  Spectral graph convolutional networks (GCNs) are particular deep models which
aim at extending neural networks to arbitrary irregular domains. The principle
of these networks consists in projecting graph signals using the
eigen-decomposition of their Laplacians, then achieving filtering in the
spectral domain prior to back-project the resulting filtered signals onto the
input graph domain. However, the success of these operations is highly
dependent on the relevance of the used Laplacians which are mostly handcrafted
and this makes GCNs clearly sub-optimal. In this paper, we introduce a novel
spectral GCN that learns not only the usual convolutional parameters but also
the Laplacian operators. The latter are designed "end-to-end" as a part of a
recursive Chebyshev decomposition with the particularity of conveying both the
differential and the non-differential properties of the learned representations
-- with increasing order and discrimination power -- without overparametrizing
the trained GCNs. Extensive experiments, conducted on the challenging task of
skeleton-based action recognition, show the generalization ability and the
outperformance of our proposed Laplacian design w.r.t. different baselines
(built upon handcrafted and other learned Laplacians) as well as the related
work.
