Computer Modelling 2

The clustering aims at assigning a set of objects to clusters in such a way that objects within the same cluster have a high degree of similarity, while objects belonging to different clusters are dissimilar. The clustering methods can be divided into hierarchical and nonhierarchical (partitioning) methods. In this paper, clustering by minimisation of a criterion function will be considered. The most traditional clustering methods are "hard" partitioning i.e. every object belongs to one group. In such a partition boundaries among clusters are sharp. However, in practice, the boundaries are not strict but ambiguous. Thus, soft partitioning is more suitable in this case. However, the fuzzy set theory proposed by Zadeh [1] performs soft partitioning. The most popular method of fuzzy clustering is the fuzzy c-means (FCM) method proposed by Bezdek [2]. Unfortunately the FCM method is sensitive to presence of outliers and noise in clustered data. In real applications, the data are corrupted by noise and assumed models such a Gaussian distribution are never exact. This method is a prototype-based method, where the prototypes are weighted (fuzzy) means. The performance of a linear estimation of prototypes is optimal for the Gaussian model of data distribution. The Gaussian model is inadequate in an impulsive environment. Impulsive signals are more accurately modelled by distributions which density functions have heavier tails than the Gaussian distribution [3, 4]. This paper is divided into four sections. In the section 2, the weighted myriad (trated as fuzzy myriad) and its properties are described. Next, in the subsection 2.2 is introduced an objective function and its optimal arguments: cluster prototypes and partition matrix. The subsection 2.3 discusses the method of estimation of myriad linearity parameter value. The section 3 presents experimental results. Finally, in section 4 conclusions are presented.