Projection Pursuit Indices Based on the Empirical Distribution Function

Exploratory projection pursuit is a technique for finding interesting low-dimensional projections of multivariate data. To reach this goal, one optimizes an index, assigned to every projection, that characterizes the structure present in the projection. Most indices require the estimation of the marginal density of the projected data. Such estimations involve a tuning parameter that greatly influences the behavior of the index. However, the optimization is usually performed with an ad hoc, often fixed value for this parameter. This article proposes indices based on the empirical distribution function that do not require to be tuned. This allows users to use exploratory projection pursuit without having to predetermine an "esoteric" tuning parameter.