Abstract.
In this paper we develop a method for classifying an unknown data vector as belonging to one of several classes. This method is based on the statistical methods of maximum likehood and borrowed strength estimation. We develop an MPEC procedure (for Mathematical Program with Equilibrium Constraints) for the classification of a multi-dimensional observation, using a finite set of observed training data as the inputs to a bilevel optimization problem. We present a penalty interior point method for solving the resulting MPEC and report numerical results for a multispectral minefield classification application. Related approaches based on conventional maximum likehood estimation and a bivariate normal mixture model, as well as alternative surrogate classification objective functions, are described.
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Received: October 26, 1998 / Accepted: June 11, 2001¶Published online March 24, 2003
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ID="***"The authors of this work were all partially supported by the Wright Patterson Air Force Base via Veda Contract F33615-94-D-1400. The first and third author were also supported by the National Science Foundation under grant DMS-9705220.
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ID="*"The work of this author was based on research supported by the U.S. National Science Foundation under grant CCR-9624018.
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ID="**"The work of this author was supported by the Office of Naval Research under grant N00014-95-1-0777.
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Olson, T., Pang, JS. & Priebe, C. A likelihood-MPEC approach to target classification. Math. Program. 96, 1–31 (2003). https://doi.org/10.1007/s10107-003-0242-8
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DOI: https://doi.org/10.1007/s10107-003-0242-8