Learning kernel combination from noisy pairwise constraints

We consider the problem of learning the combination of multiple kernels given noisy pairwise constraints, which is in contrast to most of the existing studies that assume perfect pairwise constraints. This problem is particularly important when the pairwise constraints are derived from side information such as hyperlinks and paper citations. We propose a probabilistic approach for learning the combination of multiple kernels and show that under appropriate assumptions, the combination weights learned by the proposed approach from the noisy pairwise constraints converge to the optimal weights learned from perfectly labeled pairwise constraints. Empirical studies on data clustering using the learned combined kernel verify the effectiveness of the proposed approach.