Selecting Coherent and Relevant Plots in Large Scatterplot Matrices

The scatterplot matrix (SPLOM) is a well‐established technique to visually explore high‐dimensional data sets. It is characterized by the number of scatterplots (plots) of which it consists of. Unfortunately, this number quadratically grows with the number of the data set’s dimensions. Thus, an SPLOM scales very poorly. Consequently, the usefulness of SPLOMs is restricted to a small number of dimensions. For this, several approaches already exist to explore such ‘small’ SPLOMs. Those approaches address the scalability problem just indirectly and without solving it. Therefore, we introduce a new greedy approach to manage ‘large’ SPLOMs with more than 100 dimensions. We establish a combined visualization and interaction scheme that produces intuitively interpretable SPLOMs by combining known quality measures, a pre‐process reordering and a perception‐based abstraction. With this scheme, the user can interactively find large amounts of relevant plots in large SPLOMs.     

Visual Exploration of High‐Dimensional Data through Subspace Analysis and Dynamic Projections

We introduce a novel interactive framework for visualizing and exploring high‐dimensional datasets based on subspace analysis and dynamic projections. We assume the high‐dimensional dataset can be represented by a mixture of low‐dimensional linear subspaces with mixed dimensions, and provide a method to reliably estimate the intrinsic dimension and linear basis of each subspace extracted from the subspace clustering. Subsequently, we use these bases to define unique 2D linear projections as viewpoints from which to visualize the data. To understand the relationships among the different projections and to discover hidden patterns, we connect these projections through dynamic projections that create smooth animated transitions between pairs of projections. We introduce the view transition graph, which provides flexible navigation among these projections to facilitate an intuitive exploration. Finally, we provide detailed comparisons with related systems, and use real‐world examples to demonstrate the novelty and usability of our proposed framework.     

Direct Visualization of Deformation in Volumes

Deformation is a topic of interest in many disciplines. In particular in medical research, deformations of surfaces and even entire volumetric structures are of interest. Clear visualization of such deformations can lead to important insight into growth processes and progression of disease.
We present new techniques for direct focus+context visualization of deformation fields representing transformations between pairs of volumetric datasets. Typically, such fields are computed by performing a non-rigid registration between two data volumes. Our visualization is based on direct volume rendering and uses the GPU to compute and interactively visualize features of these deformation fields in real-time. We integrate visualization of the deformation field with visualization of the scalar volume affected by the deformations. Furthermore, we present a novel use of texturing in volume rendered visualizations to show additional properties of the vector field on surfaces in the volume.     

Topology‐based Visualization of Transformation Pathways in Complex Chemical Systems

Studying transformation in a chemical system by considering its energy as a function of coordinates of the system's components provides insight and changes our understanding of this process. Currently, a lack of effective visualization techniques for high‐dimensional energy functions limits chemists to plot energy with respect to one or two coordinates at a time. In some complex systems, developing a comprehensive understanding requires new visualization techniques that show relationships between all coordinates at the same time. We propose a new visualization technique that combines concepts from topological analysis, multi‐dimensional scaling, and graph layout to enable the analysis of energy functions for a wide range of molecular structures. We demonstrate our technique by studying the energy function of a dimer of formic and acetic acids and a LTA zeolite structure, in which we consider diffusion of methane.     

Evaluation of Cluster Identification Performance for Different PCP Variants

Parallel coordinate plots (PCPs) are a well‐known visualization technique for viewing multivariate data. In the past, various visual modifications to PCPs have been proposed to facilitate tasks such as correlation and cluster identification, to reduce visual clutter, and to increase their information throughput. Most modifications pertain to the use of color and opacity, smooth curves, or the use of animation. Although many of these seem valid improvements, only few user studies have been performed to investigate this, especially with respect to cluster identification. We performed a user study to evaluate cluster identification performance – with respect to response time and correctness – of nine PCP variations, including standard PCPs. To generate the variations, we focused on covering existing techniques as well as possible while keeping testing feasible. This was done by adapting and merging techniques, which led to the following novel variations. The first is an effective way of embedding scatter plots into PCPs. The second is a technique for highlighting fuzzy clusters based on neighborhood density. The third is a spline‐based drawing technique to reduce ambiguity. The last is a pair of animation schemes for PCP rotation. We present an overview of the tested PCP variations and the results of our study. The most important result is that a fair number of the seemingly valid improvements, with the exception of scatter plots embedded into PCPs, do not result in significant performance gains.     

