Error Estimation Procedure for Large Dimensionality Data with Small Sample Sizes

Using multivariate data analysis to estimate the classification error rates and separability between sets of data samples is a useful tool for understanding the characteristics of data sets. By understanding the classifiability and separability of the data, one can better direct the appropriate resources and effort to achieve the desired performance. The following report describes our procedure for estimating the separability of given data sets. The multivariate tools described in this paper include calculating the intrinsic dimensionality estimates, Bayes error estimates, and the Friedman-Rafsky tests. These analysis techniques are based on previous work used to evaluate data for synthetic aperture radar (SAR) automatic target recognition (ATR), but the current work is unique in the methods used to analyze large dimensionality sets with a small number of samples. The results of this report show that our procedure can quantitatively measure the performance between two data sets in both the measure and feature space with the Bayes error estimator procedure and the Friedman-Rafsky test, respectively. Our procedure, which included the error estimation and Friedman-Rafsky test, is used to evaluate SAR data but can be used as effective ways to measure the classifiability of many other multidimensional data sets.