Abstract:

Could there be a meaningful framework for reasoning about clustering
independently of any particular algorithm, objective function or
generative data model? A formal mathematical axiomatization of
clustering tasks could shed light on the merits and limitations of
different clustering approaches, provide model selection principles,
as well as help discover novel clustering paradigms.  However, the
task seems elusive and there has been surprisingly little work
pursuing the development of such a framework.  I shall discuss several
attempts to provide an abstract axiomatic basis for the definition,
taxonomy and analysis of clustering. I shall outline the current state
of knowledge and present some concrete significant open questions
along this line of research.