Linear Discriminative Star Coordinates for Exploring Class and Cluster Separation of High Dimensional Data

One main task for domain experts in analysing their nD data is to detect and interpret class/cluster separations and outliers. In fact, an important question is, which features/dimensions separate classes best or allow a cluster‐based data classification. Common approaches rely on projections from nD to 2D, which comes with some challenges, such as: The space of projection contains an infinite number of items. How to find the right one? The projection approaches suffers from distortions and misleading effects. How to rely to the projected class/cluster separation? The projections involve the complete set of dimensions/features. How to identify irrelevant dimensions? Thus, to address these challenges, we introduce a visual analytics concept for the feature selection based on linear discriminative star coordinates (DSC), which generate optimal cluster separating views in a linear sense for both labeled and unlabeled data. This way the user is able to explore how each dimension contributes to clustering. To support to explore relations between clusters and data dimensions, we provide a set of cluster‐aware interactions allowing to smartly iterate through subspaces of both records and features in a guided manner. We demonstrate our features selection approach for optimal cluster/class separation analysis with a couple of experiments on real‐life benchmark high‐dimensional data sets.     

Visual Analysis of Biomolecular Cavities: State of the Art

In this report we review and structure the branch of molecular visualization that is concerned with the visual analysis of cavities in macromolecular protein structures. First the necessary background, the domain terminology, and the goals of analytical reasoning are introduced. Based on a comprehensive collection of relevant research works, we present a novel classification for cavity detection approaches and structure them into four distinct classes: grid‐based, Voronoi‐based, surface‐based, and probe‐based methods. The subclasses are then formed by their combinations. We match these approaches with corresponding visualization technologies starting with direct 3D visualization, followed with non‐spatial visualization techniques that for example abstract the interactions between structures into a relational graph, straighten the cavity of interest to see its profile in one view, or aggregate the time sequence into a single contour plot. We also discuss the current state of methods for the visual analysis of cavities in dynamic data such as molecular dynamics simulations. Finally, we give an overview of the most common tools that are actively developed and used in the structural biology and biochemistry research. Our report is concluded by an outlook on future challenges in the field.     

Structural Decomposition Trees

Researchers and analysts in modern industrial and academic environments are faced with a daunting amount of multi‐dimensional data. While there has been significant development in the areas of data mining and knowledge discovery, there is still the need for improved visualizations and generic solutions. The state‐of‐the‐art in visual analytics and exploratory data visualization is to incorporate more profound analysis methods while focusing on fast interactive abilities. The common trend in these scenarios is to either visualize an abstraction of the data set or to better utilize screen‐space. This paper presents a novel technique that combines clustering, dimension reduction and multi‐dimensional data representation to form a multivariate data visualization that incorporates both detail and overview. This amalgamation counters the individual drawbacks of common projection and multi‐dimensional data visualization techniques, namely ambiguity and clutter. A specific clustering criterion is used to decompose a multi‐dimensional data set into a hierarchical tree structure. This decomposition is embedded in a novel Dimensional Anchor visualization through the use of a weighted linear dimension reduction technique. The resulting Structural Decomposition Tree (SDT) provides not only an insight of the data set's inherent structure, but also conveys detailed coordinate value information. Further, fast and intuitive interaction techniques are explored in order to guide the user in highlighting, brushing, and filtering of the data.     

