3M algorithm: finding an optimal fuzzy cluster scheme for proximity data

In order to find an optimal fuzzy cluster scheme for proximity data, where just pairwise distances among objects are given, two conditions are necessary: A good cluster validity function, which can be applied to proximity data for evaluation of the goodness of cluster schemes for varying number of clusters; a good cluster algorithm that can deal with proximity data and produce an optimal solution for a fixed number of clusters. To satisfy the first condition, a new validity function is proposed, which works well even when the number of clusters is very large. For the second condition, we give a new algorithm called multi-step maxmin and merging algorithm (3M algorithm). Experiments show that, when used in conjunction with the new cluster validity function, the 3M algorithm produces satisfactory results.