Active kernel learning

Identifying the appropriate kernel function/matrix for a given dataset is essential to all kernel-based learning techniques. A number of kernel learning algorithms have been proposed to learn kernel functions or matrices from side information (e.g., either labeled examples or pairwise constraints). However, most previous studies are limited to "passive" kernel learning in which side information is provided beforehand. In this paper we present a framework of Active Kernel Learning (AKL) that actively identifies the most informative pairwise constraints for kernel learning. The key challenge of active kernel learning is how to measure the informativeness of an example pair given its class label is unknown. To this end, we propose a min-max approach for active kernel learning that selects the example pair that results in a large classification margin regardless of its assigned class label. We furthermore approximate the related optimization problem into a convex programming problem. We evaluate the effectiveness of the proposed algorithm by comparing it to two other implementations of active kernel learning. Empirical study with nine datasets on semi-supervised data clustering shows that the proposed algorithm is more effective than its competitors.