Maximum Likelihood Estimation of Label Imperfection Probabilities and Its Use in the Identification of Mislabeled Patterns

This paper presents the problem of estimating label imperfections and the use of the estimation in identifying mislabeled patterns. Expressions for the maximum likelihood estimates of classification errors and a priori probabilities are derived from the classification of a set of labeled and unlabeled patterns. Expressions also are presented for the asymptotic variances of probability of correct classification and proportions. Simple models are developed for imperfections in the labels and for classification errors and are used in the formulation of a maximum likelihood estimation scheme. Schemes are presented for the identification of mislabeled patterns in terms of thresholds on the discriminant functions for both two-class and multiclass cases. Expressions are derived for the probability that the imperfect label identifi´cation scheme will result in a wrong decision and are used in computing thresholds. Furthermore, the results of practical applications of these techniques in the processing of remotely sensed multispectral data are presented.