# Clustering Problem

Suppose we are in the unsupervised learning setting and we have a sense of distance on $A$, $d(\cdot, \cdot)$ (we assume $d(x,y) = d(y,x)$ for $x,y \in A$). We want to find $B$ a set of categories and a function $f: A \to B$ such that $f$ maps items that are close to one another to the same category.