Skinny-dip: Clustering in a Sea of Noise
Samuel Maurus*, Helmholtz Zentrum München; Claudia Plant
Can we ﬁnd heterogeneous clusters hidden in data sets with 80% noise? Although such settings occur in the real-world, we struggle to ﬁnd methods from the abundance of clustering techniques that perform well with noise at this level. Indeed, perhaps this is enough of a departure from classical cluster-ing to warrant its study as a separate problem. In this paper we present SkinnyDip which, based on Hartigan’s elegant dip test of unimodality, represents an intriguing approach to clustering with an attractive set of properties. Speciﬁcally, SkinnyDip is highly noise-robust, practically parameter-free and completely deterministic. SkinnyDip never performs multivariate distance calculations, but rather employs in-sightful recursion based on “dips” into univariate projections of the data. It is able to detect a range of cluster shapes and densities, assuming only that each cluster admits a unimodal shape. Practically, its run-time grows linearly with the data. Finally, for high-dimensional data, continuity properties of the dip enable SkinnyDip to exploit multimodal projection pursuit in order to ﬁnd an appropriate basis for clustering. Although not without its limitations, SkinnyDip compares favorably to a variety of clustering approaches on synthetic and real data, particularly in high-noise settings.