DBSCAN

Imagine we’re tasked with analyzing a geographical dataset containing the locations of mobile phone towers in a region. Our goal is to identify clusters of towers that exhibit similar traffic patterns, which could help optimize network resources and improve service quality. The challenge is that we have no prior knowledge of how many distinct clusters or traffic patterns exist, making it impossible to apply traditional clustering techniques that require specifying the number of clusters in advance.

In such a scenario, the Density-Based Spatial Clustering of Applications with Noise (DBSCAN) becomes an invaluable tool. Unlike k-means or mini-batch k-means, DBSCAN doesn’t rely on a predefined number of clusters, which makes it particularly useful when dealing with data where the cluster distribution is unclear or when the number of clusters varies across different regions of the dataset.

DBSCAN operates by identifying clusters based on the density of data points within a region. We start by selecting a random data point and expand the cluster by connecting neighboring points that are sufficiently dense. This process continues until we identify regions of varying densities, effectively partitioning the data into clusters of different shapes and sizes.

In our mobile tower example, DBSCAN can help us discover clusters of towers with similar usage patterns, even when the number of clusters and the spatial distribution of towers are unknown in advance. DBSCAN’s flexibility and adaptability make it an excellent choice for exploratory data analysis and situations where the underlying data structure is not well-defined, demonstrating its utility in real-world applications where traditional clustering methods may fall short.

These characteristics can make DBSCAN particularly useful in exploratory stages or in cases where the distribution of the clusters is unclear.

The DBSCAN algorithm

The algorithm works by defining two parameters: epsilon, or ε (eps), and the minimum number of points required to form a dense region (min_samples). For each data point, the algorithm identifies its ε-neighborhood (i.e., all data points within a radius of ε from that point). If the number of points in the ε-neighborhood is greater than or equal to min_samples, then that point is considered a core point. Core points are essential for forming dense regions or clusters. The algorithm then expands the cluster by including all points in the ε-neighborhood of the core point. This process continues until no more points can be added to the cluster.

Let’s see how we can use DBSCAN in scikit-learn: