What is the best way to group objects on a plane?

Question

Algorithms

The task is to group objects on a plane.
For example: from this:

You need to get something similar to this:

While the idea came to mind - break it into hexagons and go through all the points by enumeration. But there are cases when objects with different densities fill the entire plane, and if I simply divide into equal intervals, I will get a grid with bold dots located at the same distance from each other, looks so-so. What are the grouping algorithms?

Answer 1

I understand that you need a clustering algorithm , provided that you do not know the number of classters.
There is also an option to implement auto-detection of the number of clusters for k-means. We set three random classter centers, carry out classterization (in this case, the centers of the classters are shifted), then we either leave everything as it is, or divide these three classters by two more. These two centers will either shift and form their own classters, or converge to one point. In this way, it is quite easy to perform classifierization without knowing the exact number of classters.
True, there are more efficient algorithms for this.