Multidimensional Visualization and its Applications
Prof. Alfred Inselberg
Visualization systematically incorporates our fantastic pattern recognition ability into the problem-solving process. With parallel coordinates the perceptual barrier imposed by our 3-dimensional habitation is breached enabling the visualization of multidimensional problems. Beginning with some projective geometry the mathematical foundations are developed. Multidimensional lines and (hyper)planes are recognized even in the presence of errors. Applications include Collision Avoidance Algorithms for Air Traffic Control, Data Mining for High-Dimensional datasets (some with hundreds of variables), Automatic Classification (feature extraction), and more. Properties of (hyper)surfaces are visually detected from their representation, convexity is seen in any dimension as well as non-convexities (i.e. folds, bumps, depressions etc) also non-orientability (i.e. Moebius Strip). The topics are illustrated with many interactive demonstrations and further applications on Decision Support (Trade-off Analysis), Topics in Statistics, Process Control, Analysis of Large Networks, Visualizing Complex Valued Functions. The course is suitable for good 2nd & 3rd year as well as M.Sc. and Ph.D. students. Linear Algebra and a course on Algorithms with Data Structures are prerequisites — or consent of the instructor.
IMPORTANT. A complete overview of the course with demos will be given in the first lecture.
Beautiful website Milestones in Thematic Cartography by M. Friendly et al:
www.math.yorku.ca/scs/SCS/Gallery/milestones – take a look.