Exploring multivariate data using directions of high density

The most common techniques for graphically presenting a multivariate dataset involve projection onto a one or two-dimensional subspace. Interpretation of such plots is not always straightforward because projections are smoothing operations in that structure can be obscured by projection but never enhanced. In this paper an alternative procedure for finding interesting features is proposed that is based on locating the modes of an induced hyperspherical density function, and a simple algorithm for this purpose is developed. Emphasis is placed on identifying the non-linear effects, such as clustering, so to this end the data are firstly sphered to remove all of the location, scale and correlational structure. A set of simulated bivariate data and artistic qualities of painters data are used as examples.