A mean-square performance criterion for adaptive pattern classification systems

A performance criterion for an adaptive pattern classification system is presented that does not require the probability density function associated with each class to be known. Any decision rule that consists of a discriminant function that is a linear combination of scalar functions of the pattern vector may be chosen on the basis of a priori knowledge about the classes, engineering judgment, and economic considerations. The performance criterion is used to measure the system\´s performance on a set of "typical patterns" or "training samples." The proposed performance criterion is suitable for the use of multivariable search techniques in order to find the optimum parameters of the discriminant function. It is shown that, as the number of training samples approaches infinity, the resulting discriminant function of the form chosen at the outset approximates the optimum Bayes\´ discriminant function in the mean-square sense. This short paper extends and solidifies a performance criterion for the adaptive pattern classification system described by Patterson and Womack [11]. The improved criterion gives added assurance that a control loop can adapt the system to the desired operating point. Recursive algorithms as described by Kashyap and Blaydon [12], Pitt and Womack [13], and Nikolic and Fu [14] can accelerate the adapting process. Typical of the possible applications for this criterion is the control of the pass/reject phase of the output of a semiconductor manufacturing process. It is at this point in the process that a decision must be made quickly and efficiently as to whether a device does or does not meet specifications. One conventional test procedure is to make individual measurements on n different parameters which results in a parameter acceptance subregion defined by an - dimensional parallelepiped. The discriminant function approach utilized in this short paper is effectively a many-to-one mapping procedure, where the parameter acceptance subr- - egion is defined by an -dimensional ellipsoid. This increases the yield of the process and improves the test procedure.