2018/10/31 by Jennifer Jang, Heinrich Jiang, Jang, Jennifer +1 · 1 citation
Computer Science · #Advanced Clustering Algorithms Research #Bayesian Methods and Mixture Models #Data Management and Algorithms #FOS: Computer and information sciences #Machine Learning (cs.LG) #Machine Learning (stat.ML)
paper · pdf · doi:10.48550/arxiv.1810.13105
openalex publication_date 2018/10/31 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.