Fuzzy clustering with high contrast

In a fuzzy clustering an object typically receives strictly positive memberships to all clusters, even when the object clearly belongs to one particular cluster. Consequently, each clusterʹs estimated center and scatter matrix are influenced by many objects that have small positive memberships to it. This effect may keep the fuzzy method from finding the true clusters. We analyze the cause and propose a remedy, which is a modification of the objective function and the corresponding algorithm. The resulting clustering has a high contrast in the sense that outlying and bridging objects remain fuzzy, whereas the other objects become crisp. The enhanced version of fuzzy k-means is illustrated with an example, as well as the enhanced version of the fuzzy minimum volume method.