From visual data exploration to visual data mining: a survey <s> Taxonomy of Techniques by Keim <s> Abstract A novel method of representing multivariate data is presented. Each point in k-dimensional space, k≤18, is represented by a cartoon of a face whose features, such as length of nose and curvature of mouth, correspond to components of the point. Thus every multivariate observation is visualized as a computer-drawn face. This presentation makes it easy for the human mind to grasp many of the essential regularities and irregularities present in the data. Other graphical representations are described briefly. <s> BIB001 </s> From visual data exploration to visual data mining: a survey <s> Taxonomy of Techniques by Keim <s> A methodology for visualizing analytic and synthetic geometry in R/sup N/ is presented. It is based on a system of parallel coordinates which induces a nonprojective mapping between N-dimensional and two-dimensional sets. Hypersurfaces are represented by their planar images which have some geometrical properties analogous to the properties of the hypersurface that they represent. A point from to line duality when N=2 generalizes to lines and hyperplanes enabling the representation of polyhedra in R/sup N/. The representation of a class of convex and non-convex hypersurfaces is discussed, together with an algorithm for constructing and displaying any interior point. The display shows some local properties of the hypersurface and provides information on the point's proximity to the boundary. Applications are discussed.<<ETX>> <s> BIB002 </s> From visual data exploration to visual data mining: a survey <s> Taxonomy of Techniques by Keim <s> The author presents a simple and flexible method of sharp coding for higher dimensional data sets that allows the database operator or the scientist quick access to promising patterns within and among records or samples. The example used is a 13-parameter set of solar wind, magnetosphere, and ground observation data collected hourly for 21 days in 1976. The software system is a prototype developed to demonstrate the glyph approach to depicting higher-dimensional data sets. The experiment was to depict all parameters simultaneously, to see if any global or local patterns emerged. This experiment proves that much more complex data can be presented for visual pattern extraction than standard methods allow. > <s> BIB003 </s> From visual data exploration to visual data mining: a survey <s> Taxonomy of Techniques by Keim <s> The authors present a tool for the display and analysis of N-dimensional data based on a technique called dimensional stacking. This technique is described. The primary goal is to create a tool that enables the user to project data of arbitrary dimensions onto a two-dimensional image. Of equal importance is the ability to control the viewing parameters, so that one can interactively adjust what ranges of values each dimension takes and the form in which the dimensions are displayed. This will allow an intuitive feel for the data to be developed as the database is explored. The system uses dimensional stacking, to collapse and N-dimension space down into a 2-D space and then render the values contained therein. Each value can then be represented as a pixel or rectangular region on a 2-D screen whose intensity corresponds to the data value at that point. > <s> BIB004 </s> From visual data exploration to visual data mining: a survey <s> Taxonomy of Techniques by Keim <s> Multiparameter data collection is becoming increasingly common in many scientific disciplines. The need exists for integrated displays to enable the scientist to see the combined information, some of which may not be adequately perceived or may not be perceived at all when viewed individually. In order for such displays to succeed, they must exploit the visual perceptual capabilities as much as possible. We present a new technique that harnesses color and texture perception to create integrated displays of two-dimensional "imagelike" multiparameter distributions. The power of the new technique is demonstrated by an example of a synthesized dataset comparing it with several other proposed techniques. We discuss the nature of studies required to measure objectively and accurately the effectiveness of such displays. <s> BIB005 </s> From visual data exploration to visual data mining: a survey <s> Taxonomy of Techniques by Keim <s> The task of managing and accessing large information spaces is a problem in large scale cognition. Enwrging technologies for 3D visualization and interactive aninlaiion offer potential solutions to this problenl, especially when the structure of the information can be visualized. We describe one of these Information Visualtzaiion techniques, called the Cone Tree, which is used for visualizing hierarchical information structures. The hierarchy is presented in 3D to nlaxilnize effective use of available screen space and enable visualization of the whole structure. Interactive aninlation is used (,o shift sonle of the user’s cognitive load to the human perceptual system, <s> BIB006 </s> From visual data exploration to visual data mining: a survey <s> Taxonomy of Techniques by Keim <s> This paper is aimed at the exploratory visualization of networks where there is a strength or weight associated with each link, and makes use of any hierarchy present on the nodes to aid the investigation of large networks. It describes a method of placing nodes on the plane that gives meaning to their relative positions. The paper discusses how linking and interaction principles aid the user in the exploration. Two examples are given; one