Dynamic Multi‐View Exploration of Shape Spaces

Statistical shape modeling is a widely used technique for the representation and analysis of the shapes and shape variations present in a population. A statistical shape model models the distribution in a high dimensional shape space, where each shape is represented by a single point. We present a design study on the intuitive exploration and visualization of shape spaces and shape models. Our approach focuses on the dual‐space nature of these spaces. The high‐dimensional shape space represents the population, whereas object space represents the shape of the 3D object associated with a point in shape space. A 3D object view provides local details for a single shape. The high dimensional points in shape space are visualized using a 2D scatter plot projection, the axes of which can be manipulated interactively. This results in a dynamic scatter plot, with the further extension that each point is visualized as a small version of the object shape that it represents. We further enhance the population‐object duality with a new type of view aimed at shape comparison. This new “shape evolution view” visualizes shape variability along a single trajectory in shape space, and serves as a link between the two spaces described above. Our three‐view exploration concept strongly emphasizes linked interaction between all spaces. Moving the cursor over the scatter plot or evolution views, shapes are dynamically interpolated and shown in the object view. Conversely, camera manipulation in the object view affects the object visualizations in the other views. We present a GPU‐accelerated implementation, and show the effectiveness of the three‐view approach using a number of real‐world cases. In these, we demonstrate how this multi‐view approach can be used to visually explore important aspects of a statistical shape model, including specificity, compactness and reconstruction error.     

Visualization and Quantification for Interactive Analysis of Neural Connectivity in Drosophila

Neurobiologists investigate the brain of the common fruit fly Drosophila melanogaster to discover neural circuits and link them to complex behaviour. Formulating new hypotheses about connectivity requires potential connectivity information between individual neurons, indicated by overlaps of arborizations of two or more neurons. As the number of higher order overlaps (i.e. overlaps of three or more arborizations) increases exponentially with the number of neurons under investigation, visualization is impeded by clutter and quantification becomes a burden. Existing solutions are restricted to visual or quantitative analysis of pairwise overlaps, as they rely on precomputed overlap data. We present a novel tool that complements existing methods for potential connectivity exploration by providing for the first time the possibility to compute and visualize higher order arborization overlaps on the fly and to interactively explore this information in both its spatial anatomical context and on a quantitative level. Qualitative evaluation by neuroscientists and non‐experts demonstrated the utility and usability of the tool.     

Hierarchical Stochastic Neighbor Embedding

In recent years, dimensionality‐reduction techniques have been developed and are widely used for hypothesis generation in Exploratory Data Analysis. However, these techniques are confronted with overcoming the trade‐off between computation time and the quality of the provided dimensionality reduction. In this work, we address this limitation, by introducing Hierarchical Stochastic Neighbor Embedding (Hierarchical‐SNE). Using a hierarchical representation of the data, we incorporate the well‐known mantra of Overview‐First, Details‐On‐Demand in non‐linear dimensionality reduction. First, the analysis shows an embedding, that reveals only the dominant structures in the data (Overview). Then, by selecting structures that are visible in the overview, the user can filter the data and drill down in the hierarchy. While the user descends into the hierarchy, detailed visualizations of the high‐dimensional structures will lead to new insights. In this paper, we explain how Hierarchical‐SNE scales to the analysis of big datasets. In addition, we show its application potential in the visualization of Deep‐Learning architectures and the analysis of hyperspectral images.     

A Maximum Enhancing Higher‐Order Tensor Glyph

Glyphs are a fundamental tool in tensor visualization, since they provide an intuitive geometric representation of the full tensor information. The Higher‐Order Maximum Enhancing (HOME) glyph, a generalization of the second‐order tensor ellipsoid, was recently shown to emphasize the orientational information in the tensor through a pointed shape around maxima. This paper states and formally proves several important properties of this novel glyph, presents its first three‐dimensional implementation, and proposes a new coloring scheme that reflects peak direction and sharpness. Application to data from High Angular Resolution Diffusion Imaging (HARDI) shows that the method allows for interactive data exploration and confirms that the HOME glyph conveys fiber spread and crossings more effectively than the conventional polar plot.     

Fast Extraction of High‐quality Crease Surfaces for Visual Analysis

We present a novel algorithm for the efficient extraction and visualization of high‐quality ridge and valley surfaces from numerical datasets. Despite their rapidly increasing popularity in visualization, these so‐called crease surfaces remain challenging to compute owing to their strongly nonlinear and non‐orientable nature, and their complex boundaries. In this context, existing meshing techniques require an extremely dense sampling that is computationally prohibitive. Our proposed solution intertwines sampling and meshing steps to yield an accurate approximation of the underlying surfaces while ensuring the geometric quality of the resulting mesh. Using the computation power of the GPU, we propose a fast, parallel method for sampling. Additionally, we present a new front propagation meshing strategy that leverages CPU multiprocessing. Results are shown for synthetic, medical and fluid dynamics datasets.     

