How to determine groups of points

Question

Assume that I have a coordinate system with points. Human can determine, that they are arranged into aggregations. Is there any algorithm which can divide these points into groups? Here is an illustrative example:

Answer 1

This is part of a very general class of problems known as clustering. Given the immense amount of research done on this topic, I doubt a single answer would suffice without knowing more about the problem.

I would suggest you start looking at some basic ones such as k-means clustering.

If you can use a library, SVM is also an excellent choice.