On fuzzy competitive exception learning

A competitive exception learning algorithm (CELA) is proposed which derives exceptional patterns from a given set of data pairs. In the first step of the algorithm, the output space is fuzzily partitioned (using a competitive learning algorithm) and then characterized by a so-called unconditional cluster membership distribution. In the second step, the input space is fuzzily partitioned as well by again using competitive learning. After learning, the input clusters represent locations in the input space which correspond to the most exceptional patterns in the output space. These patterns are characterized by so-termed conditional cluster membership distributions. In the third step, a fuzzy rule base is set up describing the exceptions in linguistic terms. In addition, the complete fuzzy input-output map can be estimated using a mathematical function. Besides describing the various steps of the new algorithm, a theoretical framework is introduced using an information-theoretical point of view: all output data points are supposed to be generated by a non-stationary stochastic, fuzzy information source. A summary concerning the results of certain simulations completes the description of CELA. The article is concluded with a discussion and outlook.