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.


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