Density-based spatial clustering of applications with noise (DBSCAN) is a data clustering algorithm proposed in [Ester96]. It is a density-based clustering non-parametric algorithm: given a set of observations in some space, it groups together observations that are closely packed together (observations with many nearby neighbors), marking as outliers observations that lie alone in low-density regions (whose nearest neighbors are too far away).


Computational methods

Programming Interface


Default method




Mathematical formulation#


Given the set \(X = \{x_1 = (x_{11}, \ldots, x_{1p}), \ldots, x_n = (x_{n1}, \ldots, x_{np})\}\) of \(n\) \(p\)-dimensional feature vectors (further referred as observations), a positive floating-point number epsilon and a positive integer minObservations, the problem is to get clustering assignments for each input observation, based on the definitions below [Ester96]: two observations \(x\) and \(y\) are considered to be in the same cluster if there is a core observation \(z\), and \(x\) and \(y\) are both reachable from \(z\).

Each cluster gets a unique identifier, an integer number from \(0\) to \(\text{total number of clusters } – 1\). Each observation is assigned an identifier of the cluster it belongs to, or \(-1\) if the observation considered to be a noise observation.

Programming Interface#

Refer to API Reference: DBSCAN.

Distributed mode#

The algorithm supports distributed execution in SPMD mode (only on GPU).

Usage Example#


void run_compute(const table& data,
                           const table& weights) {
   double epsilon = 1.0;
   std::int64_t max_observations = 5;
   const auto dbscan_desc = kmeans::descriptor<float>{epsilon, max_observations}

   const auto result = compute(dbscan_desc, data, weights);

   print_table("responses", result.get_responses());


Batch Processing: