Learning graph convolutional networks (GCNs) is an emerging field which aims at generalizing deep learning to arbitrary non-regular domains. Most of the existing GCNs follow a neighborhood aggregation scheme, where the representation of a node is recursively obtained by aggregating its neighboring node representations using averaging or sorting operations. However, these operations are either ill-posed or weak to be discriminant or increase the number of training parameters and thereby the computational complexity and the risk of overfitting. In this paper, we introduce a novel GCN framework that achieves spatial graph convolution in a reproducing kernel Hilbert space. The latter makes it possible to design, via implicit kernel representations, convolutional graph filters in a high dimensional and more discriminating space without increasing the number of training parameters. The particularity of our GCN model also resides in its ability to achieve convolutions without explicitly realigning nodes in the receptive fields of the learned graph filters with those of the input graphs, thereby making convolutions permutation agnostic and well defined. Experiments conducted on the challenging task of skeleton-based action recognition show the superiority of the proposed method against different baselines as well as the related work.

Learning graph convolutional networks (GCNs) is an emerging field which aims at generalizing convolutional operations to arbitrary non-regular domains. In particular, GCNs operating on spatial domains show superior performances compared to spectral ones, however their success is highly dependent on how the topology of input graphs is defined. In this paper, we introduce a novel framework for graph convolutional networks that learns the topological properties of graphs. The design principle of our method is based on the optimization of a constrained objective function which learns not only the usual convolutional parameters in GCNs but also a transformation basis that conveys the most relevant topological relationships in these graphs. Experiments conducted on the challenging task of skeleton-based action recognition shows the superiority of the proposed method compared to handcrafted graph design as well as the related work.