Structured estimation - Sample size reduction for adaptive pattern classification

Abstract

The Gaussian two-category classification problem with known category mean value vectors and identical but unknown category covariance matrices is considered. The weight vector depends on the unknown common covariance matrix, so the procedure is to estimate the covariance matrix in order to obtain an estimate of the optimum weight vector. The measure of performance for the adapted classifier is the output signal-to-interference noise ratio (SIR). A simple approximation for the expected SIR is gained by using the general sample covariance matrix estimator; this performance is both signal and true covariance matrix independent. An approximation is also found for the expected SIR obtained by using a Toeplitz form covariance matrix estimator; this performance is found to be dependent on both the signal and the true covariance matrix.