HDBSCAN vs. DBSCAN

We have discussed DBSCAN and its scalable alternative, DBSCAN++, in this newsletter before: DBSCAN and DBSCAN++.

Today, I want to dive into HDBSCAN and share how it differs from DBSCAN.

Why DBSCAN?

While KMeans is widely used due to its simplicity and effectiveness as a clustering algorithm, it has many limitations:

• It does not account for cluster covariance.

• It can only produce spherical clusters. As shown below, even if the data has non-circular clusters, it still produces round clusters.

Density-based algorithms, like DBSCAN, quite effectively address these limitations, as depicted below:

Coming back to the topic…

But, of course, like any other algorithm, DBSCAN also has some limitations.

To begin, DBSCAN assumes that the local density of data points is (somewhat) globally uniform. This is governed by its eps parameter.

Thus, it may struggle to identify clusters with varying densities. This may need several hyperparameter tuning attempts to get promising results.

HDBSCAN can be a better choice for density-based clustering.

It relaxes the assumption of local uniform density, which makes it more robust to clusters of varying densities by exploring many different density scales.

For instance, consider the clustering results obtained with DBSCAN on the dummy dataset below, where each cluster has different densities:

It is clear that DBSCAN produces bad clustering results.

Now compare it with HDBSCAN results depicted below:

On a dataset with three clusters, each with varying densities, HDBSCAN is found to be more robust.

There’s one more thing I love about HDBSCAN:

• DBSCAN is a scale variant algorithm. Thus, clustering results for data X, 2X, 3X, etc., can be entirely different.

• On the other hand, HDBSCAN is scale-invariant. So, clustering results remain the same across different scales of data.

This is depicted below:

• We have DBSCAN on the left, and we can see that the results vary with the scale of the data.

• However, clustering from HDBSCAN (on the right) remains unaltered with the scale for HDBSCAN.

Isn’t that cool?

I have been wanting to write an extensive article about HDBSCAN for some time now. Let me know if you are interested in learning more about it:

👉 Over to you: Can you explain why HDBSCAN is scale-invariant?

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• A Beginner-friendly Introduction to Kolmogorov Arnold Networks (KANs).

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• You Are Probably Building Inconsistent Classification Models Without Even Realizing.

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