A likelihood-MPEC approach to target classification

In this paper we develop a method for classifying an unknown data vector as belonging to one of several classes. This method is based on the statistical methods of maximum likelihood and borrowed strength estimation. We develop an MPEC procedure (for Mathematical Procedure with Equilibrium Constraints) for the classification of a multi-dimensional observation, using a finite set of observed training data as the inputs to a bilevel optimization problem. We present a penalty interior point method for solving the resulting MPEC and report numerical results for a multispectral minefield classification application. Related approaches based on conventional maximum likelihood estimation and a bivariate normal mixture model, as well as alternative surrogate classification objective functions, are described.