A game theoretic approach for feature clustering and its application to feature selection

In this paper, we develop a game theoretic approach for clustering features in a learning problem. Feature clustering can serve as an important preprocessing step in many problems such as feature selection, dimensionality reduction, etc. In this approach, we view features as rational players of a coalitional game where they form coalitions (or clusters) among themselves in order to maximize their individual payoffs. We show how Nash Stable Partition (NSP), a well known concept in the coalitional game theory, provides a natural way of clustering features. Through this approach, one can obtain some desirable properties of the clusters by choosing appropriate payoff functions. For a small number of features, the NSP based clustering can be found by solving an integer linear program (ILP). However, for large number of features, the ILP based approach does not scale well and hence we propose a hierarchical approach. Interestingly, a key result that we prove on the equivalence between a k-size NSP of a coalitional game and minimum k-cut of an appropriately constructed graph comes in handy for large scale problems. In this paper, we use feature selection problem (in a classification setting) as a running example to illustrate our approach. We conduct experiments to illustrate the efficacy of our approach