  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
(RKHS). 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.
