Edward J. Wegman

Hyperdimensional Data Analysis Using Parallel Coordinates

Abstract This article presents the basic results of using the parallel coordinate representation as a high-dimensional data analysis tool. Several alternatives are reviewed. The basic algorithm for parallel coordinates is laid out and a discussion of its properties as a projective transformation is given. Several duality results are discussed along with their interpretations as data analysis tools. Permutations of the parallel coordinate axes are discussed, and some examples are given. Some extensions of the parallel coordinate idea are given. The article closes with a discussion of implementation and some of my experiences.

High Dimensional Clustering Using Parallel Coordinates and the Grand Tour.

In this paper, we present some graphical techniques for cluster analysis of high-dimensional data. Parallel coordinate plots and parallel coordinate density plots are graphical techniques which map multivariate data into a two-dimensional display. The method has some elegant duality properties with ordinary Cartesian plots so that higher-dimensional mathematical structures can be analyzed. Our high interaction software allows for rapid editing of data to remove outliers and isolate clusters by brushing. Our brushing techniques allow not only for hue adjustment, but also for saturation adjustment. Saturation adjustment allows for the handling of comparatively massive data sets by using the α-channel of the Silicon Graphics workstation to compensate for heavy overplotting.

Huge Data Sets and the Frontiers of Computational Feasibility

Abstract Recently, Huber offered a taxonomy of data set sizes ranging from tiny (102 bytes) to huge (1010 bytes). This taxonomy is particularly appealing because it quantifies the meaning of tiny, small, medium, large, and huge. Indeed, some investigators consider 300 small and 10,000 large while others consider 10,000 small. In Hubers taxonomy, most statistical and visualization techniques are computationally feasible with tiny data sets. With larger data sets, however, computers run out of computational horsepower and graphics displays run out of resolution fairly quickly. In this article, I discuss aspects of data set size and computational feasibility for general classes of algorithms in the context of CPU performance, memory size, hard disk capacity, screen resolution and massively parallel architectures. I discuss some strategies such as recursive formulations that mitigate the impact of size. I also discuss the potential for scalable parallelization that will mitigate the effects of computational ...

RETRACTED: Social networks of author--coauthor relationships

Social network analysis has proven to be a useful tool in analysis of many situations. We begin by giving an overview of social network analysis. We then illustrate the concepts by examining the social networks of co-authors of scholarly publications. Scholarly publication is in many ways the lifeblood of academic institutions and there are strong incentives, both in terms of prestige and financial compensation, for faculty members to publish. Different disciplines and individuals have evolved distinguishable mechanisms for coping with the publication pressures. We examine the co-authorship networks of a number of prominent scholars. Based on the clustering within the co-author social network, we distinguish several styles of co-authorship including solo models (no co-authors), mentor models, entrepreneurial models, and team models. We conjecture that certain styles of co-authorship lead to the possibility of group-think, reduced creativity, and the possibility of less rigorous reviewing processes.

26 Statistical graphics and visualization

Publisher Summary This chapter focuses on the use of graphics and visualization methods for statistical analysis. The traditional use of graphics in statistics had been principally relegated to simple two-dimensional graphics, such as scatterplots and histograms. However, modern computer graphics methods introduce a host of new techniques that literally allow an explosion of new methods for a much more geometric understanding of statistical and scientific data. Computer graphics allows an easy leap to visualizing three-dimensional data and to using animation, lighting, rendering, transparency, and a host of other techniques. The chapter covers some of the basic elements of computer-based graphics and gives an overview of some of the resulting statistical graphics and visualization methods. Geographic information system (GIS) is one of the spin-off technologies from the revolution in computers and computer graphics and is closely linked to spatial data representation via graphics. Geometry clearly plays a central role in computer and statistical graphics. If geometry plays a pivotal role in graphics and visualization, an equally pivotal role is played by the area of the vision theory.

On Some Techniques for Streaming Data: A Case Study of Internet Packet Headers

We consider the implications of streaming data for data analysis and data mining. Streaming data are becoming widely available from a variety of sources. In our case we consider the implications arising from Internet traffic data. By implication, streaming data are unlikely to be time homogeneous so that standard statistical and data mining procedures do not necessarily apply. Because it is essentially impossible to store streaming data, we consider recursive algorithms, algorithms which are adaptive and discount the past and also algorithms that create finite pseudo-samples. We also suggest some evolutionary graphics procedures that are suitable for streaming data. We begin our discussion with a discussion of Internet traffic in order to give the reader some sense of the time and data scale and visual resolution needed for such problems.

The Bumpy Road to the Mode Forest

Abstract The mode tree of Minnotte and Scott provides a valuable method of investigating features such as modes and bumps in a unknown density. By examining kernel density estimates for a range of bandwidths, we can learn a lot about the structure of a data set. Unfortunately, the basic mode tree can be strongly affected by small changes in the data, and gives no way to differentiate between important modes and those caused, for example, by outliers. The mode forest overcomes these difficulties by looking simultaneously at a large collection of mode trees, all based on some variation of the original data, by means such as resampling or jittering. The resulting graphic tool is both visually appealing and informative.

The Grand Tour in k-Dimensions

The grand tour introduced by Asimov (1985) is based on the idea that one method of searching for structure in d-dimensional data is to “look at it from all possible angles,” more mathematically, to project the data sequentially in to all possible two-planes. The collection of two-planes in a d-dimensional space is called a Grassmannian manifold. A key feature of the grand tour is that the projection planes are chosen according to a dense, continuous path through the Grassmannian manifold which yields the visual impression of points moving continuously.

Immersive Projection Technology for Visual Data Mining

The PlatoCAVE, the MiniCAVE, and the C2 are immersive stereoscopic projectionbased virtual reality environments oriented toward group interactions. As such they are particularly suited to collaborative efforts in data analysis and visual data mining. In this article, we provide an overview of virtual reality in general, including immersive projection technology, and the use of stereoscopic displays for data visualization. We discuss design considerations for the construction of these immersive environments including one-wall versus four-wall implementations, augmented reality, stereoscopic placement, head tracking, the use of LCD devices, polarized light stereo, voice control, and image synchronization.

Visual clustering and classification: The Oronsay particle size data set revisited

SummaryInteractive statistical graphics can be effectively used to find natural groupings in observations. In this paper we want to demonstrate how clustering and classification can be done with three approaches based on highly interactive graphical environments: high-dimensional scatterplots as available in XGobi, parallel coordinate plots as available in EXPLORN, and linked low-dimensional views as available in MANET. We will point out the strenghts and the weaknesses of these techniques by comparing their behaviour when applied to the Oronsay particle size data set.