Discriminative indefinite kernel classifier from pairwise constraints and unlabeled data

Hui Xue, Songcan Chen, Jijian Huang

Abstract: Semi-supervised classification from pairwise constraints is a challenge in pattern recognition, since the constraints just represent the relationships between data pairs rather than the definite labels. In the last few years, several methods have been proposed, however, they still utilize either the discriminability within the constraints or the abundant unlabeled data insufficiently. In this paper, we present a novel discriminative indefinite kernel classifier. We first transform the constrained data pairs into newly-labeled samples by an outer product transformation, and then introduce an indefinite discriminative regularizer in the transformed space in order to further embed the discriminative and structural information involved in the newly labeled and unlabeled samples into the classifier design. We validate that such classifier naturally lies in the more general Reproducing Kernel Krein Space rather than the common Reproducing Kernel Hilbert Space. Experiments show the superiority of our method.