One of the basic problems of learning is to separate available data,
assigning it to one of  several clusters.  Even given an infinite
amount of (unlabeled) data, i.e., the whole underlying probability
distribution,  it is often unclear how to draw the boundary. In my
talk I will discuss certain geometric intuitions, allowing one to
provide a formal definition of optimal clustering and will describe
some recent work, connecting this notion to spectral clustering and
some ideas from semi-supervised learning.