Crisp and fuzzy methods of optimal clustering on networks of objects

The aim of the paper is to show two methods of optimal clustering based on general dissimilarity measures. Since these methods use objects and the pairwise dissimilarity alone and not the intrinsic properties of the space in which the objects are put, a network of objects are under consideration and therefore clustering is studied on this network. The first method uses the meta-heuristic techniques for optimization, which include local search, simulated annealing, genetic algorithms, and tabu search, have been applied to many real problems. The paper investigates their usefulness in optimal clustering. The above four meta-heuristic methods are applied and which of the various options in those methods are appropriate is investigated by numerical experiments. Moreover a parameterized objective function is considered and a suitable parameter is found. The second method is fuzzy clustering that is a variation of fuzzy c-means for Euclidean space. A relatively simple algorithm is developed and numerical examples are also discussed.