Major research challenges for theoretical foundations of clustering
Clustering is an area of huge practical relevance but rather meager theoretical foundations.
I will discuss some fundamental challenges that a theory of clustering needs to face. In particular, I'll describe two different approaches to addressing those challenges;
an axiomatic approach and a statistical/machine-learning perspective.
If time permits, I will also discuss the computational complexity of some common clustering formulations - another area in which our theoretical understanding lags far behind the practical scene.
I will outline recent progress made along these directions, as well as allude to some common misconceptions and potential pitfalls. The talk is geared towards stimulating discussions and highlighting open questions more than to providing answers or boasting definitive results.