Robust unsupervised classification with uncertain models

A classification procedure that estimates the parameters of an unsupervised vectored sample where the exact form of the underlying probability density of the samples is not known is developed. Following the estimation, the measurements are classified on the basis of maximized a-posteriori probability of classification. Since the Gaussianity assumption is at most an approximation to a realistic data set and gross errors are likely to appear, robustification and efficiency are emphasized. The data are only partially observed, and an a-priori model for the observed sample is not known, so that an uncertain modeling of the observations is desired. The missing data situation is handled by using the expectation maximization (EM) algorithm to estimate the unobserved quantities. The class of weighted M-estimators is defined and used in the robust classifier. An efficient simple numerical method for the solution of the weighted M-estimate for the large class of in contaminated distributions is presented. An extension to the case where samples of a particular class are known to be correlated is discussed, and a postprocessing step to re-estimate the parameters is proposed.<>