Kernel Optimization using Pairwise Constraints for Semi-Supervised Clustering

A critical problem related to kernel-based methods is the selection of an optimal kernel for the problem at hand. The kernel function in use must conform with the learning target in order to obtain meaningful results. While solutions to estimate optimal kernel functions and their parameters have been proposed in a supervised setting, the problem presents open challenges when no labeled data are provided, and all we have available is a set of pairwise must-link and cannot-link constraints. In this paper we address the problem of optimizing the kernel function using pairwise constraints for semi-supervised clustering. To this end we derive a new optimization criterion to automatically estimate the optimal parameters of composite Gaussian kernels, directly from the data and the given constraints. We combine the optimal kernel function computed by our technique with a recently introduced semi-supervised kernel-based algorithm to demonstrate experimentally the effectivess of our approach. The results show that our method enables the practical utilization of powerful kernel-based semi-supervised clustering approaches by providing a mechanism to automatically set the involved critical parameters.