# What Classification Algorithm Do I need to Use to Solve this Problem?

I am trying to solve the following problem it is to classify the the red points and green points in image 1 into two cases. The cluster of green or red points can be anywhere and there can be any number of green or red clusters; different coloured clusters do not mix or bleed into each other; at least one green and one red cluster always exists. An example of points to classify is given in image 1.

So I guess there are two ways to do this

1. Classify then with boundaries as shown in image 2, with some algorithm, then use a some post processing step to link the separate classes that have the same colour.

2. Use some algorithm to directly find the classification boundaries as shown in image 3.

So my question is what is the algorithm or algorithm can I use for 1) and 2)?

It seems it can be solved using the MLE algorithm in some way.   • Step $3$ implies that the colors are known by the clustering algorithm. If this is the case, then it would be trivial to draw $2$ clusters that separate red and green. Is this what you had intended? – Varun Vejalla Aug 21 '20 at 18:44
• @VarunVejalla I am not sure what you mean since there is not a step 3 in my question. I don't know why it would be trivial, because I do not know what clustering algorithm can be used to solve.the problem.The above is just a specific example – Z.E. Aug 21 '20 at 21:32
• I meant whatever step was taken to get image $3$. I was thinking it would be trivial because a cluster could be drawn to specifically fit the green/red points. However, this may not be smooth. – Varun Vejalla Aug 21 '20 at 23:43
• @VarunVejalla I don't think it is triivial because there are an arbitrary number of clusters and their positions can be anywhere as stated in the question (in the 2D plane) -so if you had a specific fit for one cluster,in the specific example above,you would not expect it to work for the general case – Z.E. Aug 22 '20 at 10:25
• I was thinking the approach would be: Make the cluster around exactly one red point. While at least one red point is not in the cluster, expand the cluster to include the red point (and only that point). Repeat for green. This would result in two separate clusters that only enclose the points of a single color. – Varun Vejalla Aug 22 '20 at 13:44