An Evolving Fuzzy Neural Network Based on the Mapping of Similarities

Abstract

<para xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> Evolving fuzzy systems (EFSs) use online learning to extract knowledge from data, perform a high-level adaptation of the network structure, and learn parameters. In this paper, we describe the performance of an EFS that is called similarity mapping, where the training pairs (<formula formulatype="inline"><tex Notation="TeX">${\bf x}_i$</tex></formula> and <formula formulatype="inline"><tex Notation="TeX">${\bf z}_i$</tex></formula>) are compressed into input and output clusters. The predictive error is minimized using a procedure that is very similar to the one implemented in fuzzy-adaptive resonance theory map (ARTMAP) and resource-allocation networks. However, in the recall phase, a fuzzy membership grade is calculated for each input cluster and used in the weighting of the output clusters to obtain the final output vector. By modifying the spread of the cluster membership function, different approximative interpolating functions can be implemented. A similarity function, which was initially proposed for ART 1 implementations, is extended to the processing of analog vectors and used to calculate the membership grades of the input clusters. Several examples show the behavior of the network, as well as its capability to classify, eliminate noise, and predict chaotic time series. </para>