In this section, we concentrate on three main streams of software for interactive and dynamic statistical graphics: Software developed by researchers affiliated with the University of Augsburg, in particular REGARD, MANET, and Mondrian; software developed by researchers affiliated with George Mason University (GMU), in particular ExplorN and CrystalVision; and software developed by researchers affiliated with Bell Labs, AT&T, and Iowa State University (ISU), in particular XGobi and GGobi. [193] contains an in depth review of software for interactive statistical graphics. [194] is one of the few publications where the different interactive graphical concepts provided by these three main streams (represented by MANET, ExplorN, and XGobi, respectively) are applied to the same data set and thus allow a direct comparison of their features and capabilities in visual clustering and classification.
In this section we present a series of software developments that was initiated in the late 1980's by John Haslett and Antony Unwin at Trinity College, Dublin, and later was continued by Antony Unwin and his collaborators at the Institut für Mathematik, University of Augsburg. Other main collaborators that contributed to the development of these software tools that should be mentioned here are Heike Hofmann, Martin Theus, Adalbert Wilhelm, and Graham Wills.
Some of the early developments are Diamond Fast ([173]) and Spider ([60]). Diamond Fast is a software package for the exploration of multiple time series with interactive graphics. Spider is a software package for the exploration of spatially referenced data. Among its main features are moving statistics, an extension of brushing for spatial data ([60]). Spider also supports histograms, density estimates, scatterplot matrices, and linked brushing. It runs on Macintosh computers only.
REGARD ([174,169]) is a software package that also provides high interaction graphics tools for spatial data. REGARD stands for ''Radical Effective Graphical Analysis of Regional Data'' and runs on Macintosh computers only. REGARD supports four types of layers of spatial data, i.e., points, regions, lines, and pictures. The central display in REGARD is the map window that is linked to statistical displays such as boxplots, scatterplots, and rotating plots. A map may be loaded as one picture in a picture layer or as several pictures in several layers, thus allowing to turn on or off different aspects of a map (such as state boundaries or a road network). Additional interactive features are interrogation, highlighting, resizing, and rescaling. Advanced features include zooming into submaps, animation across ordered variables, cross-layer linking, network analysis tools, and interactive query tools across all graphical displays.
MANET ([172]) is a statistical graphics research program for EDA and written in C++. MANET stands for ''Missings Are Now Equally Treated'' and runs on Macintosh computers only. It is freely available from the following Web site: http://www1.math.uni-augsburg.de/Manet/.
MANET offers all standard one- and two-dimensional graphics for continuous data as well as for discrete data: dotplots, scatterplots, histograms, boxplots, bar charts. Some special graphics for discrete and spatial data are integrated: spine plots, mosaic plots and polygon plots. MANET grew out of a project to keep track of missing values in statistical graphics. In MANET all displays are fully linked and instantaneously updated. Displays are kept as simple as possible so they do not distract the user.
The standard use of linked views in MANET is to highlight clusters that are apparent in one dimension and to see these one-dimensional clusters in the light of other variables. By systematically subsetting the sample points, we can also detect two- and higher-dimensional clusters. Once a cluster has been detected, a classification rule can be set up by taking the boundary values of the cluster. In MANET those values can easily be obtained by interrogating the plot symbols.
One-dimensional views show the one-dimensional clusters directly. Two-dimensional clusters become visible by highlighting a subset in one variable and conditioning another plot on this subset. For three- and higher-dimensional clusters, we have to combine various subsets in different plots into one conditioning set and then we have to look at the remaining plots to check for clusters. The generation of such combined selections is not only possible in MANET but it is also very efficiently implemented through selection sequences.
In MANET, both dotplots and boxplots are drawn in a non-standard way. In dotplots the brightness of a point shows the frequency of its occurrence. This method, called tonal highlighting, is used to visualize overplotting of points. A bright color represents many points while a dark color represents just a few points. There is no tonal highlighting for selected points in MANET. The layout of boxplots is changed so that a standard boxplot can be superimposed for selected points. The inner fifty percent box is drawn as a dark grey box. The outer regions, usually represented as whiskers, are drawn as light grey boxes.
