[Paper Review] DBSCAN++: Towards fast and scalable density clustering

Jennifer Jang, Heinrich Jiang|arXiv (Cornell University)|Oct 31, 2018

Advanced Clustering Algorithms Research43 citations

TL;DR

DBSCAN++ is a sub-quadratic variant of DBSCAN that computes densities for a subset of points, yielding faster clustering with competitive accuracy and robustness to bandwidth.

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.

Motivation & Objective

• Motivate the need for faster density-based clustering on large datasets where DBSCAN has quadratic worst-case complexity.
• Introduce DBSCAN++ as a modification that computes densities for a subset of points to reduce computations.
• Establish statistical consistency guarantees and quantify the trade-off between computation and estimation rates.
• Demonstrate empirical speedups and robust clustering performance across hyperparameters on real and simulated data.

Proposed method

• Define core-points as points with at least minPts within an eps-neighborhood.
• Propose DBSCAN++ which selects a subset S of m points to compute densities and builds a core-point graph from S.
• Use uniform sampling (Algorithm 2) or greedy K-center initialization (Algorithm 3) to choose the subset S.
• Construct a neighborhood graph on core-points and obtain clusters as connected components, assigning non-core points to nearest core-points.
• Analyze time complexity as O(nm) and show consistency with respect to the density level-set estimation.
• Provide pruning of core-points to improve robustness and prevent false connections between distant components.

Experimental results

Research questions

• RQ1 Can computing densities for only a subset of points still recover the density level-set and connected components as in DBSCAN?
• RQ2 What is the trade-off between the subset size m and the estimation rate and clustering accuracy?
• RQ3 Do uniform sampling and K-center-based sampling provide theoretical guarantees and practical robustness advantages over DBSCAN?
• RQ4 How does DBSCAN++ perform in terms of speed and robustness across real datasets and different hyperparameters?

Key findings

• DBSCAN++ achieves sub-quadratic runtime O(nm) by querying densities for only m points.
• Corollary: with m ≈ n^{D/(2β+D)}, DBSCAN++ attains minimax optimal rate for level-set estimation up to log factors.
• DBSCAN++ maintains consistency guarantees for density level-set estimation analogous to DBSCAN.
• Uniform and K-center initializations provide competitive or superior clustering performance and robustness across ε and minPts settings.
• Empirical results show substantial speedups over DBSCAN while achieving similar or better clustering scores on real datasets and image segmentation tasks.