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Optimal Solution of Linear Inequalities with Applications to Pattern Recognition
June 1981 (vol. 3 no. 6)
pp. 643-655
D. C. Clark, Department of Computer Science, University of Tennessee, Knoxville, TN 37916; Pattern Analysis and Recognition Corporation, Los Angeles, CA 90045.
R. C. Gonzalez, SENIOR MEMBER, IEEE, Department of Electrical Engineering, University of Tennessee, Knoxville, TN 37916.
An algorithm for the optimal solution of consistent and inconsistent linear inequalities is presented, where the optimality criterion is the maximization of the number of constraints satisfied. In the terminology of pattern recognition, the algorithm finds a linear decision function which minimizes the number of patterns misclassified. The algorithm is developed as a nonenumerative search procedure based on several new results established in this paper. Bounds on the search are also developed and the method is experimentally evaluated and shown to be computationally superior to other techniques for finding minimum-error solutions.
D. C. Clark, R. C. Gonzalez, "Optimal Solution of Linear Inequalities with Applications to Pattern Recognition," IEEE Transactions on Pattern Analysis and Machine Intelligence, vol. 3, no. 6, pp. 643-655, June 1981, doi:10.1109/TPAMI.1981.4767165
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