INTRODUCTION

Examples of the pattern classification problem (known variously as: pattern recognition, discriminant analysis, and pattern grouping) are widespread. In general such problems involve the need to assign objects to various groups, or classes, and include such applications as: (i) the assignment of production items to either defective or non-defective classes as based upon the results of tests performed on each part, (ii) the assignment of personnel to jobs as based upon their test scores and/or physical attributes, (iii) the assignment of an object detected by radar to either a friendly or unfriendly category, (iv) the categorization of investment opportunities into those that are attractive and those that are not, and so on. Early (scientific) efforts to model and solve the pattern classification problem utilized, for the most part, statistical approaches. In turn, these approaches usually rely upon the somewhat restrictive assumptions of multivariate normal distributions and certain types of (and conditions on) covariance matrices. More recent attempts have employed expert systems, linear programming (LP) and, in particular, neural networks. In this paper, we describe the development of an approach that combines linear programming (specifically, traditional linear programming and/or linear goal programming [Ignizio, 1982]) with neural networks, wherein the combined technique is itself monitored and controlled by an expert systems interface.

More specifically, we describe the use of expert systems and linear programming in the simultaneous design and training of neural networks for the pattern classification problem.