Performance Bounds of a Class of Sample-Based Classification Procedures.

摘要

Performance bounds of a class of sample-based classification procedures using the K-nearest-neighbor rule (k-NNR) are considered in this paper. By using K-NNR for decision, we show that the lower bounds of the probability of correct decision are very close to that obtained with the Bayes linear discriminant analysis based on the assumption of two multivariate Gaussian densities with different mean vectors but equal covariance matrices. This surprisingly good result suggests that the nonparametric method is very effective at small sample size situation which is of much practical signficance. By using the k-NNR for density estimates, an upper bound of the probability of correct decision provides an optimistic estimate of the performance which again indicated the effectiveness of the nonparametric technique. (Author)