Error minimizing algorithms for nearest neighbor classifiers

Stack Filters define a large class of discrete nonlinear filter first introduced in image and signal processing for noise removal. In recent years we have suggested their application to classification problems, and investigated their relationship to other types of discrete classifiers such as Decision Trees. In this paper we focus on a continuous domain version of Stack Filter Classifiers which we call Ordered Hypothesis Machines (OHM), and investigate their relationship to Nearest Neighbor classifiers. We show that OHM classifiers provide a novel framework in which to train Nearest Neighbor type classifiers by minimizing empirical error based loss functions. We use the framework to investigate a new cost sensitive loss function that allows us to train a Nearest Neighbor type classifier for low false alarm rate applications. We report results on both synthetic data and real-world image data.