  Graph autoencoders (GAEs) are powerful tools in representation learning for
graph embedding. However, the performance of GAEs is very dependent on the
quality of the graph structure, i.e., of the adjacency matrix. In other words,
GAEs would perform poorly when the adjacency matrix is incomplete or be
disturbed. In this paper, two novel unsupervised graph embedding methods,
unsupervised graph embedding via adaptive graph learning (BAGE) and
unsupervised graph embedding via variational adaptive graph learning (VBAGE)
are proposed. The proposed methods expand the application range of GAEs on
graph embedding, i.e, on the general datasets without graph structure.
Meanwhile, the adaptive learning mechanism can initialize the adjacency matrix
without be affected by the parameter. Besides that, the latent representations
are embedded in the laplacian graph structure to preserve the topology
structure of the graph in the vector space. Moreover, the adjacency matrix can
be self-learned for better embedding performance when the original graph
structure is incomplete. With adaptive learning, the proposed method is much
more robust to the graph structure. Experimental studies on several datasets
validate our design and demonstrate that our methods outperform baselines by a
wide margin in node clustering, node classification, and graph visualization
tasks.
