Evolving Fuzzy Prototypes for Efficient Data Clustering

number of prototypes used to represent each class, the position of each prototype within its class and the membership function associated with each prototype. This paper proposes a novel, evolutionary approach to data clustering and classification which overcomes many of the limitations of traditional systems. The approach rests on the optimisation of both the number and positions of fuzzy prototypes using a real-valued genetic algorithm (GA). Because the GA acts on all of the classes at once, the system benefits naturally from global information about possible class interactions. In addition, the concept of a receptive field for each prototype is used to replace the classical distance-based membership function by an infinite fuzzy support, multi-dimensional, Gaussian function centred over the prototype and with unique variance in each dimension, reflecting the tightness of the cluster. Hence, the notion of nearest-neighbour is replaced by that of nearest attracting prototype (NAP). The proposed model is a completely self-optimising, fuzzy system called GA-NAP. Most data clustering algorithms, including the popular K-means algorithm, require a priori knowledge about the problem domain to fix the number and starting positions of the prototypes. Although such knowledge may be assumed for domains whose dimensionality is fairly small or whose underlying structure is relatively intuitive, it is clearly much less accessible in hyperdimensional settings, where the number of input parameters may be very large. Classical systems also suffer from the fact that they can only define clusters for one class at a time. Hence, no account is made of potential interactions among classes. These drawbacks are further compounded by the fact that the ensuing classification is typically based on a fixed, distancebased membership function for all prototypes. This paper proposes a novel approach to data clustering and classification which overcomes the aforementioned limitations of traditional systems. The model is based on the genetic evolution of fuzzy prototypes. A realvalued genetic algorithm (GA) is used to optimise both the number and positions of prototypes. Because the GA acts on all of the classes at once and measures fitness as classification accuracy, the system naturally profits from global information about class interaction. The concept of a receptive field for each prototype is also presented and used to replace the classical, fixed distance-based function by an infinite fuzzy support membership function. The new membership function is inspired by that used in the hidden layer of RBF networks. It consists of a multi-dimensional Gaussian function centred over the prototype and with a unique variance in each dimension that reflects the tightness of the cluster. During classification, the notion of nearestneighbour is replaced by that of nearest attracting prototype (NAP). The proposed model is a completely self-optimising, fuzzy system called GA-NAP.