of electronic mail communication over eight months within a department, another concerned with changes to a large section of a computer program. > <s> BIB007 </s> From visual data exploration to visual data mining: a survey <s> Taxonomy of Techniques by Keim <s> The field of auditory data representation has produced several intriguing proof-of-concept systems, but up until now there has been little formal research to measure the effectiveness of auditory data displays or to increase our understanding of how they work and how to improve them. Formal assessment is necessary throughout the process of developing new auditory display technologies in order to learn how to restrict the universe of possible sound attributes to those that are most effective for data representation. The capability to run quick psychometric tests to obtain quantitative figures of merit for alternative auditory representations is a requirement for auditory-display researchers engaged in the development of new technologies. For the first time, this capability is realized with a special-purpose workstation designed to generate and administer psychometric tests automatically using test patterns generated from statistically well-specified synthetic data. We describe the characteristics of one such workstation we have developed. We also describe a testing methodology we propose for the development of new auditory data displays of a type that we have been working with for the last few years. Finally, we describe a specific set of studies we are now beginning to conduct. <s> BIB008 </s> From visual data exploration to visual data mining: a survey <s> Taxonomy of Techniques by Keim <s> Visual data mining techniques have proven to be of high value in exploratory data analysis, and they also have a high potential for mining large databases. In this article, we describe and evaluate a new visualization-based approach to mining large databases. The basic idea of our visual data mining techniques is to represent as many data items as possible on the screen at the same time by mapping each data value to a pixel of the screen and arranging the pixels adequately. The major goal of this article is to evaluate our visual data mining techniques and to compare them to other well-known visualization techniques for multidimensional data: the parallel coordinate and stick-figure visualization techniques. For the evaluation of visual data mining techniques, the perception of data properties counts most, while the CPU time and the number of secondary storage accesses are only of secondary importance. In addition to testing the visualization techniques using real data, we developed a testing environment for database visualizations similar to the benchmark approach used for comparing the performance of database systems. The testing environment allows the generation of test data sets with predefined data characteristics which are important for comparing the perceptual abilities of visual data mining techniques. <s> BIB009 </s> From visual data exploration to visual data mining: a survey <s> Taxonomy of Techniques by Keim <s> In this paper , we describe a novel technique for visualizing large amounts of high-dimensio nal data, called ‘circle segments’. The technique uses one colored pixel per data value and can therefore be classified as a pixel-per-value technique [Kei 96]. The basic idea of the ‘circle segments’ visualization technique is to display the data dimensions as segments of a circle. If the data consists of k dimensions, the circle is partitioned into k segments, each representing one data dimension. Inside the segments, the data values belonging to one dimension are arranged from the center of the circle to the outside in a back and forth manner orthogonal to the line that halves the segment. Our first results show that the ‘circle segment’ technique is very powerful for visualizing large amounts of data, providing more expressive visualizations than other wellknown techniques such as the ‘recursive pattern’ technique and traditional ‘line graphs’. <s> BIB010 </s> From visual data exploration to visual data mining: a survey <s> Taxonomy of Techniques by Keim <s> The display of multivariate datasets in parallel coordinates, transforms the search for relations among the variables into a 2-D pattern recognition problem. This is the basis for the application to visual data mining. The knowledge discovery process together with some general guidelines are illustrated on a dataset from the production of a VLSI chip. The special strength of parallel coordinates is in modeling relations. As an example, a simplified economic model is constructed with data from various economic sectors of a real country. The visual model shows the interelationship and dependencies between the sectors, circumstances where there is competition for the same resource, and feasible economic policies. Interactively, the model can be used to do trade-off analyses, discover sensitivities, do approximate optimization, monitor (as in a process) and provide decision support. <s> BIB011 </s> From visual data exploration to visual data mining: a survey <s> Taxonomy of Techniques by Keim <s> Our ability to accumulate large, complex (multivariate) data sets has far exceeded our ability to effectively process them in searching for patterns, anomalies and other interesting features. Conventional multivariate visualization techniques generally do not scale well with respect to the size of the data set. The focus of this paper is on the interactive visualization of large multivariate data sets based on a number of novel extensions to the parallel coordinates display