document: Making every bit count : fast nonlinear axis scaling 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 .
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