Semi-Supervised Relational Fuzzy clustering with Local Distance Measure Learning

We introduce a new fuzzy semi-supervised clustering technique with adaptive local distance measure (SURF-LDML). The proposed algorithm learns the underlying cluster-dependent dissimilarity measure while finding compact clusters in the given data set. This objective is achieved by integrating penalty and reward cost functions in the objective function. These cost functions are dependent on the local distance and are weighted by fuzzy membership degrees. Moreover, they use side-information in the form of a small set of constraints on which instances should or should not reside in the same cluster. The proposed algorithm uses only the pairwise relation between the feature vectors. This makes it applicable when similar objects cannot be represented by a single prototype.