Never before in history has data been generated at such high volumes as it is today. Exploring and analyzing the vast volumes of data is becoming increasingly difficult. Information visualization and visual data mining can help to deal with the flood of information. The advantage of visual data exploration is that the user is directly involved in the data mining process. There are a large number of information visualization techniques which have been developed over the last decade to support the exploration of large data sets. In this paper, we propose a classification of information visualization and visual data mining techniques which is based on the data type to be visualized, the visualization technique, and the interaction and distortion technique. We exemplify the classification using a few examples, most of them referring to techniques and systems presented in this special section.

We propose a rudimentary taxonomy of interactive data visualization based on a triad of data analytic tasks: finding Gestalt, posing queries, and making comparisons. These tasks are supported by three classes of nteractive view manipulation: focusing, linking and arranging views. This discussion extends earlier work on the principles of focusing and linking and sets them on a firmer base. Next, we give a high-level introduction to a particular system for multivariate data visualization: XGobi. This introduction is not comprehensive but emphasizes XGobi tools that are examples of focusing, linking and arranging views, namely: high-dimensional projections, linked scatterplot brusing, and matrices of conditional plots.

Structural comparison of large trees is a difficult task that is only partially supported by current visualization techniques, which are mainly designed for browsing. We present TreeJuxtaposer, a system designed to support the comparison task for large trees of several hundred thousand nodes. We introduce the idea of “guaranteed visibility”, where highlighted areas are treated as landmarks that must remain visually apparent at all times. We propose a new methodology for detailed structural comparison between two trees and provide a new nearly-linear algorithm for computing the best corresponding node from one tree to another. In addition, we present a new rectilinear Focus+Context technique for navigation that is well suited to the dynamic linking of side-by-side views while guaranteeing landmark visibility and constant frame rates. These three contributions result in a system delivering a fluid exploration experience that scales both in the size of the dataset and the number of pixels in the display. We have based the design decisions for our system on the needs of a target audience of biologists who must understand the structural details of many phylogenetic, or evolutionary, trees. Our tool is also useful in many other application domains where tree comparison is needed, ranging from network management to call graph optimization to genealogy.

We address the question: How should N n-dimensional subspaces of m-dimensional Euclidean space be arranged so that they are as far apart as possible? The results of extensive computations for modest values of N; n; m are described, as well as a reformulation of the problem that was suggested by these computations. The reformulation gives a way to describe n- dimensional subspaces of m-space as points on a sphere in dimension (m \Gamma 1)(m+2), which provides a (usually) lowerdimensional representation than the Pl ucker embedding, and leads to a proof that many of the new packings are optimal. The results have applications to the graphical display of multidimensional data via Asimov's grand tour method.

AbstractÐVisualization techniques are ofincreasing importance in exploring and analyzing large amounts ofmultidimensional information. One important class of visualization techniques which is particularly interesting for visualizing very large multidimensional data sets is the class ofthe pixel-oriented techniques. The basic idea ofpixel-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 ofthe 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 ofissues which are ofhigh importance in developing pixel-oriented visualization techniques. The major goal ofthis 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 ofwell-defined optimization problems. This is true for the mapping ofthe data values to colors, the arrangement ofpixels inside the subwindows, the shape ofthe subwindows, and the ordering ofthe dimension subwindows. The paper also discusses the design issues of special variants of pixel-oriented techniques for visualizing large spatial data sets. The optimization functions for the mentioned design decisions are important for the effectiveness of the resulting visualizations. We show this by evaluating the optimization functions and comparing it the results to the visualization obtained in a number of different application. Index TermsÐInformation visualization, visualizing large data sets, visualizing multidimensional and multivariate data, visual data exploration, visual data mining. 1

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, in the first place the perception of properties of the data counts, and only in the second place the CPU time and the number of secondary storage accesses are important. In addition to testing the visualization techniques using re...

The grand tour and projection pursuit are two methods for exploring multivariate data. We show how to combine them into a dynamic graphical tool for exploratory data analysis, called a projection pursuit guided tour. This tool assists in clustering data when clusters are oddly shaped and in finding general low-dimensional structure in high dimensional, and in particular, sparse data. An example shows that the method, which is projection-based, can be quite powerful in situations which may cause methods based on kernel-smoothing grief. The projection pursuit guided tour is also useful for comparing and developing projection pursuit indices and illustrating some types of asymptotic results. 1 Introduction In this paper we show that two graphical methods for exploring high (say p) dimensional data, the grand tour (Asimov, 1985; Buja and Asimov, 1986), a dynamic tool, and projection pursuit (Kruskal, 1969; Friedman and Tukey, 1974; Huber, 1985), a static tool, naturally complement each o...

We present a survey of multidimensional multivariate (mdmv) visualization techniques developed during the last three decades. This subfield of scientific visualization deals with the analysis of data with multiple parameters or factors, and the key relationships among them. The course of development is roughly organized into four stages, within which major milestones are discussed. Recently developed techniques are explored with examples. 1 Introduction Multidimensional multivariate visualization is an important subfield of scientific visualization. It was studied separately by statisticians and psychologists long before computer science was deemed a discipline. The appearance of low-priced personal computers and workstations during the 1980's breathed new life into graphical analysis of mdmv data. This research topic was among one of the short-term goals included in the 1987 National Science Foundation (NSF) sponsored workshop on Visualization in Scientific Computing [MDB87]. Th...

This article is intended to be the published standard reference to the XGobi system. The article gives an overview of the functionality of the system as well as a discussion

The quest to find models usefully characterizing data is a process central to the scientific method, and has been carried out on many fronts. Researchers from an expanding number of fields have designed algorithms to discover rules or equations that capture key relationships between variables in a database. The task of this chapter is to provide a perspective on statistical techniques applicable to KDD; accordingly, we review below some major advances in statistics in the last few decades. We next highlight some distinctives of what may be called a "statistical viewpoint." Finally we overview some influential classical and modern statistical methods for practical model induction.