Parallel Coordinates Visual Multidimensional Geometry and Its Applications - Inselberg, Alfred; SpringerLink (Online service) (New York, NY : Springer New York, 2009)
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.
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.
Keywords: Mathematics; Philosophy and science; Data mining; Image processing; Algebra; Visualization; Geometry; Mathematics; Visualization; Philosophy of Science; Algebra; Image Processing and Computer Vision; Geometry; Data Mining and Knowledge Discovery; Electronic books