  In this article we propose a method to refine the clustering results obtained
with the nonnegative matrix factorization (NMF) technique, imposing consistency
constraints on the final labeling of the data. The research community focused
its effort on the initialization and on the optimization part of this method,
without paying attention to the final cluster assignments. We propose a game
theoretic framework in which each object to be clustered is represented as a
player, which has to choose its cluster membership. The information obtained
with NMF is used to initialize the strategy space of the players and a weighted
graph is used to model the interactions among the players. These interactions
allow the players to choose a cluster which is coherent with the clusters
chosen by similar players, a property which is not guaranteed by NMF, since it
produces a soft clustering of the data. The results on common benchmarks show
that our model is able to improve the performances of many NMF formulations.