technique. We develop a multi-resolution view of the data via hierarchical clustering, and use a variation of parallel coordinates to convey aggregation information for the resulting clusters. Users can then navigate the resulting structure until the desired focus region and level of detail is reached, using our suite of navigational and filtering tools. We describe the design and implementation of our hierarchical parallel coordinates system which is based on extending the XmdvTool system. Lastly, we show examples of the tools and techniques applied to large (hundreds of thousands of records) multivariate data sets. <s> BIB012 </s> From visual data exploration to visual data mining: a survey <s> Taxonomy of Techniques by Keim <s> Interactive selection is a critical component in exploratory visualization, allowing users to isolate subsets of the displayed information for highlighting, deleting, analysis, or focussed investigation. Brushing, a popular method for implementing the selection process, has traditionally been performed in either screen space or data space. We introduce the concept of a structure-based brush, which can be used to perform selection in hierarchically structured data sets. Our structure-based brush allows users to navigate hierarchies by specifying focal extents and level-of-detail on a visual representation of the structure. Proximity-based coloring, which maps similar colors to data that are closely related within the structure, helps convey both structural relationships and anomalies. We describe the design and implementation of our structure-based brushing tool. We also validate its usefulness using two distinct hierarchical visualization techniques, namely hierarchical parallel coordinates and tree-maps. <s> BIB013 </s> From visual data exploration to visual data mining: a survey <s> Taxonomy of Techniques by Keim <s> We present a visualization technique that allows a user to identify and detect patterns and structures within a multivariate data set. Our research builds on previous efforts to represent multivariate data in a 2D information display through the use of icon plots. Although the icon plot work done by Pickett and Brinstein is similar to our approach, we improve on their efforts in several ways. Our technique allows analysis of a time series without using animation; promotes visual differentiation of information clusters based on measures of variance; and facilitates exploration through direct manipulation of geometry based on scales of variance. Our goal is to provide a visualization that implicitly conveys the degree to which an elements ordered collection of attributes varies from the prevailing pattern of attributes for other elements in the collection. We apply this technique to multivariate abstract data nd use it to locate exceptional elements in a data set and divisions among clusters.© (2000) COPYRIGHT SPIE--The International Society for Optical Engineering. Downloading of the abstract is permitted for personal use only. <s> BIB014 </s> From visual data exploration to visual data mining: a survey <s> Taxonomy of Techniques by Keim <s> Visualization techniques are of increasing importance in exploring and analyzing large amounts of multidimensional information. One important class of visualization techniques which is particularly interesting for visualizing very large multidimensional data sets is the class of pixel-oriented techniques. The basic idea of pixel-oriented visualization techniques is to represent as many data objects as possible on the screen at the same time by mapping each data value to a pixel of the screen and arranging the pixels adequately. A number of different pixel-oriented visualization techniques have been proposed in recent years and it has been shown that the techniques are useful for visual data exploration in a number of different application contexts. In this paper, we discuss a number of issues which are important in developing pixel-oriented visualization techniques. The major goal of this article is to provide a formal basis of pixel-oriented visualization techniques and show that the design decisions in developing them can be seen as solutions of well-defined optimization problems. This is true for the mapping of the data values to colors, the arrangement of pixels inside the subwindows, the shape of the subwindows, and the ordering of the dimension subwindows. The paper also discusses the design issues of special variants of pixel-oriented techniques for visualizing large spatial data sets. <s> BIB015 </s> From visual data exploration to visual data mining: a survey <s> Taxonomy of Techniques by Keim <s> By means ofParallel Coordinates planar “graphs” of multivariate relations are obtained. Certain properties of the relationship correspond tothe geometrical properties of its graph. On the plane a point ←→ line duality with several interesting properties is induced. A new duality betweenbounded and unbounded convex sets and hstars (a generalization of hyperbolas) and between Convex Unions and Intersections is found. This motivates some efficient Convexity algorithms and other results inComputational Geometry. There is also a suprising “cusp” ←→ “inflection point” duality. The narrative ends with a preview of the corresponding results inR N . <s> BIB016