General Projective Maps for Multidimensional Data Projection

To project high‐dimensional data to a 2D domain, there are two well‐established classes of approaches: RadViz and Star Coordinates. Both are well‐explored in terms of accuracy, completeness, distortions, and interaction issues. We present a generalization of both RadViz and Star Coordinates such that it unifies both approaches. We do so by considering the space of all projective projections. This gives additional degrees of freedom, which we use for three things: Firstly, we define a smooth transition between RadViz and Star Coordinates allowing the user to exploit the advantages of both approaches. Secondly, we define a data‐dependent magic lens to explore the data. Thirdly, we optimize the new degrees of freedom to minimize distortion. We apply our approach to a number of high‐dimensional benchmark datasets.     

Illustrative Hybrid Visualization and Exploration of Anatomical and Functional Brain Data

Common practice in brain research and brain surgery involves the multi‐modal acquisition of brain anatomy and brain activation data. These highly complex three‐dimensional data have to be displayed simultaneously in order to convey spatial relationships. Unique challenges in information and interaction design have to be solved in order to keep the visualization sufficiently complete and uncluttered at the same time. The visualization method presented in this paper addresses these issues by using a hybrid combination of polygonal rendering of brain structures and direct volume rendering of activation data. Advanced rendering techniques including illustrative display styles and ambient occlusion calculations enhance the clarity of the visual output. The presented rendering pipeline produces real‐time frame rates and offers a high degree of configurability. Newly designed interaction and measurement tools are provided, which enable the user to explore the data at large, but also to inspect specific features closely. We demonstrate the system in the context of a cognitive neurosciences dataset. An initial informal evaluation shows that our visualization method is deemed useful for clinical research.     

Visualization and Analysis of Eddies in a Global Ocean Simulation

We present analysis and visualization of flow data from a high‐resolution simulation of the dynamical behavior of the global ocean. Of particular scientific interest are coherent vortical features called mesoscale eddies. We first extract high‐vorticity features using a metric from the oceanography community called the Okubo‐Weiss parameter. We then use a new circularity criterion to differentiate eddies from other non‐eddy features like meanders in strong background currents. From these data, we generate visualizations showing the three‐dimensional structure and distribution of ocean eddies. Additionally, the characteristics of each eddy are recorded to form an eddy census that can be used to investigate correlations among variables such as eddy thickness, depth, and location. From these analyses, we gain insight into the role eddies play in large‐scale ocean circulation.     

Fast High‐Dimensional Filtering Using the Permutohedral Lattice

Many useful algorithms for processing images and geometry fall under the general framework of high‐dimensional Gaussian filtering. This family of algorithms includes bilateral filtering and non‐local means. We propose a new way to perform such filters using the permutohedral lattice, which tessellates high‐dimensional space with uniform simplices. Our algorithm is the first implementation of a high‐dimensional Gaussian filter that is both linear in input size and polynomial in dimensionality. Furthermore it is parameter‐free, apart from the filter size, and achieves a consistently high accuracy relative to ground truth (> 45 dB). We use this to demonstrate a number of interactive‐rate applications of filters in as high as eight dimensions.     

Real‐Time Temporal‐Coherent Color Contrast Enhancement for Dichromats

We present an automatic image‐recoloring technique for enhancing color contrast for dichromats whose computational cost varies linearly with the number of input pixels. Our approach can be efficiently implemented on GPUs, and we show that for typical image sizes it is up to two orders of magnitude faster than the current state‐of‐the‐art technique. Unlike previous approaches, ours preserve temporal coherence and, therefore, is suitable for video recoloring. We demonstrate the effectiveness of our technique by integrating it into a visualization system and showing, for the first time, real‐time high‐quality recolored visualizations for dichromats.