Gradient descent learning of nearest neighbor classifiers with outlier rejection

The nearest neighbor classification rule is extended to reject outlier data and is implemented with an analog electronic circuit. A continuous membership function is derived from an optimization formulation of the classification rule. A learning algorithm is then presented for arranging prototype patterns to their optimal places and adjusting the radius of outlier rejection. The place of prototypes and the rejection radius are incrementally updated at every presentation of training patterns in the steepest descent direction of the error of the membership of the presented pattern from its correct value. Some elementary experiments examplify the convergence of the present learning algorithm.