A recent new development, Mondrian (Theus, [163], [164]), is a data visualization system written in JAVA and therefore runs on any hardware platform. Mondrian is freely available from the following Web site: http://www.rosuda.org/Mondrian/.
The main emphasis of Mondrian is on visualization techniques for categorical and geographical data. All plots in Mondrian (see Fig. 10.4) are fully linked and offer various interrogations. Any case selected in one plot in Mondrian is highlighted in all other linked plots. Currently, implemented plots comprise mosaic plots, scatterplots, maps, bar charts, boxplots, histograms, and parallel coordinate plots. Mosaic plots in Mondrian are fully interactive. This includes not only linking, highlighting and interrogations, but also an interactive graphical modeling technique for loglinear models.
In this section we present a series of software developments that was initiated in the late 1980's by Daniel B. Carr (initially with Battelle Pacific Northwest Laboratories) and Edward J. Wegman at GMU. Other main collaborators that contributed to the development of these software tools that should be mentioned here are Qiang Luo and Wesley L. Nicholson.
EXPLOR4
([35]) is a research tool, originally implemented on a VAX
and written in FORTRAN. Its main features are rotation,
masking, scatterplots and scatterplot matrix, ray glyph plots, and
stereo views.
HyperVision, presented in [17], is a software product that has been implemented in PASCAL on an IBM RT under the AIX operating system as well as for MS-DOS machines. The latter implementation has a mouse-driven painting capability and can do real-time rotations of 3D scatterplots. Other displays are parallel coordinate plots, parallel coordinate density plots, relative slope plots, and color histograms. The main interactive features in HyperVision in addition to linked brushing are highlighting, zooming, and nonlinear rescaling of each axis.
ExplorN ([44]) is a more advanced software package than HyperVision and EXPLOR4, but with similar basic features. It runs on SGI workstations only, using either the GL or the OpenGL tools. ExplorN is freely available from the following ftp site: ftp://www.galaxy.gmu.edu/pub/software/.
ExplorN
supports scatterplot matrices, parallel coordinate plots,
icon-enhanced three-dimensional stereoscopic plots, 
-dimensional
grand tours and partial grand tours (i.e., tours based on a subset of
the variables with the remaining variables being held fixed), and
saturation brushing all in a high interaction graphics package.
The ExplorN software is intended to demonstrate principles rather than to be an operational tool so that some refinements normally found in operational software are not there. These include history tracking, easy point identification, identification of mixture weights in the grand tour, relabeling of axes during and after a grand tour as well as simultaneous multiple window views.
Although ExplorN
also supports conventional scatterplots and scatterplot matrices, one
of its outstanding features are parallel coordinate displays and
partial grand tours. Since it is easy to see pairwise relationships
for adjacent variables in parallel coordinate plots, but less easy for
nonadjacent variables, a complete parallel coordinate investigation
would require running through all possible permutations. Instead of
this, we recommend using the -dimensional parallel coordinate grand
tour that is implemented in ExplorN.
An important interactive procedure for finding clusters using parallel
coordinate plots is via the brush-tour.
CrystalVision is a recently developed successor of ExplorN, freely accessible at ftp://www.galaxy.gmu.edu/pub/software/. Its main advantage over the older package is that it is available for PCs. Similar to ExplorN, CrystalVision's (see Fig. 10.3) main focus is on parallel coordinate plots, scatterplots, and grand tour animations. Examples of its use, e.g., its EDA techniques applied to scanner data provided by the U.S. Bureau of Labor Statistics (BLS), can be found in [186].
In this section we present a series of software developments that was initiated in the mid 1980's by Andreas Buja, Deborah F. Swayne, and Dianne Cook at the University of Washington, Bellcore, AT&T Bell Labs, and ISU. Other main collaborators that contributed to the development of these software tools that should be mentioned here are Catherine Hurley, John A. McDonald, and Duncan Temple Lang.
