Multimodal Projection Pursuit using the Dip Statistics

Projection pursuit is the search for interesting low-dimensional projections of high-dimensional data. It optimizes projection indices, which increase with the interestingness of the projection image. Most classical approaches equate interestingness with non-gaussianity. However, in cluster analysis one should more be interested in departure from unimodality. The dip is an efficient nonparametric test measuring the distance of distributions from the class of unimodal distributions with respect to the maximum norm. In this paper, we demonstrate how the dip can be used in projection pursuit. We establish continuity and differentiability properties and develop efficient algorithms to search for projections maximizing the dip and extend them to find multiple interesting projections. Our algorithms are empirically evaluated on several surrogate and real-world data sets.