Abstract:

For people working on multivariate (multidimensional) problems, it is important to understand the underlying geometry, as it may dictate what is possible and what is not. For example, in 1917 the physicist Ehrenfest showed that planetary orbits are stable only in dimension 3. Another dimensionality result is that rotating bodies have an axis of rotation only in odd-integer dimensions. The applications presented here will be more down to earth!

From a system of parallel coordinates a one-to-one mapping between subsets of N-space and subsets of 2-space is obtained. This leads to synthetic construction algorithms in N-space involving intersections, proximity, interior point construction and "Line and Plane Topologies" useful in Computer Vision and Geometric Modeling, as well as Collision Avoidance Algorithms for Air Traffic Control. Applications to Visual Data Mining are illustrated with real datasets on Process Control, VLSI production, Financial Analysis, Feature Extraction from LandSat Data etc. A new geometric Automatic Classifier is demonstrated on several high-dimensional datasets. Time permitting, a Decision Support system capable of doing Feasibility, Trade-Off and Sensitivity Analyses will be included.