Effective global approaches for mutual information based feature selection

Most current mutual information (MI) based feature selection techniques are greedy in nature thus are prone to sub-optimal decisions. Potential performance improvements could be gained by systematically posing MI-based feature selection as a global optimization problem. A rare attempt at providing a global solution for the MI-based feature selection is the recently proposed Quadratic Programming Feature Selection (QPFS) approach. We point out that the QPFS formulation faces several non-trivial issues, in particular, how to properly treat feature `self-redundancy' while ensuring the convexity of the objective function. In this paper, we take a systematic approach to the problem of global MI-based feature selection. We show how the resulting NP-hard global optimization problem could be efficiently approximately solved via spectral relaxation and semi-definite programming techniques. We experimentally demonstrate the efficiency and effectiveness of these novel feature selection frameworks.