DBSCAN++: Towards fast and scalable density clustering

TL;DR

DBSCAN++ is a modified density-based clustering algorithm that reduces computational complexity by sampling density calculations, achieving faster runtime and robustness while maintaining statistical guarantees and optimal estimation rates.

Contribution

It introduces a sampling-based modification to DBSCAN that is faster, robust, and retains statistical consistency and optimal estimation rates.

Findings

DBSCAN++ is sub-quadratic in runtime.

It maintains minimax optimal rates for level-set estimation.

Empirical results show competitive performance with traditional DBSCAN.

Abstract

DBSCAN is a classical density-based clustering procedure with tremendous practical relevance. However, DBSCAN implicitly needs to compute the empirical density for each sample point, leading to a quadratic worst-case time complexity, which is too slow on large datasets. We propose DBSCAN++, a simple modification of DBSCAN which only requires computing the densities for a chosen subset of points. We show empirically that, compared to traditional DBSCAN, DBSCAN++ can provide not only competitive performance but also added robustness in the bandwidth hyperparameter while taking a fraction of the runtime. We also present statistical consistency guarantees showing the trade-off between computational cost and estimation rates. Surprisingly, up to a certain point, we can enjoy the same estimation rates while lowering computational cost, showing that DBSCAN++ is a sub-quadratic algorithm that attains minimax optimal rates for level-set estimation, a quality that may be of independent interest.