  Convolution Neural Networks on Graphs are important generalization and
extension of classical CNNs. While previous works generally assumed that the
graph structures of samples are regular with unified dimensions, in many
applications, they are highly diverse or even not well defined. Under some
circumstances, e.g. chemical molecular data, clustering or coarsening for
simplifying the graphs is hard to be justified chemically. In this paper, we
propose a more general and flexible graph convolution network (EGCN) fed by
batch of arbitrarily shaped data together with their evolving graph Laplacians
trained in supervised fashion. Extensive experiments have been conducted to
demonstrate the superior performance in terms of both the acceleration of
parameter fitting and the significantly improved prediction accuracy on
multiple graph-structured datasets.
