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Mathematics - Computational Science & Engineering | Parallel Coordinates - Visual Multidimensional Geometry and Its Applications

Parallel Coordinates

Visual Multidimensional Geometry and Its Applications

Inselberg, Alfred

2009, XXVI, 554 p.

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  • All contents of the CD ROM is included as Extras through Springer, saving the reader hours of typing. Access Extras here: http://extras.springer.com/2009/978-0-387-68628-8 and http://extras.springer.com/2009/978-0-387-56216-2
  • Offers readers an authoritative account from the developer of the theory
  • Details applications to visual and automatic data mining, collision avoidance algorithms for air traffic control, geometric modeling and computer vision, decision support, information visualization
  • Only text to build theory from the foundations of projective geometry, giving readers a deeper understanding of the material

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.

Content Level » Lower undergraduate

Keywords » Algebra - Computer Vision - Information Visualization - cognition - data mining - linear algebra - visualization

Related subjects » Algebra - Computational Science & Engineering - Database Management & Information Retrieval - Epistemology & Philosophy of Science - Geometry & Topology - Image Processing

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.

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