Feature Selection With Redundancy-Constrained Class Separability

Scatter-matrix-based class separability is a simple and efficient feature selection criterion in the literature. However, the conventional trace-based formulation does not take feature redundancy into account and is prone to selecting a set of discriminative but mutually redundant features. In this brief, we first theoretically prove that in the context of this trace-based criterion the existence of sufficiently correlated features can always prevent selecting the optimal feature set. Then, on top of this criterion, we propose the redundancy-constrained feature selection (RCFS). To ensure the algorithm´s efficiency and scalability, we study the characteristic of the constraints with which the resulted constrained 0-1 optimization can be efficiently and globally solved. By using the totally unimodular (TUM) concept in integer programming, a necessary condition for such constraints is derived. This condition reveals an interesting special case in which qualified redundancy constraints can be conveniently generated via a clustering of features. We study this special case and develop an efficient feature selection approach based on Dinkelbach´s algorithm. Experiments on benchmark data sets demonstrate the superior performance of our approach to those without redundancy constraints.