a number of examples we demonstrate the use of our approach for high-quality rendering of high resolution surface models.

Vector-to-Closest-Point Octree for Surface Ray-Casting

We model directional data, i.e., we estimate a pdf, using parametric mixture models. Another approach to approximate densities is nonparametric, where a pdf is estimated directly from the observations. The histogram is the most prevalent density estimator, while a more accurate method is the kernel density estimate [1]. A histogram is simple to construct, but suffers from major drawbacks: It involves an arbitrary choice for the starting point and group boundaries, which can potentially distort the presented information. Moreover, just like the smoother nonparametric density estimators, it requires the amount of smoothing of the estimate – the bin width – as input. Depending on the smoothing parameter, the shape of the density estimate can vary significantly. A very small amount can exhibit spurious fine structures, the number of “bumps” decreasing as the amount of smoothing increases, to the extent that the multimodality of a pdf can be obscured (cf. Fig. 1(a) and (b)). Furthermore, deriving additional quantitative information automatically, such as the modes of the pdf, is not trivial. Even if the modes can be assessed visually by the number of “bumps” or the local peaks of the density, the number of significant peaks, their locations and sizes still need to be determined. Because we use the modes not only to visualize the modality, but also to find the degree to which ensemble members agree in their behavior, we preferred a parametric model to a non-parametric one; parametric mixture models provide not only the approximated pdfs, but also the modes and their characteristics (cf. Fig. 1(c)).

Ismail Demir

Papers

Visual Abstractions for Analyzing Uncertain Multidimensional Data

Vector-to-Closest-Point Octree for Surface Ray-Casting

Comparative Visual Analysis of Vector Field Ensembles: Appendix