The maximum likelihood decision rule and estimation of the resulting m-class probability of misclassification are discussed. A bound on the variance of a proposed unbiased estimator of the m-class probability of error is derived. The problem of estimating the a priori probabilities for two classes is covered. When the estimator is counting the proportion of classified samples assigned to each class, a bound on the error of the estimate is derived. The problem of m-class feature selection using the Bhattacharyya distance is also addressed. The particular case in which each class density is assumed to be a mixture of multivariate normal densities is considered in detail. In conclusion, the extension of spectral signatures in space and time is also discussed.

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