Ideas for a DBSCAN with different epsilon values in each dimension?

Hi Community

Im clustering some 3D data points usiang DBSCAN.

I want to define a non uniform neighnorhood radio for my DBSCAN. For example, using epsilon = 15 for X and Y axis, but epsilon = 5 for the Z axis.

Some ideas?

Thx

Answer 1

[Sreeram]

Hi Felipe,

I understand that you want to define a non-uniform neighbourhood radius for DBSCAN in MATLAB. However according to the documentation, the dbscan function in MATLAB does not allow non-uniform epsilon values.

In DBSCAN, the epsilon parameter defines the radius of the neighbourhood around each point. For your example, by scaling the Z-axis data by the ratio of epsilon along X and Y axes to epsilon along Z axis, you effectively normalize the different epsilon value for the Z axis. You can pass the epsilon value along X and Y axis to the dbscan function. This ensures that the distance calculations in the DBSCAN algorithm make use of the desired non-uniform neighbourhood radius.

Here's how you can code it:

% Desired epsilons

epsilon_xy = 15;

epsilon_z = 5;

% Scale the Z-axis data

scale_z = epsilon_xy / epsilon_z; % Scaling factor

scaled_data = data;

scaled_data(:, 3) = scaled_data(:, 3) * scale_z;

% Apply DBSCAN on the scaled data

labels = dbscan(scaled_data, epsilon_xy, minPts); % Note that epsilon_xy is used here

You may read more about how DBSCAN works here: https://www.mathworks.com/help/stats/dbscan-clustering.html

Hope it helps.