  Graph convolutional neural networks (GCNNs) have received much attention
recently, owing to their capability in handling graph-structured data. Among
the existing GCNNs, many methods can be viewed as instances of a neural message
passing motif; features of nodes are passed around their neighbors, aggregated
and transformed to produce better nodes' representations. Nevertheless, these
methods seldom use node transition probabilities, a measure that has been found
useful in exploring graphs. Furthermore, when the transition probabilities are
used, their transition direction is often improperly considered in the feature
aggregation step, resulting in an inefficient weighting scheme. In addition,
although a great number of GCNN models with increasing level of complexity have
been introduced, the GCNNs often suffer from over-fitting when being trained on
small graphs. Another issue of the GCNNs is over-smoothing, which tends to make
nodes' representations indistinguishable. This work presents a new method to
improve the message passing process based on node transition probabilities by
properly considering the transition direction, leading to a better weighting
scheme in nodes' features aggregation compared to the existing counterpart.
Moreover, we propose a novel regularization method termed DropNode to address
the over-fitting and over-smoothing issues simultaneously. DropNode randomly
discards part of a graph, thus it creates multiple deformed versions of the
graph, leading to data augmentation regularization effect. Additionally,
DropNode lessens the connectivity of the graph, mitigating the effect of
over-smoothing in deep GCNNs. Extensive experiments on eight benchmark datasets
for node and graph classification tasks demonstrate the effectiveness of the
proposed methods in comparison with the state of the art.
