# DBSCAN Clustering in MATLAB

URL: https://yarpiz.com/dbscan-clustering-ypml110
Author: Mostapha Kalami Heris
Published: 2015-09-06
Updated: 2026-10-30
Topics: Machine Learning

> Implement DBSCAN in MATLAB with core, border, and noise points, two clustering parameters, and an example with irregularly shaped clusters.

DBSCAN groups nearby dense regions while leaving points outside those regions unassigned as noise. It uses a neighborhood radius and a minimum point count rather than a preset number of clusters. Martin Ester, Hans-Peter Kriegel, Jörg Sander, and Xiaowei Xu introduced the method in 1996. For background, see the [Wikipedia article on DBSCAN](https://en.wikipedia.org/wiki/DBSCAN).

This MATLAB implementation demonstrates how core points expand clusters and how border points join without expanding them. It can identify irregularly shaped groups separated by low-density regions, but one global density scale may not suit every dataset.

## How DBSCAN works

DBSCAN has two parameters: the radius $\varepsilon$ and the minimum number of points `MinPts`. The $\varepsilon$-neighborhood of a point $p$ is the set of data points within distance $\varepsilon$ of it:

$$
N_\varepsilon(p) = \{\, q : \lVert p - q \rVert \le \varepsilon \,\}
$$

In this code, the neighborhood includes the point itself. Based on its neighborhood, every point has one of three roles:

- A **core point** has at least `MinPts` points in its $\varepsilon$-neighborhood.
- A **border point** is not a core point, but it lies in the neighborhood of a core point.
- A **noise point** is neither of these.

The algorithm visits the points one by one. When it finds an unvisited core point, it starts a new cluster and adds all its neighbors. Each neighbor that is also a core point adds its own neighbors to the list, so the cluster grows until no new points can be reached. Border points join the cluster but do not expand it. The points that no cluster reaches remain noise.

## Choosing the parameters

The result depends mainly on $\varepsilon$ and `MinPts`. A small $\varepsilon$ splits clusters and marks many points as noise. A large $\varepsilon$ merges clusters that should be separate. A common rule of thumb is to set `MinPts` to at least the number of dimensions plus one, often about twice the number of dimensions. Then $\varepsilon$ can be read from a plot of the sorted distances of each point to its `MinPts`-th nearest neighbor: a good value is near the point where the curve bends sharply upward.

## How to run it

Run `main.m` in MATLAB. It loads the sample data from `mydata.mat`, runs DBSCAN with the values in the script, and plots the result with `PlotClusterinResult.m`:

```matlab {title="Run DBSCAN with density thresholds"}
epsilon=0.5;
MinPts=10;
IDX=DBSCAN(X,epsilon,MinPts);
```

The function `[IDX, isnoise] = DBSCAN(X, epsilon, MinPts)` in `DBSCAN.m` takes a data matrix `X` with one sample per row. It returns the cluster index of every point in `IDX`, where 0 means noise, and the logical vector `isnoise`. To cluster your own data, load your matrix into `X` and adjust `epsilon` and `MinPts`.

The function computes the full distance matrix with `pdist2`, so it probably needs the Statistics and Machine Learning Toolbox. The full distance matrix requires memory proportional to the square of the number of points, so estimate its size before using a large dataset. MATLAB R2019a and later versions also include a built-in `dbscan` function in the Statistics and Machine Learning Toolbox.

## Example result

The figure below shows a sample result. DBSCAN finds the two clusters, a round one and a crescent shaped one around it, and also marks the noisy points. The algorithm parameters are shown above the figure.

::: figure {src="https://yarpiz.com/wp-content/uploads/2015/09/dbscan-result.png" alt="DBSCAN result in MATLAB with epsilon 0.5 and MinPts 10: a round cluster, a crescent shaped cluster around it, and a few noise points" align="center" width=660}
Sample result of the MATLAB implementation of DBSCAN clustering
:::

## Check the result

Inspect how the labels change when varying `epsilon` and `MinPts`, and review feature scaling before interpreting distances. A point labeled noise is not automatically an error or a real-world anomaly. Nearby clusters of different densities may not be separated well by one radius. The example includes each point in its own neighborhood, so use the same counting convention when comparing implementations.

## Applications

DBSCAN is used where clusters have irregular shapes or where the data contains outliers, for example in the analysis of spatial and geographic data, anomaly detection and image segmentation.

## Related posts

- [Evolutionary Data Clustering in MATLAB](https://yarpiz.com/evolutionary-clustering-ypml101), clustering and automatic clustering with GA, PSO and DE.
- [Neural Gas and GNG Networks in MATLAB](https://yarpiz.com/neural-gas-network-ypml111), for clustering and topology learning.

## How to cite

Mostapha Kalami Heris, DBSCAN Clustering in MATLAB (YPML110), Yarpiz, 2015. https://yarpiz.com/dbscan-clustering-ypml110