Relational fuzzy c-means and kernel fuzzy c-means using an object-wise β -spread transformation

Clustering methods of relational data are often based on the assumption that a given set of relational data is Euclidean, and kernelized clustering methods are often based on the assumption that a given kernel is positive semidefinite. In practice, non-Euclidean relational data and an indefinite kernel may arise, and a β -spread transformation was proposed for such cases, which modified a given set of relational data or a give a kernel Gram matrix such that the modified β value is common to all objects. In this paper, we propose an object-wiseβ -spread transformation for use in both relational and kernelized fuzzy c-means clustering. The proposed system retains the given data better than conventional methods, and numerical examples show that our method is efficient for both relational and kernel fuzzy c-means.