Power SVM: Generalization with exemplar classification uncertainty

The human vision tends to recognize more variants of a distinctive exemplar. This observation suggests that discriminative power of training exemplars could be utilized for shaping a desirable global classifier that generalizes maximally from a few exemplars. We propose to derive classification uncertainty for each exemplar, using a local classification task to separate the exemplar from those in other categories. We then design a global classifier by incorporating these uncertainties into constraints on the classifier margins. We show through the dual form that the classification criterion can be interpreted as finding closest points between convex hulls in the feature space augmented by classification uncertainty. We call this scheme Power SVM (as in Power Diagram), since each exemplar is no longer a singular point in the feature space, but a super-point with its own governing power in the classifier space. We test Power SVM on digit recognition, indoor-outdoor categorization, and large-scale scene classification tasks. It shows consistent improvement over SVM and uncertainty weighted SVM, especially when the number of training exemplars is small.