  One of the most prominent challenges in clustering is "the user's dilemma,"
which is the problem of selecting an appropriate clustering algorithm for a
specific task. A formal approach for addressing this problem relies on the
identification of succinct, user-friendly properties that formally capture when
certain clustering methods are preferred over others.
  Until now these properties focused on advantages of classical Linkage-Based
algorithms, failing to identify when other clustering paradigms, such as
popular center-based methods, are preferable. We present surprisingly simple
new properties that delineate the differences between common clustering
paradigms, which clearly and formally demonstrates advantages of center-based
approaches for some applications. These properties address how sensitive
algorithms are to changes in element frequencies, which we capture in a
generalized setting where every element is associated with a real-valued
weight.
