New technologies in the form of improved instrumentation have made it
possible to take detailed measurements over recognition patterns. This increase in the
number of features or parameters for each pattern of interest not necessarily generates
better classification performance. In fact, in problems where the number of training
samples is less than the number of parameters, i.e. “small sample size” problems, not
all parameters can be estimated and traditional classifiers often used to analyse lower
dimensional data deteriorate. The Bayes plug-in classifier has been successfully applied
to discriminate high dimensional data. This classifier is based on similarity
measures that involve the inverse of the sample group covariance matrices. However,
these matrices are singular in “small sample size” problems. Thus, several other
methods of covariance estimation have been proposed where the sample group covariance
estimate is replaced by covariance matrices of various forms. In this report,
some of these approaches are reviewed and a new covariance estimator is proposed.
The new estimator does not require an optimisation procedure, but an eigenvectoreigenvalue
ordering process to select information from the projected sample group
covariance matrices whenever possible and the pooled covariance otherwise. The effectiveness
of the method is shown by some experimental results.