We extend Macqueen's version of the k-means algorithm (Macqueen, 1967) by assuming that the algorithm involves two players. Player 1, the sender, equipped with its type, emits data at no cost, and Player 2, the receiver, equipped with Player 1's data, chooses an action. In particular, data are pooled with regard to the action they are associated with. Pure perfect Bayesian equilibria (PBE) in this game are characterized by partitions of the types, in which no type prefers to be pooled with types it is not currently pooled with, given the decisions of the receiver, optimally chosen at each cell of the partition. In this context, the inductive step of the $k$-means algorithm proceeds as follows: (i) the sender is in charge of moving a type from its cell to a cell it prefers; (ii) the receiver readjusts the cell-contingent actions accordingly. Since players might have different objective functions, the simple convergence argument invoked in Macqueen's context (monotonicity of stages (i) and (ii) with regard to the intra or inter variances) no more holds. Instead, we use a combinatorial argument to achieve convergence, for every initial partition and every path taken by the algorithm. We do this for utility functions that are single-peaked and single-crossing, with an upward bias for the sender. The family covers, but goes much beyond, the usual Euclidean distance. However, our argument crucially relies on the order on types and actions.