Affinity Propagation Based Closed-Form Semi-supervised Metric Learning Framework

Recent state-of-the-art deep metric learning approaches require large number of labeled examples for their success. They cannot directly exploit unlabeled data. When labeled data is scarce, it is very essential to be able to make use of additionally available unlabeled data to learn a distance metric in a semi-supervised manner. Despite the presence of a few traditional, non-deep semi-supervised metric learning approaches, they mostly rely on the min-max principle to encode the pairwise constraints, although there are a number of other ways as offered by traditional weakly-supervised metric learning approaches. Moreover, there is no flow of information from the available pairwise constraints to the unlabeled data, which could be beneficial. This paper proposes to learn a new metric by constraining it to be close to a prior metric while propagating the affinities among pairwise constraints to the unlabeled data via a closed-form solution. The choice of a different prior metric thus enables encoding of the pairwise constraints by following formulations other than the min-max principle.