Modern Parallel Coordinates

Abstract

The desire to augment our 3-dimensional perception and the need to understand multivariate problems spawned several multidimensional visualization methodologies. Understanding the underlying geometry of a multivariate problem provides insight into what is possible and what is not. After a short overview, Parallel Coordinates are introduced and developed rigorously showing, using new didactic software, how multidimensional lines, hyperplanes, flats, curves and smooth hypersurfaces can be visualized unambiguously. The development is interlaced with applications including Visual Data Mining (EDA) on real datasets (i.e. Feature extraction, GIS, Financial, Process Control, and others with hundreds of variables). There follow collision avoidance algorithms for air trafic control and detection of coplanarity and near-coplanarity with numerous applications. A geometric automatic classifier is applied to challenging clustering and classification problems. It provides the classification rule explicity and visually. Nonlinear VISUAL models in terms of hypersurfaces are constructed from data and used interactively for Decision Support discovering Feasibilites, Interelations, Sensitivities, enabling Constraint and Trade-Off Analysis. Our goal is to concentrate the relational information within a dataset into clear patterns eliminating the polygonal lines altogether. In view of recent results this prospect is becoming attainable as illustrated with a difficult problem central to many applications(Computer Vision, Geometric Modeling, Statistics).