Extracting Rules from Artificial Neural Networks with Kernel-Based Representation

In Neural Networks models the knowledge synthesized from the training process is represented in a subsymbolic fashion (weights, kernels, combination of numerical descriptions) that makes diicult its interpretation. The interpretation of the internal representation of a successful Neural Network can be useful to understand the nature of the problem and its solution, to use the Neural "model" as a tool that gives insights about the problem solved and not just as a solving mechanism treated as a black box. The internal representation used by the family of kernel-based Neural Networks (including Radial Basis Functions, Support Vector machines, Coulomb potential methods, and some prob-abilistic Neural Networks) can be seen as a set of positive instances of classiication and, thereafter, used to derive fuzzy rules suitable for explanation or inference processes. The probabilistic nature of the kernel-based Neural Networks is captured by the membership functions associated to the components of the rules extracted. In this work we propose a method to extract fuzzy rules from trained Neural Networks of the family mentioned ; comparing the quality of the knowledge extracted by diierent methods using known machine learning benchmarks. 1 Motivation At a certain level of abstraction, neural learning can be seen as a case-based learning. The Neural Network stores only a selected set of examples (or a combination of examples) and uses them to nd the best approximation for new instances of the problem, according to its generalization ability. The system learns from examples , not rules, but the examples are instances of the application of (partially) unknown rules in a given domain. A successful Neural Network synthesizes in a subsymbolic representation the rules needed to solve instances of a problem in a given domain; but its mechanism does not give signiicant feedback to the designer that could contribute to the understanding of the problem domain. In Neural Networks models the knowledge synthesized from the training process is represented in a subsymbolic fashion (weights, kernels, combination of