Keim and Kriegel BIB009 and Keim  grouped visual data exploration techniques for multivariate, multidimensional data into six classes, namely, geometric projection, iconbased, pixel-oriented, hierarchical, graph-based, and hybrid. In both works, an overall description and a comparison of the most representative techniques are provided. A summary of techniques mentioned by these and other authors is provided in  . Geometric projection techniques support users in the task of finding informative projections of multidimensional data sets. This class includes exploratory statistics techniques typically used for data processing, such as principal component analysis, factor analysis, and multidimensional scaling, and also the traditional Scatterplots [23] , in which two data attributes are projected along the x and y axes of a Cartesian coordinate system. Scatter plot matrices provide a variation targeted at multidimensional data in which multiple pairwise projections of the data attributes are shown simultaneously in a panel matrix. Another wellknown technique is Parallel Coordinates BIB011 , BIB016 , BIB002 , which maps a k-dimensional data or object space onto the 2D display by drawing k equally spaced axes parallel to one of the display axes. Each axis is associated with a data attribute and is linearly scaled within its corresponding attribute data range, which may be normalized if necessary. Each data item is presented as a polygonal line that intersects each axis at the point corresponding to the item's associated attribute data value. The technique is effective for revealing a wide range of data characteristics, such as different data distributions and functional dependencies. A major limitation, however, is that, even for relatively small data sets (say, with more than a few thousand data items), visual clutter and overlap can severely hamper the user's ability to interpret the visualizations and interact with them. Hoffman  adopts a radial arrangement of the axes and calls it Circular Parallel Coordinates and Fua et al. BIB012 present an extension tailored to cope with large and very large data sets. Their approach consists of displaying aggregation information derived from a hierarchical clustering of the data. Data clusters can be displayed at different levels of abstraction and using a color-coding approach based on cluster proximity, as depicted in Fig. 1 . They also introduce an interaction mechanism for dynamically navigating and filtering the hierarchy, called structure-based brushing BIB013 . Another high-dimensional geometric-based technique is the Radial Coordinate Visualization, RadViz  . For an n-dimensional visualization, n lines emanate radially from the center of a circle and terminate at its perimeter, each line associated with one attribute, as shown in Fig. 2 . Spring constants attached to the data attribute values define the positions of the data points (or, better, of their graphical representations) along the lines. The icon-based or iconographic display techniques map each multidimensional data item to an icon (or glyph) whose visual features vary depending on the data values. One of the first approaches is the Chernoff faces technique BIB001 ,  . Two data attributes are mapped to the 2D position of a face icon in the display and the remaining attributes are mapped to the properties of the face icon-the shape of nose, mouth, eyes, and the shape of the face itself. A shortcoming is that the different visual features are not really comparable to each other, except for some pairs. Additionally, some features are usually more salient than others to the human eye-for example, people usually pay more attention to eyes than to ears. The "stick figure" is another classical glyph example  ,  in which the icon is a figure with five limbs (see Fig. 3 ). Again, two attributes are mapped to the display dimensions and the remaining ones are mapped to the angles of the icon's limbs. If the data items are relatively dense with respect to the display dimensions, the resulting plots exhibit shifting textures, creating visual boundaries between texture regions that identify a shift in the characteristics of the represented data items. By drawing attention to shifts in the visual field, rather than to the actual features of individual glyphs, a user is able to quickly assess where shifts in characteristics occur within a large collection of items, as can be observed in Fig. 4 . Pickett's original stick figure provided exactly five attributes per icon, as he proposed using the orientation of the five "limbs" plus the (x, y) location, allowing a total of seven attributes. Additional attributes may be mapped to length, color, and other geometrical features or other visual attributes of the stick figure limbs. The concept of data-driven geometric icons has been extended to sound icons BIB008 in which data attributes determine sound parameters such as attack rate, intensity, and timbre, and to color icons BIB005 , which use color, texture, and shape. Shape coding is another icon-based technique BIB003 that allows visualization of an arbitrary number of attributes. The idea is to map the attributes to a small array of pixels so that each data item is represented by a pixel array taking the form of a square or rectangle. The pixels are mapped to a gray or color scale according to the value of their corresponding attributes, with the small squares or rectangles arranged successively in a line-by-line fashion. The basic concept of the stick figure is extended in BIB014 , whose authors also define a data-controlled glyph consisting of an ordered series of connected "feature segments," each segment mapped to a data attribute. The horizontal and vertical components of each feature segment are controlled by two measures on its associated attribute (the authors are using variances). If feature segments are represented as line segments, a noticeable gradual drift appears in each icon and in the resulting visualization. This