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 beta-spread transformation. In this article we compare five methods for Euclideanizing D to (D) over tilde. The quality of (D) over tilde 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) over tilde than the other four methods. This leads to a new algorithm which we call the improved RFCM (iRFCM). (C) 2014 Elsevier Ltd. All rights reserved.