# DBSCAN¶

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).

 Operation Computational methods Programming Interface Compute Default method compute(…) compute_input compute_result

## Mathematical formulation¶

### Computation¶

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 SMPD mode (only on GPU).

## Usage example¶

### Compute¶

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}
.set_result_options(dal::dbscan::result_options::responses);

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

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


## Examples¶

Batch Processing: