Parallel Coordinates: Interactive visualization for High Dimensions

Abstract

This story is about multidimensional visualization with Parallel Coordinates (abbr. ||-coords) which transform the search for relations in multivariate datasets into a 2-dimensional pattern recognition problem. The discovery process is illustrated by finding: ground features from remote sensing satellite data, and useful rules for gold, foreign currencies and stockmarket trading from a financial dataset. A complex dataset with two categories is classified using a geometric classification algorithm based on ||-coords. The minimal set of variables required to state the rule is found and ordered by their predictive value. A visual model of a real country’s economy is constructed showing how multivariate relations can be modeled by means of hypersurfaces. Interior points corresponding to feasible economic policies are constructed interactively finding that two sectors unknowingly compete for the same group of workers. An overview of modern ||-coords provides foundational understanding. The representation of an M -dimensional hypersurface is obtained from its (M −1) subsets which are constructed recursively from its points. There are examples of surfaces where convexity can be seen in any dimension as well as nonorientability(as in the Möbius strip), and features like folds, crevices, bumps which are hidden or distorted in other types of displays. This is a prelude of what is on the way: recursive multidimensional interactivity for uncovering the secrets in massive datasets.