I just graduated in Computer Science, with a very theoretical background but without any kind of Data Science or Artificial Intelligence experience, and I working on my own to discover those two fields. More precisely, I try to work on a toy subspace clustering k-means-like algorithm, and I think I successfully learned basic optimization techniques.
So now I have some ad-hoc subspace clustering algorithm, and... I'm stuck. How do I validate it? During my studies, I studied a lot of formal proving or model checking techniques, but I feel they are totally irrelevant here. I read several AI papers, and it seems that there is a strong tradition of experimental validation in Clustering, with a lot of validity measures. My problem is that they mean nothing to me. I don't understand what they prove, or even why they are relevant. I would be very interested in a general course about the experimental validation methodology (if it actually is a thing!), if possible with theoretical justification.
Moreover, I don't really know what are the good properties people are looking for in clustering algorithms. What general theorems should I aim for? I understand this may be a question too related to what I am working on - a generic answer for k-means-like algorithms would be enough.