Improvements to the relational fuzzy c-means clustering algorithm

Relational fuzzy c-means (RFCM) is an algorithm for clustering objects represented in a pairwise dissimilarity values in a dissimilarity data matrix D. RFCM is dual to the fuzzy c-means (FCM) object data algorithm when D is a Euclidean matrix. When D is not Euclidean, RFCM can fail to execute if it encounters negative relational distances. To overcome this problem we can Euclideanize the relation D prior to clustering. There are different ways to Euclideanize D such as the β-spread transformation. In this article we compare five methods for Euclideanizing D to D ˜ . The quality of D ˜ for our purpose is judged by the ability of RFCM to discover the apparent cluster structure of the objects underlying the data matrix D. The subdominant ultrametric transformation is a clear winner, producing much better partitions of D ˜ than the other four methods. This leads to a new algorithm which we call the improved RFCM (iRFCM).