can be eliminated by representing the feature segment as a small image, scaled along the horizontal and vertical axes according to the feature's associated measures. Because the interest is in the variance that a glyph exhibits from its counterparts, rather than in identifying individual components, glyphs can be stacked on top of one another at a single horizontal position, considerably increasing the number of data elements that can be shown. The authors illustrate their approach with visualizations of a document data set. The technique supports visual segregation of clusters of information elements based on degrees of variance with the prevailing characteristics of the collection. A hierarchy of variance can be displayed which the user can control to discover clusters, patterns, and exceptions. In pixel-based techniques, a pixel is used to represent data values: Different attributes are exhibited in different subwindows and the range of possible data values are mapped to pixels according to a fixed color map BIB015 , BIB009 ,  (Fig. 5 ). The techniques, suitable for large multidimensional data sets, are further categorized as "query independent" or "query dependent." In the query independent techniques, the arrangement of the pixels in the subwindows is fixed, independently of the data values themselves. In the query dependent ones, a query item is provided and distances from the data values to the given query value are computed using some metrics. The mapping of colors to pixels is based on the computed distances for each attribute and pixels in each subwindow are arranged according to their overall distances to the query data item. Fig. 5  illustrates visualizations using two of the possible arrangements of pixels, namely, spiral and axes arrangements (left and right, respectively), produced from a synthetic data set with uniform distribution and five 1 . Sequence of visualizations, at increasing levels of detail (from top left to bottom right), produced from a hierarchical clustering of a data set on fatal accidents with 230,000 data items. A hierarchical tree is created in which each node represents a nested collection of enclosed subclusters or data points. Variable width opacity bands are used to represent the information at each node, with color coding based on cluster proximity in the tree. The top left visualization shows a view of information at the root node of the tree, which provides a coarser level of detail, and the one at the bottom right shows a view of data at the leaf nodes, providing fine detail. From Fua et al. BIB012 . clusters. The data set has 7,000 data items with eight attributes. The color coding adopted ranges from bright yellow to green, blue, dark red, and almost black, based on the distance from a data item to the correct answers to a query: Data items that better satisfy a query are colored bright yellow and those further away from it are colored black. In Fig. 5 , the top left subwindows in each visualization depict the color coding and also the arrangement of the data items in each case (spiral and axes). These are called overall result windows, in which pixels representing data items are positioned according to their overall distance to the exact answer to the formulated query. The remaining subwindows exhibit the behavior of the eight attributes with respect to the query. The pixels for each data item are placed at the same relative position as they appear in the overall result window. The regions of different colors allow the identification of clusters of data items with a comparable distance and correlation among different attributes. An alternative to the regular partitioning of the display area into rectangular subwindows is proposed by Ankerst et al. BIB010 . They suggest displaying the range of values for each data attribute within a segment of a circle, as depicted in Fig. 6 , assuming a data set with eight attributes. Data items are arranged within a segment, as indicated by the arrows in the Fig. 6 so that a single data item appears in the same position at the different segments. The ordering of the data items within the segments, as well as their color, are determined, as in the previous arrangements, by their overall distance to those data items satisfying a user specified query. Hierarchical techniques subdivide the k-dimensional data space and present subspaces in a hierarchical fashion. Well-known representatives are n-Vision, also known as "Worlds-within-Worlds"  ,  and Dimension Stacking BIB004 . Both techniques can map Table Data , described in a k-dimensional nonhierarchical data space, onto a hierarchical 2D display space. Treemaps  and Cone Trees BIB006 are also examples of hierarchical visualization techniques, but they assume hierarchical structures within the data space and are thus not directly targeted at Table Data . Graph-based techniques visualize large graphs using specific layout algorithms, query languages, and abstraction techniques  ,  , BIB007 ,  to convey their meaning clearly and quickly. There are several approaches and systems targeted at this specific domain, which appear under the Network category in the taxonomy by Card et al., discussed in Section 3.2. Hybrid techniques integrate multiple visualization techniques, either in one or multiple windows, to enhance the expressiveness of the visualizations. Linking between visualization windows is a useful resource and most techniques rely heavily on dynamics and interaction (discussed in Section 3.4). An overview of multidimensional techniques under this categorization and a concise picture of their major characteristics are provided in Table 2 .