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Compound Decision Procedures for Pattern Classification

Report Number: AMRL TR 67-10
Author: Abend, Kenneth
Corporate Author: Philco-Ford Corporation
Laboratory: Biomedical Laboratory
Date of Publication: 1967-12
Pages: 107
Contract: AF 33(615)-2966
Project: 7233 - Biological Information Handling Systems and Their Functional Analogs
Task: 723305 - Theory of Information Handling
AD Number: AD0667570

Compound decision theory is shown to be powerful as a general theoretical framework for pattern recognition, leading to nonparametric methods, methods of threshold adjustment, and methods for taking context into account. The finite-sample-size performance of the Fix-Hodges nearest-neighbor nonparametric classification procedure is derived for independent binary patterns. The optimum (Bayes) sequential compound decision procedure, for known distributions and dependent states of nature is derived. When the states of nature form a Markov chain, the procedure is recursive, easily implemented, and immediately applicable to the use of context. A similar procedure, in which a decision depends on previous observations only through the decision about the preceding state of nature, can (when the populations are not well separated) yield results significantly worse than a procedure that does not depend on previous observations at all. When the populations are well separated, however, an improvement almost equal to that of the optimum sequential rule is achieved.

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