Generalized smart evolving fuzzy systems
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- Lughofer, E., Cernuda, C., Kindermann, S. et al. Evolving Systems (2015) 6: 269. doi:10.1007/s12530-015-9132-6
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In this paper, we propose a new methodology for learning evolving fuzzy systems (EFS) from data streams in terms of on-line regression/system identification problems. It comes with enhanced dynamic complexity reduction steps, acting on model components and on the input structure and by employing generalized fuzzy rules in arbitrarily rotated position. It is thus termed as Gen-Smart-EFS (GS-EFS), short for generalized smart evolving fuzzy systems. Equipped with a new projection concept for high-dimensional kernels onto one-dimensional fuzzy sets, our approach is able to provide equivalent conventional TS fuzzy systems with axis-parallel rules, thus maintaining interpretability when inferring new query samples. The on-line complexity reduction on rule level integrates a new merging concept based on a combined adjacency–homogeneity relation between two clusters (rules). On input structure level, complexity reduction is motivated by a combined statistical-geometric concept and acts in a smooth and soft manner by incrementally adapting feature weights: features may get smoothly out-weighted over time (\(\rightarrow\)soft on-line dimension reduction) but also may become reactivated at a later stage. Out-weighted features will contribute little to the rule evolution criterion, which prevents the generation of unnecessary rules and reduces over-fitting due to curse of dimensionality. The criterion relies on a newly developed re-scaled Mahalanobis distance measure for assuring monotonicity between feature weights and distance values. Gen-Smart-EFS will be evaluated based on high-dimensional real-world data (streaming) sets and compared with other well-known (evolving) fuzzy systems approaches. The results show improved accuracy with lower rule base complexity as well as smaller rule length when using Gen-Smart-EFS.