Clustering different class - machine-learning

Question

I would like to cluster my dataset which has multiple classes (up to 10). But this clustering problem is different than usual clustering. I need to cluster different classes (as shown in the image; https://ibb.co/iiNbqv) instead same/similar classes. Which method should I use? what would you recommend?
The problem as follow;
I have several frames/images (up to 10), and each frame has hundred of thousand detections. So, as the data I am processing is the location (x and y coordinates) of the detection. What I am going to do that how much detections are overlapped within these frames with a certain distance threshold. The constraint is that each detection of a frame shouldn't be in the same overlapped cluster more than once as seen in the picture. So basically, I should find the nearest detection of a point from other frames, and put them in same cluster. But once I do that every point in the cluster shouldn't be far each other more than distant threshold
Cheers

Answer 1

Based on your image and the circles you drew, this seems a problem of clustering different data points based on distance between them. A simple euclidian distance based clustering algorithm should provide the results you are looking for.
Something like this would cluster data points according to a measure of distance between them. The only parameter is the distance threshold, which you should set to one that is consistent with your problem.
#PSEUDO-CODE!
#p is a list of all data points
for i=all points
if( p(i).used == false)
{
#Create new cluster c
p(i).cluster = c
for n=1:all_Points
{
if ( p(n).used == false)
{
if p(n).class not in cluster
{
d=dist(p(i),p(n))
if d<max
{
p(n).cluster = c;
p(n).used = true;
}
}
}
}
This basically goes to each point and finds which of them are near it, and assigns them to the same cluster. There are a lot of variations of this clustering routine that achieve different goals.
For example, you can compare the distance between the current centroid of the cluster rather than the point that initialized the cluster, or compare with the last added point to the cluster rather than the first one. Depends on what would work better for the nature of your data.

Answer 2

Clustering won't help you much here, because it is too exploratory.
You should instead look into optimization in general. In particular, your problem has similarities to the set cover problem. For all I can tell, you want to cover all instances with sets of three, such that the three elements are in different "classes" and most similar?
Based on the optimization theory results, you will likely be able to prove that this problem is NP hard, and therefore a greedy approximation algorithm is the preferable way of handling this.