Making every bit count: fast nonlinear axis scaling

Leejay Wu, Christos Faloutsos

Abstract: Existing axis scaling and dimensionality methods focus on preserving structure, usually determined via the Euclidean distance. In other words, they inherently assume that the Euclidean distance is already correct. We instead propose a novel nonlinear approach driven by an information-theoretic viewpoint, which we show is also strongly linked to intrinsic dimensionality, or degrees of freedom; and uniformity. Nonlinear transformations based on common probability distributions, combined with information-driven selection, simultaneously reduce the number of dimensions required and increase the value of those we retain. Experiments on real data confirm that this approach reveals correlations, finds novel attributes, and scales well.