Clustering of Spatial Data in R or Python

I am new to GIS.

Problem Domain :-
I have a stoppage data of different vehicle i.e. the point where vehicle stopped.There are some specific vehicle which stops at some particular point. So, I am trying to find out such specific point(anomaly detection) in the midst of random stoppages. I am assuming that Cluster analysis would let me know about the Percentage of vehicle at that stoppage point. If only a particular vehicle stops at that point , then obviously that's an anomaly point.

I have a large set of (latitude and longitude)spatial data. I am confused on which clustering method to adopt. I have came across two density based approach: DBSCAN and OPTICS. I am doubtful about the two approach since I don't have a particular minPts( 1 in my case). Obviously, I can't use K-means approach , K is unknown.

I have come across one more approach i.e X-means.