The Data Viewer (Buja et al., [24], [22]; Hurley, [97], [98]; Hurley and Buja, [99]) is a software package originally developed on a Symbolics Lisp Machine that supports object-oriented programming. The Data Viewer is a system for the exploratory analysis of high-dimensional data sets that allows interactive labeling, identification, brushing, and linked windows. Additional features are viewport transformations such as expanding or shrinking of the data and shifting of the data. The Data Viewer supports several types of projections, including simple 3D rotations, correlation tour ([22]), and grand tour.
Many of the design and layout concepts of the Data Viewer as well as parts of its functionality provided the basic ideas for the follow-up XGobi (see Fig. 10.1), first described in [143] and [142]. Development on XGobi took place for about a decade; its almost final version is documented in [144]. XGobi is implemented in the X Windows System, so it runs on any UNIX system, and it runs under Microsoft Windows or the Macintosh operating system if an X emulator is used. XGobi can be freely downloaded from http://www.research.att.com/areas/stat/xgobi/.
XGobi is a data visualization system with interactive and dynamic methods for the manipulation of views of data. It offers 2D displays of projections of points and lines in high-dimensional spaces, as well as parallel coordinate plots. Projection tools include dotplots and ASH of single variables, scatterplots of pairs of variables, 3D data rotations, and grand tours. Views of the data can be panned and zoomed. Points can be labeled and brushed with glyphs and colors. Lines can be edited and colored. Several XGobi processes can be run simultaneously and linked for labeling, brushing, and sharing of projections. Missing data are accommodated and their patterns can be examined; multiple imputations can be given to XGobi for rapid visual diagnostics ([141]). XGobi can be cloned, i.e., an identical new XGobi process with exactly the same data and all brushing information can be invoked.
Rotating plots are nowadays implemented in most statistical packages, but the implementation in XGobi goes beyond most of the others. In addition to the standard grand tour, XGobi supports the projection pursuit guided tour. More details on projection pursuit indices available in XGobi can be found in Cook ([53], [54]). Additional index functions that result in speed improvements of the calculations have been presented in [108].
GGobi ([145]) is a direct descendant of XGobi, but it has been thoroughly redesigned. GGobi (see Fig. 10.2) can be freely downloaded from http://www.ggobi.org/.
At first glance, GGobi looks quite unlike XGobi because GGobi uses a newer graphical toolkit called GTK+ (http://www.gtk.org), with a more contemporary look and feel and a larger set of user interface components. Through the use of GTK+, GGobi can be used directly on Microsoft Windows, without any emulator. In addition, GGobi can be used on any UNIX and Linux system.
In contrast to XGobi, the plot window in GGobi has been separated from the control panel. In XGobi, there is in general a single plot per process; to look at multiple views of the same data, we have to launch multiple XGobi processes. In contrast, a single GGobi session can support multiple plots of various types: scatterplots, parallel coordinate plots, scatterplot matrices, and time series plots have been implemented so far. Other changes in GGobi's appearance and repertoire of tools (when compared to XGobi) include an interactive color lookup table manager, the ability to add variables ''on the fly'', and a new interface for view scaling (panning and zooming). At this point, some of the advanced grand tour and projection pursuit guided tour features from XGobi have not been fully reimplemented in GGobi (but hopefully will be available in the near future).
While the previous sections summarize software that focuses on interactive and dynamic graphics, there exist several statistical languages that provide a tight integration of interactive graphics and numerical computations. Examples for such languages are S/S-PLUS ([12,11,45]), R ([100]), and XploRe ([84]). Other examples of software that link interactive graphics, computation, and spread sheets, often through the Web, are the Data Representation System (DRS) by [101], DAVIS by [95], KyPlot by [200], and the XploRe Quantlet Client/Server (XQC/XQS) architecture ([107]).