Classification and clustering are often grouped together as topics within pattern recognition. This grouping is reasonable owing to their similarities: classifiers and clusterers both operate on points, and their performances are judged according to the correctness of operator output. This chapter and the next concern optimal classification and optimal clustering under model uncertainty. The underlying random processes for classification and clustering are feature-label distributions and random point processes, respectively. For classification, if the feature-label distribution is known, then one can derive an optimal classifier with minimum classification error. For clustering, if the random point process is known, then one can derive an optimal cluster operator with minimum clustering error. When these probability models are unknown and belong to uncertainty classes, then the best approach to take is to find an optimal robust classifier or optimal robust clusterer. This chapter treats classification, focusing on optimal Bayesian classifiers, a special case being intrinsically Bayesian robust classifiers when there are no training data. In the next chapter, we consider intrinsically Bayesian robust clustering.
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