Hierarchical Aggregation for Information Visualization: Overview, Techniques, and Design Guidelines <s> Scatterplots <s> Much of the attention in visualization research has focussed on data rooted in physical phenomena, which is generally limited to three or four dimensions. However, many sources of data do not share this dimensional restriction. A critical problem in the analysis of such data is providing researchers with tools to gain insights into characteristics of the data, such as anomalies and patterns. Several visualization methods have been developed to address this problem, and each has its strengths and weaknesses. This paper describes a system named XmdvTool which integrates several of the most common methods for projecting multivariate data onto a two-dimensional screen. This integration allows users to explore their data in a variety of formats with ease. A view enhancement mechanism called an N-dimensional brush is also described. The brush allows users to gain insights into spatial relationships over N dimensions by highlighting data which falls within a user-specified subspace. > <s> BIB001 </s> Hierarchical Aggregation for Information Visualization: Overview, Techniques, and Design Guidelines <s> Scatterplots <s> The paper describes a visualization of a general hierarchical clustering algorithm that allows the user to manipulate the number of classes produced by the clustering method without requiring a radical re-drawing of the clustering tree. The visual method used, a space filling recursive division of a rectangular area, keeps the items under consideration at the same screen position, even while the number of classes is under interactive control. As well as presenting a compact representation of the clustering with different cluster numbers, this method is particularly useful in a linked views environment where additional information can be added to a display to encode other information, without this added level of detail being perturbed when changes are made to the number of clusters. <s> BIB002 </s> Hierarchical Aggregation for Information Visualization: Overview, Techniques, and Design Guidelines <s> Scatterplots <s> Abstract We propose the bagplot, a bivariate generalization of the univariate boxplot. The key notion is the half space location depth of a point relative to a bivariate dataset, which extends the univariate concept of rank. The “depth median” is the deepest location, and it is surrounded by a “bag” containing the n/2 observations with largest depth. Magnifying the bag by a factor 3 yields the “fence” (which is not plotted). Observations between the bag and the fence are marked by a light gray loop, whereas observations outside the fence are flagged as outliers. The bagplot visualizes the location, spread, correlation, skewness, and tails of the data. It is equivariant for linear transformations, and not limited to elliptical distributions. Software for drawing the bagplot is made available for the S-Plus and MATLAB environments. The bagplot is illustrated on several datasets—for example, in a scatterplot matrix of multivariate data. <s> BIB003 </s> Hierarchical Aggregation for Information Visualization: Overview, Techniques, and Design Guidelines <s> Scatterplots <s> Existing information visualization techniques are usually limited to the display of a few thousand items. This article describes new interactive techniques capable of handling a million items (effectively visible and manageable on screen). We evaluate the use of hardware-based techniques available with newer graphics cards, as well as new animation techniques and non-standard graphical features such as stereovision and overlap count. These techniques have been applied to two popular information visualizations: treemaps and scatter plot diagrams; but are generic enough to be applied to other 2D representations as well. <s> BIB004 </s> Hierarchical Aggregation for Information Visualization: Overview, Techniques, and Design Guidelines <s> Scatterplots <s> The use of random algorithms in many areas of computer science has enabled the solution of otherwise intractable problems. In this paper we propose that random sampling can make the visualisation of large datasets both more computationally efficient and more perceptually effective. We review the explicit uses of randomness and the related deterministic techniques in the visualisation literature. We then discuss how sampling can augment existing systems. Furthermore, we demonstrate a novel 2D zooming interface - the Astral Telescope Visualiser, a visualisation suggested and enabled by sampling. We conclude by considering some general usability and technical issues raised by sampling-based visualisation. <s> BIB005 </s> Hierarchical Aggregation for Information Visualization: Overview, Techniques, and Design Guidelines <s> Scatterplots <s> GGobi is a direct descendent of a data visualization system called XGobi that has been around since the early 1990s. GGobi's new features include multiple plotting windows, a color lookup table manager, and an Extensible Markup Language file format for data. Perhaps the biggest advance is that GGobi can be easily extended, either by being embedded in other software or by the