A Fuzzy Classifier with Evolutionary Design of Ellipsoidal Decision Regions

A fuzzy classifier using multiple ellipsoids approximating decision regions for classification is to be designed in this paper. An algorithm called Gustafson-Kessel algorithm (GKA) with an adaptive distance norm based on covariance matrices of prototype data points is adopted to learn the ellipsoids. GKA is able to adapt the distance norm to the underlying distribution of the prototype data points except that the sizes of ellipsoids need to be determined a priori. To overcome GKA’s inability to determine appropriate size of ellipsoid, the genetic algorithm (GA) is applied to learn the size of ellipsoid. With GA combined with GKA, it will be shown in this paper that the proposed method outperforms the benchmark algorithms as well as algorithms in the field. Keywords—ellipsoids, genetic algorithm, classification, fuzzy c-means (FCM).