Repeated Observations for Classification

We study the problem nonparametric classification with repeated observations. Let bX be the d dimensional feature vector and let Y denote the label taking values in 1,dots ,M. In contrast to usual setup with large sample size n and relatively low dimension d, this paper deals with the situation, when instead of observing a single feature vector bX we are given t repeated feature vectors bV1,dots ,bVt . Some simple classification rules are presented such that the conditional error probabilities have exponential convergence rate of convergence as t→∞. In the analysis, we investigate particular models like robust detection by nominal densities, prototype classification, linear transformation, linear classification, scaling.