Abstract

Low-rank matrix decomposition has gained great popularity recently in scaling up kernel methods to large amounts of data. However, some limitations could prevent them from working e?ectively in certain domains. For example, many existing approaches are intrinsically unsupervised, which does not incorporate side information (e.g., class labels) to produce task speci?c decompositions; also, they typically work “transductively”, i.e., the factorization does not generalize to new samples, so the complete factorization needs to be recomputed when new samples become available. To solve these problems, in this paper we propose an “inductive”-flavored method for low-rank kernel decomposition with priors. We achieve this by generalizing the Nystro?m method in a novel way. On the one hand, our approach employs a highly flexible, nonparametric structure that allows us to generalize the low-rank factors to arbitrarily new samples; on the other hand, it has linear time and space complexities, which can be orders of magnitudes faster than existing approaches and renders great eficiency in learning a low-rank kernel decomposi-