Kernelized Non-Euclidean Relational c-Means Algorithms

Successes with kernel-based classification methods have spawned many recent efforts to kernelize clustering algorithms for object data. We extend this idea to the relational data case by proposing kernelized forms of the non-Euclidean relational fuzzy (NERF) and hard (NERH) c-means algorithms. We show that these relational forms are dual to kernelized forms of fuzzy and hard c-means (FCM, HCM) that are already in the literature. Moreover, our construction can be done for pure relational data, i.e., even when there is no corresponding set of object data, provided the right type of kernel is chosen. We give an example of this type, as well as three other examples of clustering with the kernelized version of NERF to illustrate the utility of this approach. Two examples show how a visual assessment technique can be used to choose a most useful value for the Gaussian kernel parameter.