Duality in Multi-View Restricted Kernel Machines

We propose a unifying setting that combines existing restricted kernel machine methods into a single primal-dual multi-view framework for kernel principal component analysis in both supervised and unsupervised settings. We derive the primal and dual representations of the framework and relate different training and inference algorithms from a theoretical perspective. We show how to achieve full equivalence in primal and dual formulations by rescaling primal variables. Finally, we experimentally validate the equivalence and provide insight into the relationships between different methods on a number of time series data sets by recursively forecasting unseen test data and visualizing the learned features.

Semi-Supervised Classification with Graph Convolutional Kernel Machines

We present a deep Graph Convolutional Kernel Machine (GCKM) for semi-supervised node classification in graphs. First, we introduce an unsupervised kernel machine propagating the node features in a one-hop neighbourhood. Then, we specify a semi-supervised classification kernel machine through the lens of the Fenchel-Young inequality. The deep graph convolutional kernel machine is obtained by stacking multiple shallow kernel machines. After showing that unsupervised and semi-supervised layer corresponds to an eigenvalue problem and a linear system on the aggregated node features, respectively, we derive an efficient end-to-end training algorithm in the dual variables. Numerical experiments demonstrate that our approach is competitive with state-of-the-art graph neural networks for homophilious and heterophilious benchmark datasets. Notably, GCKM achieves superior performance when very few labels are available.