  Attributed graph embedding, which learns vector representations from graph
topology and node features, is a challenging task for graph analysis. Recently,
methods based on graph convolutional networks (GCNs) have made great progress
on this task. However,existing GCN-based methods have three major drawbacks.
Firstly,our experiments indicate that the entanglement of graph convolutional
filters and weight matrices will harm both the performance and robustness.
Secondly, we show that graph convolutional filters in these methods reveal to
be special cases of generalized Laplacian smoothing filters, but they do not
preserve optimal low-pass characteristics. Finally, the training objectives of
existing algorithms are usually recovering the adjacency matrix or feature
matrix, which are not always consistent with real-world applications. To
address these issues, we propose Adaptive Graph Encoder (AGE), a novel
attributed graph embedding framework. AGE consists of two modules: (1) To
better alleviate the high-frequency noises in the node features, AGE first
applies a carefully-designed Laplacian smoothing filter. (2) AGE employs an
adaptive encoder that iteratively strengthens the filtered features for better
node embeddings. We conduct experiments using four public benchmark datasets to
validate AGE on node clustering and link prediction tasks. Experimental results
show that AGE consistently outperforms state-of-the-art graph embedding methods
considerably on these tasks.
