# DBSCAN

Most of the clustering methods discussed so far are based on assumptions about the geometrical structure of the dataset. For example, K-means can find the centroids of hyperspherical regions, while spectral clustering has less limitations (in particular, using a KNN affinity matrix), but it requires you to know the desired number of clusters and such a choice conditions the result. On the other hand, spectral clustering, as well as **DBSCAN** (which stands for **Density-Based Spatial Clustering of Applications with Noise**), can work with non-convex clusters, while K-means requires such a condition.

DBSCAN is an algorithm proposed by Ester et al. (in Ester M., Kriegel H. P., Sander J., Xu X.,* A Density-Based Algorithm for Discovering Clusters in Large Spatial Databases with Noise*, Proceedings of the 2nd International Conference on Knowledge Discovery and Data Mining, AAAI Press, pp. 226-231, 1996) to overcome all these limitations.

The main assumption is that *X* represents...