A General Approach for Adaptive Kernels in Semi-Supervised Clustering

Semi-supervised clustering aims at accomplishing the clustering task by considering also labels or constraints provided by an external agent. Usually, the agent would provide the output label for a reduced number of patterns or, in the case of lack of posterior information about labels, some pairwise constraints indicating whether or not two patterns should be joined in the same cluster. Constraints may be inferred from some ad-hoc information from sampling, such as their geographical location, which are not directly considered as an input atribute. The objective is to accomplish the clustering task by considering also the pairwise constraints. In this paper we extend the previous work of Yan et al. [10] by obtaining derivative expressions for sigmoidal and polinomial kernels in order to accomplish kernel-clustering semi-supervised tasks. The resulting kernel-clustering task is optimized in relation to kernel parameters which do not need to be provided in advance like in most kernel-clustering tasks. Instead, kernel parameters are obtained as the outcome of the optimization problem.