The State-of-the-Art of Set Visualization

Sets comprise a generic data model that has been used in a variety of data analysis problems. Such problems involve analysing and visualizing set relations between multiple sets defined over the same collection of elements. However, visualizing sets is a non-trivial problem due to the large number of possible relations between them. We provide a systematic overview of state-of-the-art techniques for visualizing different kinds of set relations. We classify these techniques into six main categories according to the visual representations they use and the tasks they support. We compare the categories to provide guidance for choosing an appropriate technique for a given problem. Finally, we identify challenges in this area that need further research and propose possible directions to address these challenges. Further resources on set visualization are available at http://www.setviz.net

Visual Analysis of High-Dimensional Point Clouds using Topological Abstraction

This thesis is about visualizing a kind of data that is trivial to process by computers but difficult to imagine by humans because nature does not allow for intuition with this type of information: high-dimensional data. Such data often result from representing observations of objects under various aspects or with different properties. In many applications, a typical, laborious task is to find related objects or to group those that are similar to each other. One classic solution for this task is to imagine the data as vectors in a Euclidean space with object variables as dimensions. Utilizing Euclidean distance as a measure of similarity, objects with similar properties and values accumulate to groups, so-called clusters, that are exposed by cluster analysis on the high-dimensional point cloud. Because similar vectors can be thought of as objects that are alike in terms of their attributes, the point cloud\''s structure and individual cluster properties, like their size or compactness, summarize data categories and their relative importance. The contribution of this thesis is a novel analysis approach for visual exploration of high-dimensional point clouds without suffering from structural occlusion. The work is based on implementing two key concepts: The first idea is to discard those geometric properties that cannot be preserved and, thus, lead to the typical artifacts. Topological concepts are used instead to shift away the focus from a point-centered view on the data to a more structure-centered perspective. The advantage is that topology-driven clustering information can be extracted in the data\''s original domain and be preserved without loss in low dimensions. The second idea is to split the analysis into a topology-based global overview and a subsequent geometric local refinement. The occlusion-free overview enables the analyst to identify features and to link them to other visualizations that permit analysis of those properties not captured by the topological abstraction, e.g. cluster shape or value distributions in particular dimensions or subspaces. The advantage of separating structure from data point analysis is that restricting local analysis only to data subsets significantly reduces artifacts and the visual complexity of standard techniques. That is, the additional topological layer enables the analyst to identify structure that was hidden before and to focus on particular features by suppressing irrelevant points during local feature analysis. This thesis addresses the topology-based visual analysis of high-dimensional point clouds for both the time-invariant and the time-varying case. Time-invariant means that the points do not change in their number or positions. That is, the analyst explores the clustering of a fixed and constant set of points. The extension to the time-varying case implies the analysis of a varying clustering, where clusters appear as new, merge or split, or vanish. Especially for high-dimensional data, both tracking---which means to relate features over time---but also visualizing changing structure are difficult problems to solve

Effective Visualization Approaches For Ultra-High Dimensional Datasets

Multivariate informational data, which are abstract as well as complex, are becoming increasingly common in many areas such as scientific, medical, social, business, and so on. Displaying and analyzing large amounts of multivariate data with more than three variables of different types is quite challenging. Visualization of such multivariate data suffers from a high degree of clutter when the numbers of dimensions/variables and data observations become too large. We propose multiple approaches to effectively visualize large datasets of ultrahigh number of dimensions by generalizing two standard multivariate visualization methods, namely star plot and parallel coordinates plot. We refine three variants of the star plot, which include overlapped star plot, shifted origin plot, and multilevel star plot by embedding distribution plots, displaying dataset in groups, and supporting adjustable positioning of the star axes. We introduce a bifocal parallel coordinates plot (BPCP) based on the focus + context approach. BPCP splits vertically the overall rendering area into the focus and context regions. The focus area maps a few selected dimensions of interest at sufficiently wide spacing. The remaining dimensions are represented in the context area in a compact way to retain useful information and provide the data continuity. The focus display can be further enriched with various options, such as axes overlays, scatterplot, and nested PCPs. In order to accommodate an arbitrarily large number of dimensions, the context display supports the multi-level stacked view. Finally, we present two innovative ways of enhancing parallel coordinates axes to better understand all variables and their interrelationships in high-dimensional datasets. Histogram and circle/ellipse plots based on uniform and non-uniform frequency/density mappings are adopted to visualize distributions of numerical and categorical data values. Color-mapped axis stripes are designed in the parallel coordinates layout so that correlations can be fully realized in the same display plot irrespective of axes locations. These colors are also propagated to histograms as stacked bars and categorical values as pie charts to further facilitate data exploration. By using the datasets consisting of 25 to 130 variables of different data types we have demonstrated effectiveness of the proposed multivariate visualization enhancements

A Formalism for Visual Query Interface Design

The massive volumes and the huge variety of large knowledge bases make information exploration and analysis difficult. An important activity is data filtering and selection, in which both querying and visualization play important roles. Interfaces for data exploration environments normally include both, integrating them as tightly as possible. But many features of information exploration environments, such as visual representation of queries, visualization of query results, interactive data selection from visualizations, have only been studied separately. The intrinsic connections between them have not been described formally. The lack of formal descriptions inhibits the development of techniques that produce new representations for queries, and natural integration of visual query specification with query result visualization. This thesis describes a formalism that describes the basic components of information exploration and and their relationships in information exploration environments. The key aspect of the formalism is that it unifies querying and visualization within a single framework, which provides a foundation for designing and analysing visual query interfaces. Various innovative designs of visual query representations can be derived from the formalism. Simply comparing them with existing ones is not enough, it is more important to discover why one visual representation is better or worse than another. To do this it is necessary to understand users’ cognitive activities, and to know how these cognitive activities are enhanced or inhibited by different presentations of a query so that novel interfaces can be created and improved based on user testing. This thesis presents a new experimental methodology for evaluating query representations, which uses stimulus onset asynchrony to separate different aspects of query comprehension. This methodology was used to evaluate a new visual query representation based on Karnaugh maps, and showing that there are two qualitatively different approaches to comprehension: deductive and inductive. The Karnaugh map representation scales extremely well with query complexity, and the experiment shows that its good scaling properties occur because it strongly facilitates inductive comprehension