Determinantal consensus clustering

Random restart of a given algorithm produces many partitions that can be aggregated to yield a consensus clustering. Ensemble methods have been recognized as more robust approaches for data clustering than single clustering algorithms. We propose the use of determinantal point processes or DPPs for the random restart of clustering algorithms based on initial sets of center points, such as k-medoids or k-means. The relation between DPPs and kernel-based methods makes DPPs suitable to describe and quantify similarity between objects. DPPs favor diversity of the center points in initial sets, so that sets with similar points have less chance of being generated than sets with very distinct points. Most current inital sets are generated with center points sampled uniformly at random. We show through extensive simulations that, contrary to DPPs, this technique fails both to ensure diversity, and to obtain a good coverage of all data facets. The latter are two key properties that make DPPs achieve good performance. Simulations with artificial datasets and applications to real datasets show that determinantal consensus clustering outperforms consensus clusterings which are based on uniform random sampling of center points.