# How to partition a sample into representative subsamples?

The problem is the following: take a sample $$X$$ of the general population $$\Omega$$, whose distribution is known. Each element of $$X$$ is described by a vector of characteristics, each characteristics has a finite support (think of gender, age, education level...). Take a measure of dissimilarity between distributions (say, the Kullback-Leibler divergence), $$d$$. We want to find a partition of $$X$$ in $$n>1$$ subsamples $$(S_1,\ldots,S_n)$$ such that the subsamples are the most representative possible of the general population. In practice, we would take a criterion like minimizing the average dissimilarity between $$S_i$$ ($$i:1...n$$) and $$\Omega$$.
I am interested in any variant of the problem: e.g. where one does not choose $$n$$ ex ante, or where the $$(S_i)_{i:1...n}$$ are still mutually exclusive but do not cover all $$X$$, or with another choice of criterion. I am mostly interested in algorithmic implementation of a solution. A bibliographic research didn't give me any interesting result, but maybe I tried the wrong keywords.