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Parallel Coordinates: Visual Multidimensional Geometry and Its Applications 2009th Edition

7 customer reviews
ISBN-13: 978-0387215075
ISBN-10: 0470856181
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Editorial Reviews

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The book is very attractive visually, with enjoyable prose, rare historical references and splendid organization like the "fast track" and Interactive Learning Module (ILM).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 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)

From the Back Cover

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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Product Details

  • Hardcover: 554 pages
  • Publisher: Springer; 2009 edition (September 1, 2009)
  • Language: English
  • ISBN-10: 0470856181
  • ISBN-13: 978-0387215075
  • ASIN: 0387215077
  • Product Dimensions: 9.6 x 7.3 x 1.3 inches
  • Shipping Weight: 2.8 pounds (View shipping rates and policies)
  • Average Customer Review: 4.9 out of 5 stars  See all reviews (7 customer reviews)
  • Amazon Best Sellers Rank: #1,074,924 in Books (See Top 100 in Books)

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7 of 7 people found the following review helpful By Valle Mario on March 20, 2010
Format: Hardcover
I work in the visualization area since 1995 and parallel coordinates was
one of the first methods I played with when enlarged my horizons from
scientific visualization (few variables, mostly three-dimensional,
mature toolbox of techniques) to information visualization
(multidimensional spaces, techniques full of wild creativity).
But I must confess never got it. 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 high dimensional
datasets and a source of novel ideas even for fields far from data analysis.

Reading the book two points have caught my interest. First, parallel
coordinates are a live projective geometry laboratory where concepts,
like line-point duality, acquire a practical meaning that helps to
understand visualized patterns. That also means that it is better to
study this book before proposing "creative enhancements" to the
technique. Second, I never realized that parallel coordinates could be
applied to surfaces and volumes and not only to sets of points. This
idea increases the technique's usefulness by literally making visible
the high dimensional space under analysis.

I like to mix concepts and ideas from unrelated fields because I'm
convinced new ideas often appear on the border between disciplines. I found
the book goes exactly in this direction: the geometry, the method's
theory and the applications examples help spark novel ideas. Do you need
examples?
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8 of 9 people found the following review helpful By Bernd Hamann on January 11, 2010
Format: Hardcover
I have studied the fields of geometric modeling and especially scientific data visualization for more than twenty years, and am very impressed by the high quality of this book. Methods from differential geometry and computer aided geometric design and analysis have always been at the core of most of my efforts in scientific data processing and presentation. Alfred Inselberg's book strikes me as a wonderful example for "blending" in very effective ways fundamental concepts from geometry with relevant, practical data analysis and visualization problems encountered in an ever increasing number of scientific and engineering areas confronted with the analysis of very large, very complex, and high-dimensional data. Not only the power but also the mathematical foundations of "Parallel Coordinates" are impressive.

By learning to untangle patterns from the display of multivariate data a powerful knowledge discovery evolved. Guidelines for the exploration and good query design are attractively illustrated for real datasets (Chapter 10). Realizing that this approach is intrinsically limited leads to a deeper geometrical insight, the recognition of M-dimensional objects recursively from their (M-1)-dimensional subsets. What lies behind this striking cognitive success are the "super-planes," a class of planes whose points are represented by straight rather than polygonal lines. The absence of a corresponding analogy in Cartesian coordinates shows that parallel coordinates are an extremely powerful way of doing and seeing multidimensional geometry. It emerges that any hyperplane in N dimensions is represented by (N-1) points with N indices, i.e., two points with three indices represent a plane in three-dimensional space.

Surfaces in N dimensions are represented by (N-1) regions.
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4 of 4 people found the following review helpful By Dimitri Shvorob on October 14, 2012
Format: Hardcover
OK, you have seen a parallel-coordinates plot - is there much more to it than meets the eye, and should you get a whole book to find out? I would suggest "no" to both questions. This is a very substantial mathematics book, but if you are interested in EDA, you only get about thirty pages in Chapter 10, which showcases Parallax, the author's commercial software package. (Its key feature is brushing, i.e. highlighting a subset of observations on a plot; in Parallax GUI, subsets are defined, in point-and-click way, using filters on variables' values and mutual ratios). The author gives a good work-out to the PC plot, but it's all pretty simple to begin with. (Sometimes too simple: some not-quite-kosher statistical statements show up, and limitations of the PC plot are never mentioned). Endorsements by non-mathematicians are quite surprising: perhaps they can explain what specific visualization wisdom they picked up from the book?
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2 of 2 people found the following review helpful By Gregory Piatetsky on July 29, 2011
Format: Hardcover
I have extensive experience in data mining and have used many analytical and visualization tools. One of the first and most important tasks in data analysis is to visualize the data, but it was very hard to do in more than 3 dimensions until Alfred Inselberg's breakthrough invention of Parallel coordinates.

Parallel coordinates allow analysts to examine the data in many new ways and I was able to use them to find new and useful patterns on several projects.

This book is the definitive work on Parallel coordinates from the inventor himself. It is well written, with enjoyable prose, rare historical references and splendid organization like the "Fast track" and Interactive Learning Module (ILM). There is potential for new applications like the visualization of regression with the techniques developed in Chapters 5 and 8 as well as the detection near-coplanarity in any dimension.

The book has both a rigorous mathematical treatment and over 200 beautiful color illustrations - a visual delight. Enjoy it and discover new things in your data !

Gregory Piatetsky-Shapiro, KDnuggets
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