To find the optimal nonlinear separating boundary with maximum margin in the input data space, this paper proposes Contractive Rectifier Networks (CRNs), wherein the hidden-layer transformations are restricted to be contraction mappings. The contractive constraints ensure that the achieved separating margin in the input space is larger than or equal to the separating margin in the output layer. The training of the proposed CRNs is formulated as a linear support vector machine (SVM) in the output layer, combined with two or more contractive hidden layers. Effective algorithms have been proposed to address the optimization challenges arising from contraction constraints. Experimental results on MNIST, CIFAR-10, CIFAR-100 and MIT-67 datasets demonstrate that the proposed contractive rectifier networks consistently outperform their conventional unconstrained rectifier network counterparts.
An, S., Hayat, M., Khan, S. H., Bennamoun, M., Boussaid, F., & Sohel, F. (2015). Contractive rectifier networks for nonlinear maximum margin classification. In Proceedings of the IEEE International Conference on Computer Vision (Vol. 2015 International Conference on Computer Vision, ICCV 2015, pp. 2515–2523). Institute of Electrical and Electronics Engineers Inc. https://doi.org/10.1109/ICCV.2015.289