We propose a novel rule extraction algorithm adopting the mathematical model called Basis Pursuit (Chen, et al. 1998), where it is represented by a linear combination of kernel functions (similar to MLP or Support Vector Machines) but gives sparse function representation compared to those models. In this algorithm, a number of logical rules are set to the kernel functions in advance. Applying a linear programming method, we obtain classification rules as a small subset of them. If less logical rules are discovered, they will be the core knowledge in a database. We applied our algorithm to several known benchmark problems and its effectualness is verified.
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