Dirk J. Lehmann

Improving the visual analysis of high-dimensional datasets using quality measures

Modern visualization methods are needed to cope with very high-dimensional data. Efficient visual analytical techniques are required to extract the information content in these data. The large number of possible projections for each method, which usually grow quadrat-ically or even exponentially with the number of dimensions, urges the necessity to employ automatic reduction techniques, automatic sorting or selecting the projections, based on their information-bearing content. Different quality measures have been successfully applied for several specified user tasks and established visualization techniques, like Scatterplots, Scatterplot Matrices or Parallel Coordinates. Many other popular visualization techniques exist, but due to the structural differences, the measures are not directly applicable to them and new approaches are needed. In this paper we propose new quality measures for three popular visualization methods: Radviz, Pixel-Oriented Displays and Table Lenses. Our experiments show that these measures efficiently guide the visual analysis task.

Orthographic Star Coordinates

Star coordinates is a popular projection technique from an nD data space to a 2D/3D visualization domain. It is defined by setting n coordinate axes in the visualization domain. Since it generally defines an affine projection, strong distortions can occur: an nD sphere can be mapped to an ellipse of arbitrary size and aspect ratio. We propose to restrict star coordinates to orthographic projections which map an nD sphere of radius r to a 2D circle of radius r. We achieve this by formulating conditions for the coordinate axes to define orthographic projections, and by running a repeated non-linear optimization in the background of every modification of the coordinate axes. This way, we define a number of orthographic interaction concepts as well as orthographic data tour sequences: a scatterplot tour, a principle component tour, and a grand tour. All concepts are illustrated and evaluated with synthetic and real data.

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.

Automatic Detection and Visualization of Qualitative Hemodynamic Characteristics in Cerebral Aneurysms

Cerebral aneurysms are a pathological vessel dilatation that bear a high risk of rupture. For the understanding and evaluation of the risk of rupture, the analysis of hemodynamic information plays an important role. Besides quantitative hemodynamic information, also qualitative flow characteristics, e.g., the inflow jet and impingement zone are correlated with the risk of rupture. However, the assessment of these two characteristics is currently based on an interactive visual investigation of the flow field, obtained by computational fluid dynamics (CFD) or blood flow measurements. We present an automatic and robust detection as well as an expressive visualization of these characteristics. The detection can be used to support a comparison, e.g., of simulation results reflecting different treatment options. Our approach utilizes local streamline properties to formalize the inflow jet and impingement zone. We extract a characteristic seeding curve on the ostium, on which an inflow jet boundary contour is constructed. Based on this boundary contour we identify the impingement zone. Furthermore, we present several visualization techniques to depict both characteristics expressively. Thereby, we consider accuracy and robustness of the extracted characteristics, minimal visual clutter and occlusions. An evaluation with six domain experts confirms that our approach detects both hemodynamic characteristics reasonably.

Blood Flow Clustering and Applications inVirtual Stenting of Intracranial Aneurysms

Understanding the hemodynamics of blood flow in vascular pathologies such as intracranial aneurysms is essential for both their diagnosis and treatment. Computational fluid dynamics (CFD) simulations of blood flow based on patient-individual data are performed to better understand aneurysm initiation and progression and more recently, for predicting treatment success. In virtual stenting, a flow-diverting mesh tube (stent) is modeled inside the reconstructed vasculature and integrated in the simulation. We focus on steady-state simulation and the resulting complex multiparameter data. The blood flow pattern captured therein is assumed to be related to the success of stenting. It is often visualized by a dense and cluttered set of streamlines.We present a fully automatic approach for reducing visual clutter and exposing characteristic flow structures by clustering streamlines and computing cluster representatives. While individual clustering techniques have been applied before to streamlines in 3D flow fields, we contribute a general quantitative and a domain-specific qualitative evaluation of three state-of-the-art techniques. We show that clustering based on streamline geometry as well as on domain-specific streamline attributes contributes to comparing and evaluating different virtual stenting strategies. With our work, we aim at supporting CFD engineers and interventional neuroradiologists.

