CORRELATION AND HIGH-DIMENSIONAL CONSISTENCY IN PATTERN-RECOGNITION

Classical discriminant analysis breaks down when the feature vectors a re of extremely high dimension; for example, when the basic observatio n is a random function observed over a fine grid. Alternative methods have been developed assuming a simplified form for the covariance stru cture. We analyze the high-dimensional asymptotics of some of these me thods, emphasizing the effects of correlations such as occur when the baseline is random. For instance, the Euclidean distance classifier, w hich has been proposed for generic use in high-dimensional classificat ion problems, is dimensionally inconsistent under a simple repeated me asurement model. We provide exponential bounds for the error rates of several classifiers. We develop new dimensionally consistent methods t o deal with the effects of correlation in high-dimensional problems.