Fast Parameterless Density-Based Clustering via Random Projections

Clustering offers significant insights in data analysis. Density-based algorithms have emerged as flexible and efficient techniques, able to discover high-quality -and potentially irregularly shaped- clusters. We present two fast density-based clustering algorithms based on random projections. Both algorithms demonstrate one to two orders of magnitude speedup compared to equivalent state-of-art density based techniques, even for modest-size datasets. We give a comprehensive analysis of both our algorithms and show runtime of O(dN log(2) N), for a d-dimensional dataset. Our first algorithm can be viewed as a fast variant of the OPTICS density-based algorithm, but using a softer definition of density combined with sampling. The second algorithm is parameter-less, and identifies areas separating clusters.