Both the Chamberlin--Courant and Monroe rules are voting rules solving the problem of so-called fully proportional representation: they select committees whose members represent the voters so that voters' satisfaction with their assigned representatives is maximized. These rules suffer from a common disadvantage, being that it is computationally intractable to compute the winning committee exactly. As both of these rules, explicitly or implicitly, partition voters, they can be seen as clustering the voters so that the voters in each group share the same representative. This suggests studying approximation algorithms for these voting rules by means of cluster analysis, which is the subject of this paper. We develop several algorithms based on clustering the voters and analyze their performance experimentally.