Fuzzy relational kernel clustering with Local Scaling Parameter Learning

We introduce a new fuzzy relational clustering technique with Local Scaling Parameter Learning (LSPL). The proposed approach learns the underlying cluster dependent dissimilarity measure while finding compact clusters in the given data set. The learned measure is a Gaussian similarity function defined with respect to each cluster that allows to control the scaling of the clusters and thus, improve the final partition. We minimize one objective function for both the optimal partition and for the cluster dependent scaling parameter. This optimization is done iteratively by dynamically updating the partition and the scaling parameter in each iteration. This makes the proposed algorithm simple and fast. Moreover, as we assume that the data is available in a relational form, the proposed approach is applicable even when only the degree to which pairs of objects in the data are related is available. It is also more practical when similar objects cannot be represented by a single prototype.