  Recently, graph convolutional network (GCN) has been widely used for
semi-supervised classification and deep feature representation on
graph-structured data. However, existing GCN generally fails to consider the
local invariance constraint in learning and representation process. That is, if
two data points Xi and Xj are close in the intrinsic geometry of the data
distribution, then their labels/representations should also be close to each
other. This is known as local invariance assumption which plays an essential
role in the development of various kinds of traditional algorithms, such as
dimensionality reduction and semi-supervised learning, in machine learning
area. To overcome this limitation, we introduce a graph Laplacian GCN (gLGCN)
approach for graph data representation and semi-supervised classification. The
proposed gLGCN model is capable of encoding both graph structure and node
features together while maintains the local invariance constraint naturally for
robust data representation and semi-supervised classification. Experiments show
the benefit of the benefits the proposed gLGCN network.
