Alfred Inselberg (auth.)9780387215075, 0387215077
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.
Table of contents :
Front Matter….Pages i-xxvi
Introduction….Pages 1-5
Geometry Background….Pages 7-48
♣ FT-1 The Plane with Parallel Coordinates….Pages 49-61
Multidimensional Lines….Pages 63-113
Planes, p -Flats, and Hyperplanes….Pages 115-183
** Envelopes….Pages 185-194
Curves….Pages 195-241
Proximity of Lines, Planes, and Flats….Pages 243-295
Hypersurfaces in ℝ N ….Pages 297-377
♣ FT Data Mining and Other Applications….Pages 379-427
Recent Results….Pages 429-488
Solutions to Selected Exercises….Pages 489-529
Back Matter….Pages 531-554
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