Parallel Coordinates: Visual Multidimensional Geometry and Its Applications

The breakthrough idea of parallel coordinates has enchanted many people with its cleverness and power. Al Inselberg, the source of that cleverness and power, ?nally shares the depth and breadth of his invention in this historically important book. I’ve been waiting impatiently for this exposition since I was captivated by Inselberg’slectureattheUniversityofMarylandin1979.Hehadalreadyunderstood the potential parallel coordinates has for generating insights into high-dimensional analysis and information visualization. In the following decades he polished the arguments, built effective software, and demonstrated value in important appli- tions. Nowabroadcommunityofreaderscanbene?tfromhisinsightsandeffective presentation. I believe that Inselberg’s parallel coordinates is a transformational ideal that ´ matches the importance of Rene Descartes’ (1596–1650) invention of Cartesian coordinates. Just as Cartesian coordinates help us understand 2D and 3D geometry, parallel coordinates offer fresh ways of thinking about and proving theorems in higher-dimensional geometries. At the same time they will lead to more powerful tools for solving practical problems in a wide variety of applications. It is rare to encounter such a mind-shattering idea with such historic importance. While Inselberg’s insight and exposition opens the door to many discoveries, there is much work to be done for generations of mathematicians, computer sci- tists, programmers, and domain experts who will need to build on these innovative ideas.

Table of Contents:
Geometry Background.- ? FT-1 The Plane with Parallel Coordinates.- Multidimensional Lines.- Planes, p-Flats, and Hyperplanes.- ** Envelopes.- Curves.- Proximity of Lines, Planes, and Flats.- Hypersurfaces in ?N.- ? FT Data Mining and Other Applications.- Recent Results.- Solutions to Selected Exercises.

Review :
From the reviews: "Well done!" —Stephen Hawking, Cambridge University Parallel coordinates provide a means of visualizing geometric objects in many dimensions. They are particularly useful for displaying multivariate data and supporting multivariate analysis…  This book is written as a textbook designed for use in a one semester course in applied mathematics or computer science... There are several applications discussed in the book. These include an extended example in air traffic control and collision avoidance, (where Inselberg’s methods are used to display multiple flight trajectories), geometric modeling, computer vision, process control, statistics, automatic classification, and decision support. Inselberg is a very enthusiastic advocate of his methods and he has written a big book, bursting with ideas … . Prerequisites for the book include some familiarity with linear algebra, a bit of basic multivariable calculus, and willingness to work through extended geometrical arguments. —MAA Reviews The book is very attractive visually, with enjoyable prose, rare historical references and splendid organization like the "fast track" and Interactive Learning Module (ILM). Parallel Coordinates is the first in-depth, comprehensive book describing a geometrically beautiful and practically powerful approach to multidimensional data analysis. I can highly recommend this book to everyone concerned with data analysis and visualization problems. The book is delightful. —Bernd Hamann, Professor of Computer Science, University of California, Davis For me the parallel coordinates method was only a visualization and presentation tool, with no impact on data understanding... Now this book, from the very same parallel coordinates inventor, has  changed everything. Now I see how the method's solid geometric foundation makes it both an ideal tool to understand highdimensional datasets and a source of novel ideas even for fields far from data analysis....there are few visualization techniques with so solid geometrical and mathematical foundations like parallel coordinates and the book provides plenty of support to a broad spectrum of readers, from the results-inclined analyst to the more theory-captivated academician. —Ing. Mario Valle , Data Analysis and Visualization Group , Swiss National Supercomputing Centre (CSCS) "This text provides a detailed mathematical treatment of parallel-coordinate geometry for mathematics students and similar readers, and the ... chapters are a course in parallel-coordinate geometry, as developed by Inselberg and his collaborators." (John Wilson, Engineering & Technology, February, 2010)