Parallel Coordinates: Visual Multidimensional Geometry and Its Applications

Hardcover | September 1, 2009

byAlfred Inselberg

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This book is about visualization, systematically incorporating the fantastic human pattern recognition into the problem-solving process, and focusing on parallel coordinates. The barrier, imposed by our three-dimensional habitation and perceptual experience, has been breached by this innovative and versatile methodology. The accurate visualization of multidimensional problems and multivariate data unlocks insights into the role of dimensionality.Beginning with an introductory chapter on geometry, the mathematical foundations are intuitively developed, interlaced with applications to data mining, information visualization, computer vision, geometric modeling, collision avoidance for air traffic and process-control. Many results appear for the first time. Multidimensional lines, planes, proximities, surfaces and their properties are unambiguously recognized (i.e. convexity viewed in any dimension) enabling powerful construction algorithms (for intersections, interior-points, linear-programming).Key features of Parallel Coordinates:* An easy-to-read self-contained chapter on data mining and information visualization* Numerous exercises with solutions, from basic to advanced topics, course projects and research directions* "Fast Track" markers throughout provide a quick grasp of essential material.* Extensive bibliography, index, and a chapter containing a collection of recent results (i.e. visualizing large networks, complex-valued functions and more)Parallel Coordinates requires only an elementary knowledge of linear algebra. It is well-suited for self-study and as a textbook (or companion) for courses on information visualization, data mining, mathematics, statistics, computer science, engineering, finance, management, manufacturing, in scientific disciplines and even the arts.

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From the Publisher

This book is about visualization, systematically incorporating the fantastic human pattern recognition into the problem-solving process, and focusing on parallel coordinates. The barrier, imposed by our three-dimensional habitation and perceptual experience, has been breached by this innovative and versatile methodology. The accurate v...

From the Jacket

This book is about visualization, systematically incorporating the fantastic human pattern recognition into the problem-solving process, and focusing on parallel coordinates. The barrier, imposed by our three-dimensional habitation and perceptual experience, has been breached by this innovative and versatile methodology. The accurate v...

Format:HardcoverDimensions:580 pages, 0.93 × 0.7 × 0.04 inPublished:September 1, 2009Publisher:Springer New YorkLanguage:English

The following ISBNs are associated with this title:

ISBN - 10:0387215077

ISBN - 13:9780387215075

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Table of Contents

Foreword.- Preface.- Introduction.- Geometry Background.- The Plane with Parallel Coordinates.- Multidimensional Lines.- Hyperplanes and p-Flats RN.- Envelopes.- Curves.- Proximity of Lines, Planes, and Flats.- Hypersurfaces in RN.- Data Mining and Other Applications.- Recent Results.- Solutions to Selected Exercises.- Notation and List of Symbols.- Bibliography.- Index.

Editorial Reviews

From the reviews:"Well done!"-Stephen Hawking, Cambridge UniversityParallel 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 ReviewsThe 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, DavisFor 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 high dimensional 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)