  Graph Convolutional Networks (GCNs) have made significant advances in
semi-supervised learning, especially for classification tasks. However,
existing GCN based methods have two main drawbacks. First, to increase the
receptive field and improve the representation capability of GCNs, larger
kernels or deeper network architectures are used, which greatly increases the
computational complexity and the number of parameters. Second, methods working
on higher order graphs computed directly from adjacency matrices may alter the
relationship between graph nodes, particularly for weighted graphs. In
addition, the direct construction of higher-order graphs introduces redundant
information, which may result in lower network performance. To address the
above weaknesses, in this paper, we propose a new method of multi-hop
convolutional network on weighted graphs. The proposed method consists of
multiple convolutional branches, where each branch extracts node representation
from a $k$-hop graph with small kernels. Such design systematically aggregates
multi-scale contextual information without adding redundant information.
Furthermore, to efficiently combine the extracted information from the
multi-hop branches, an adaptive weight computation (AWC) layer is proposed. We
demonstrate the superiority of our MultiHop in six publicly available datasets,
including three citation network datasets and three medical image datasets. The
experimental results show that our proposed MultiHop method achieves the
highest classification accuracy and outperforms the state-of-the-art methods.
The source code of this work have been released on GitHub
(https://github.com/ahukui/Multi-hop-Convolutions-on-Weighted-Graphs).
