Fuzzy Clustering of Patterns Represented by Pairwise Dissimilarities

Clustering is the problem of grouping objects on the basis of a similarity measure between them. This paper considers the approaches belonging to the K-means family, in particular those based on fuzzy memberships. When patterns are represented by means of non-metric pairwise dissimilarities, these methods cannot be directly applied, since they are not guaranteed to converge. Symmetrization and shift operations have been proposed, to transform the dissimilarities between patterns from non-metric to metric. It has been shown that they modify the K-means objective function by a constant, that does not influence the optimization procedure. Some fuzzy clustering algorithms have been extended, in order to handle patterns described by means of pairwise dissimilarities. The literature, however, lacks of an explicit analysis on what happens to K-means style fuzzy clustering algorithms, when the dissimilarities are transformed to let them become metric. This paper shows how the objective functions of four clustering algorithms based on fuzzy memberships change, due to dissimilarities transformations. The experimental analysis conducted on a synthetic and a real data set shows the effect of the dissimilarities transformations for four clustering algorithms based on fuzzy memberships.