Discontinuities in Continuous Scatter Plots

The concept of continuous scatterplot (CSP) is a modern visualization technique. The idea is to define a scalar density value based on the map between an n-dimensional spatial domain and an m-dimensional data domain, which describe the CSP space. Usually the data domain is two-dimensional to visually convey the underlying, density coded, data. In this paper we investigate kinds of map-based discontinuities, especially for the practical cases n = m = 2 and n = 3 | m = 2, and we depict relations between them and attributes of the resulting CSP itself. Additionally, we show that discontinuities build critical line structures, and we introduce algorithms to detect them. Further, we introduce a discontinuity-based visualization approach - called contribution map (CM) -which establishes a relationship between the CSPs data domain and the number of connected components in the spatial domain. We show that CMs enhance the CSP-based linking & brushing interaction. Finally, we apply our approaches to a number of synthetic as well as real data sets.

Optimal Sets of Projections of High-Dimensional Data

Finding good projections of n-dimensional datasets into a 2D visualization domain is one of the most important problems in Information Visualization. Users are interested in getting maximal insight into the data by exploring a minimal number of projections. However, if the number is too small or improper projections are used, then important data patterns might be overlooked. We propose a data-driven approach to find minimal sets of projections that uniquely show certain data patterns. For this we introduce a dissimilarity measure of data projections that discards affine transformations of projections and prevents repetitions of the same data patterns. Based on this, we provide complete data tours of at most n/2 projections. Furthermore, we propose optimal paths of projection matrices for an interactive data exploration. We illustrate our technique with a set of state-of-the-art real high-dimensional benchmark datasets.

Automating Transfer Function Design with Valley Cell-Based Clustering of 2D Density Plots

Two‐dimensional transfer functions are an effective and well‐accepted tool in volume classification. The design of them mostly depends on the users experience and thus remains a challenge. Therefore, we present an approach in this paper to automate the transfer function design based on 2D density plots. By exploiting their smoothness, we adopted the Morse theory to automatically decompose the feature space into a set of valley cells. We design a simplification process based on cell separability to eliminate cells which are mainly caused by noise in the original volume data. Boundary persistence is first introduced to measure the separability between adjacent cells and to suitably merge them. Afterward, a reasonable classification result is achieved where each cell represents a potential feature in the volume data. This classification procedure is automatic and facilitates an arbitrary number and shape of features in the feature space. The opacity of each feature is determined by its persistence and size. To further incorporate the users prior knowledge, a hierarchical feature representation is created by successive merging of the cells. With this representation, the user is allowed to merge or split features of interest and set opacity and color freely. Experiments on various volumetric data sets demonstrate the effectiveness and usefulness of our approach in transfer function generation.

Visualnostics: Visual Guidance Pictograms for Analyzing Projections of High-dimensional Data

The visual analysis of multivariate projections is a challenging task, because complex visual structures occur. This causes fatigue or misinterpretations, which distorts the analysis. In fact, the same projection can lead to different analysis results. We provide visual guidance pictograms to improve objectivity of the visual search. A visual guidance pictogram is an iconic visual density map encoding the visual structure of certain data properties. By using them to guide the analysis, structures in the projection can be better understood and mentally linked to properties in the data. We introduce a systematic scheme for designing such pictograms and provide a set of pictograms for standard visual tasks, such as correlation and distribution analysis, for standard projections like scatterplots, RadVis, and Star Coordinates. We conduct a study that compares the visual analysis of real data with and without the support of guidance pictograms. Our tests show that the training effort for a visual search can be decreased and the analysis bias can be reduced by supporting the users visual search with guidance pictograms.

A Clustering-based Visualization Technique to Emphasize Meaningful Regions of Vector Fields

This paper proposes a vector field visualization approach that extracts and visualizes grouped regions of static 3D vector fields of similar curvature behavior. These regions are argued to ease the recognition of regions of potential interest and accelerate the general exploration process of vector fields. Our approach detects regions of similar geometric stream properties such as integral curvature and visualizes them by means of compact cluster boundaries. To supplement existing approaches our method combines information on relevant scales to extract meaningful semantical aspects of the overall field structure. For proof of concept we illustrate our results based on real and synthetic data sets.