DBSCAN Clustering Algorithm-with maths

 DBSCAN is a short-form of Density-Based Spatial Clustering of Applications with Noise. It is an unsupervised algorithm that will take the set of points and make them into some sets which have the same properties. It is based on the density-based clustering and it will mark the outliers also which do not lie in any of the cluster or set.

There are some terms that we need to know before we proceed further for algorithm:

Density Reachability

A point “p” is said to be density reachable from a point “q” if point “p” is within ε distance from point “q” and “q” has a sufficient number of points in its neighbors which are within distance ε.

Density Connectivity

A point “p” and “q” are said to be density connected if there exists a point “r” which has a sufficient number of points in its neighbors and both the points “p” and “q” is within the ε distance. This is a chaining process. So, if “q” is neighbor of “r”, “r” is neighbor of “s”, “s” is neighbor of “t” which in turn is neighbor of “p” implies that “q” is neighbor of “p”.

Algorithm

Let X = {x1, x2, x3, …, xn} be the set of data points. DBSCAN requires two parameters: ε (eps) and the minimum number of points required to form a cluster (minPts).

1) Start with an arbitrary starting point that has not been visited.

2) Extract the neighborhood of this point using ε (All points which are within the ε distance are neighborhood).

3) If there are sufficient neighborhoods around this point then the clustering process starts and the point is marked as visited else this point is labeled as noise (Later this point can become the part of the cluster).

4) If a point is found to be a part of the cluster then its ε neighborhood is also the part of the cluster and the above procedure from step 2 is repeated for all ε neighborhood points. This is repeated until all points in the cluster is determined.

5) A new unvisited point is retrieved and processed, leading to the discovery of a further cluster or noise.

6) This process continues until all points are marked as visited.

Advantages

1. It does not require a-priori specification of the number of clusters.
2. Able to identify noise data while clustering.
3. DBSCAN algorithm is able to find arbitrarily size and arbitrarily shaped clusters.

Disadvantages

1. DBSCAN algorithm fails in case of varying density clusters.
2. Fails in case of neck type of dataset.