A fuzzy clustering algorithm with a variable focal point

In our everyday life the number of groups of similar objects that we visually perceive is deeply constrained by how far we are from the objects and also by the direction we are approaching them. Based on this metaphor, in this work we present a generalization of partitional clustering aiming at the inclusion into the clustering process of both distance and direction of the point of observation towards the dataset. This is done by incorporating a new term in the objective function, accounting for the distance between the clusterspsila prototypes and the point of observation. It is a well known fact that the chosen number of partitions has a major effect on the objective function based partitional clustering algorithms, conditioning both the level of granularity of the data grouping and the capability of the algorithm to accurately reflect the underlying structure of the data. Thus the correct choice of the number of clusters is essential for any successful application of such algorithms. The experimental part of this work shows how the proposed algorithm can be used to produce a set of valid alternatives for the appropriate number of partitions. The proposed method can be used in order to assist the data analyst when looking for a partition that correctly reflects a particular view of the data.