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We propose a mathematical programming methodology for identifying and examining regression rules extracted from layered feed-forward neural networks. The area depicted in the rule premise covers a convex polyhedron in the input space, and the adopted approximation function for the output value is a multivariate polynomial function of x, the outside stimulus input. The mathematical programming analysis, instead of a data analysis, is proposed for identifying the convex polyhedron associated with each rule. Moreover, the mathematical programming analysis is proposed for examining the extracted rules to explore features. An implementation test on bond pricing rule extraction lends support to the proposed methodology.