A routine to choose eps and minPts for DBSCAN

DBSCAN is most cited clustering algorithm according to some literature and it can find arbitrary shape clusters based on density. It has two parameters eps (as neighborhood radius) and minPts (as minimum neighbors to consider a point as core point) which I believe it highly depends on them.

Is there any routine or commonly used method to choose these parameters?

There are plenty of publications that propose methods to choose these parameters.

The most notable is OPTICS, a DBSCAN variation that does away with the epsilon parameter; it produces a hierarchical result that can roughly be seen as "running DBSCAN with every possible epsilon".

For minPts, I do suggest to not rely on an automatic method, but on your domain knowledge.

A good clustering algorithm has parameters, that allow you to customize it to your needs.

A parameter that you overlooked is the distance function. The first thing to do for DBSCAN is to find a good distance function for your application. Do not rely on Euclidean distance being the best for every application!

• Although user can choose distance function, I doubt it is a parameter. Mar 10, 2014 at 7:06
• Of course it is. It is as much a parameter as the kernel function for any other kernelized method (you can in fact kernelize DBSCAN trivially this way), and in my experience other distances such as Canberra or Clark can significantly improve results. Mar 10, 2014 at 7:25
• I don't underestimate the distance function influence on clustering, But I think it is somehow general, not specific to dbscan or every other clustering algorithm; while eps and minPts are explicitly dbscan parameters. Mar 10, 2014 at 11:26
• There are plenty of non-distance-based algorithms, too. And when you consider minPts to be the same as e.g. k for nearest neighbor classification, then you could say the same for the minPts parameter. I guess the main difference is that for distance, there is an "often" sensible default: Euclidean distance; whereas for minPts the value will be data specific. Mar 10, 2014 at 11:40
• OPTICS itself will not give you partitions, but a cluster order. To get partitions, use the xi extraction described in the OPTICS paper. See each variants paper to understand the differences. Feb 5, 2018 at 7:45

minPts is selected based on the domain knowledge. If you do not have domain understanding, a rule of thumb is to derive minPts from the number of dimensions D in the data set. minPts >= D + 1. For 2D data, take minPts = 4. For larger datasets, with much noise, it suggested to go with minPts = 2 * D.

Once you have the appropriate minPts, in order to determine the optimal eps, follow these steps -

Let's say minPts = 24

1. For every point in dataset, compute the distance of it's 24th nearest neighbor.(generally we use euclidean distance, but you can experiment with different distance metrics).
2. Sort the distances in the increasing order.
3. Plot the chart of distances on Y-axis v/s the index of the datapoints on X-axis.
4. Observe the sudden increase or what we popularly call as an 'elbow' or 'knee' in the plot. Select the distance value that corresponds to the 'elbow' as optimal eps.

Maybe a bit late, but I would like to add an answer here for future knowledge. One way to find the best $$\epsilon$$ for DBSCAN is to compute the knn, then sort the distances and see where the "knee" is located.

Example in python, because is the language I manage.:

from sklearn.neighbors import NearestNeighbors
import plotly.express as px

neighbors = 6
nbrs = NearestNeighbors(n_neighbors=neighbors ).fit(X_embedded)
distances, indices = nbrs.kneighbors(X_embedded)
distance_desc = sorted(distances[:,ns-1], reverse=True)
px.line(x=list(range(1,len(distance_desc )+1)),y= distance_desc )


Then, to find the "knee", you can use another package: (pip install kneed)

from kneed import KneeLocator
kneedle = KneeLocator(range(1,len(distanceDec)+1),  #x values
distanceDec, # y values
S=1.0, #parameter suggested from paper
curve="convex", #parameter from figure
direction="decreasing") #parameter from figure


To see where the "knee" is, you can run

kneedle.plot_knee_normalized()


the commands kneedle.elbow or kneedle.knee returns the index of the x array, and the kneedle.knee_y returns the optimum value for $$\epsilon$$.

• what does 'ns' refer to in distance_desc = sorted(distances[:,ns-1], reverse=True) ?
– Arun
Oct 11, 2021 at 5:04
• @Arun sorry I forgot to write its meaning. Ir it just for a indexing, it means number of samples
– L F
Oct 11, 2021 at 5:05