addition of plugins; either way, it can be controlled using an Application Programming Interface. An illustration of its extensibility is that it can be embedded in R. The result is a full marriage between GGobi's direct manipulation graphical environment and R's familiar extensible environment for statistical data analysis. <s> BIB006 </s> Hierarchical Aggregation for Information Visualization: Overview, Techniques, and Design Guidelines <s> Scatterplots <s> The huge amount of different automatic clustering methods emphasizes one thing: there is no optimal clustering method for all possible cases. In certain application domains, like genomics and natural language processing, it is not even clear if any of the already known clustering methods suffice. In such cases, an automatic clustering method is often followed by manual refinement. The refined version may then be used as either an illustration, a reference, or even an input for a rule based or other machine learning algorithm as a new clustering method. In this paper, we describe a novel interaction technique to manual cluster refinement using the metaphor of soap bubbles, represented by special implicit surfaces (blobs). For instance, entities can simply be moved inside and outside of these blobs. A modified force-directed layout process automatically arranges entities equidistant on the screen. The modifications include a reduction to the expected amount of computation per iteration down to O(|V| log |V|+|E|) in order to achieve a high response time for use in an interactive system. We also spend a considerable amount of effort making the display of blobs fast enough for an interactive system. <s> BIB007 </s> Hierarchical Aggregation for Information Visualization: Overview, Techniques, and Design Guidelines <s> Scatterplots <s> In many applications, it is important to understand the individual values of, and relationships between, multiple related scalar variables defined across a common domain. Several approaches have been proposed for representing data in these situations. In this paper we focus on strategies for the visualization of multivariate data that rely on color mixing. In particular, through a series of controlled observer experiments, we seek to establish a fundamental understanding of the information-carrying capacities of two alternative methods for encoding multivariate information using color: color blending and color weaving. We begin with a baseline experiment in which we assess participants' abilities to accurately read numerical data encoded in six different basic color scales defined in the L*a*b* color space. We then assess participants' abilities to read combinations of 2, 3, 4 and 6 different data values represented in a common region of the domain, encoded using either color blending or color weaving. In color blending a single mixed color is formed via linear combination of the individual values in L*a*b* space, and in color weaving the original individual colors are displayed side-by-side in a high frequency texture that fills the region. A third experiment was conducted to clarify some of the trends regarding the color contrast and its effect on the magnitude of the error that was observed in the second experiment. The results indicate that when the component colors are represented side-by-side in a high frequency texture, most participants' abilities to infer the values of individual components are significantly improved, relative to when the colors are blended. Participants' performance was significantly better with color weaving particularly when more than 2 colors were used, and even when the individual colors subtended only 3 minutes of visual angle in the texture. However, the information-carrying capacity of the color weaving approach has its limits. We found that participants' abilities to accurately interpret each of the individual components in a high frequency color texture typically falls off as the number of components increases from 4 to 6. We found no significant advantages, in either color blending or color weaving, to using color scales based on component hues thatare more widely separated in the L*a*b* color space. Furthermore, we found some indications that extra difficulties may arise when opponent hues are employed. <s> BIB008 </s> Hierarchical Aggregation for Information Visualization: Overview, Techniques, and Design Guidelines <s> Scatterplots <s> We present a new method for the combined visualization of software architecture diagrams, such as UML class diagrams or component diagrams, and software metrics defined on groups of diagram elements. Our method extends an existing rendering technique for the so-called areas of interest in system architecture diagrams to visualize several metrics, possibly having missing values, defined on overlapping areas of interest. For this, we use a solution that combines texturing, blending, and smooth scattered-data point interpolation. Our new method simplifies the task of visually correlating the distribution and outlier values of a multivariate metric dataset with a system's structure. We demonstrate the application of our method on component and class diagrams extracted from real-world systems. <s> BIB009 </s> Hierarchical Aggregation for Information Visualization: Overview, Techniques, and Design Guidelines <s> Scatterplots <s> Visualisation of taxonomies and sets has recently become an active area of research. Many application fields now require more than a strict classification of elements into a hierarchy tree. Euler diagrams, one of the most natural ways of depicting intersecting sets, may provide a solution to these problems. ::: ::: In this paper, we present an approach for the automatic generation of Euler-like diagrams. This algorithm differs from previous approaches in that it has no undrawable instances of input, allowing it to be used in systems where the output is always required. We also improve the readability of Euler diagrams through the use of Bezier curves and transparent coloured textures. Our approach has been implemented using the Tulip platform. Both the source and executable program used to generate the results are freely available. <s> BIB010 </s> Hierarchical Aggregation for Information Visualization: Overview, Techniques, and Design Guidelines <s> Scatterplots <s> While many data sets contain multiple relationships, depicting more than one data relationship within a single visualization is challenging. We introduce Bubble Sets as a visualization technique for data that has both a primary data relation with a semantically significant spatial organization and a significant set membership relation in which members of the same set are not necessarily adjacent in the primary layout. In order to maintain the spatial rights of the primary data relation, we avoid layout adjustment techniques that improve set cluster continuity and density. Instead, we use a continuous, possibly concave, isocontour to delineate set membership, without disrupting the primary layout. Optimizations minimize cluster overlap and provide for calculation of the isocontours at interactive speeds. Case studies show how this technique can be used to indicate multiple sets on a variety of common visualizations. <s> BIB011
Scatterplots  ,  visualize multidimensional data by mapping data cases to graphical points in a two-or threedimensional Cartesian space defined by two or three orthogonal axes. The position of each point representing a data case depends on the data dimension assigned to each axis. Visualization tools supporting scatterplots, such as XmdvTool BIB001 , Spotfire, and GGobi BIB006 typically allow additional data dimensions to be mapped onto graphical attributes such as the size, color, and shape of the points. Because of their relative simplicity, familiarity with users, and high visual clarity, scatterplots are part of the standard vocabulary of data graphics. Scatterplots are overlapping visualizations, and rendering a large data set (or even a data set that is locally dense) will cause a lot of item overlap in the output, making estimation of effects difficult. Fekete and Plaisant BIB004 , while not focusing on aggregation per se, present a scatterplot implementation capable of visualizing a million separate items. Their examples clearly show the overlap problem (they even measure the amount of overlap), and they discuss methods involving transparency, stereovision, and interaction to reduce its impact. As outlined in Table 1 , the main visual aggregations for scatterplots involve hierarchical clustering of data points into points, boxes, hulls, and blobs. Point aggregates show only the average for each cluster, and could be seen as a sampling operation BIB005 . Originally introduced by Yang et al.  , boxes are axis-aligned two-dimensional or threedimensional bounding boxes that give an indication of the minimum and maximum values for the displayed dimensions (Fig. 1) . They can be augmented to show averages as points or using opacity where the center point of the cluster is fully opaque and the extrema are fully transparent. Wills BIB002 presents a scatterplot-based aggregation method using recursive subdivision of space with boxes. Hulls are variations on boxes in that they show the extents of the displayed dimensions, but using two-dimensional or three-dimensional convex hulls instead of axisaligned bounding boxes as a tighter visual metric (Fig. 1) . Just like for bounding boxes, center points or opacity can be used to indicate the cluster average (Fig. 8) . Bivariate boxplots  and their simplification, bagplots BIB003 , are statistical versions of this technique where concentric hulls are constructed to contain quartiles of the data. Taking extent refinement even further, the blobs technique proposed by Heine and Scheuermann BIB007 provide implicit surfaces for conveying and interacting with finegrained clustering, and can be employed for scatterplot diagrams. However, the authors point out the problem of color blending for overlapping blobs, a problem that generalizes also to boxes and hulls. The weaving approach proposed by Hagh-Shenas et al. BIB008 might come in handy for resolving this problem. Similar work includes the multivariate set visualization technique proposed by Byelas and Telea BIB009 , the automated overlapping set technique introduced by Simonetto et al. BIB010 , and the bubble set overlay mechanism presented by Collins et al. BIB011 .