  Existing deep learning models may encounter great challenges in handling
graph structured data. In this paper, we introduce a new deep learning model
for graph data specifically, namely the deep loopy neural network.
Significantly different from the previous deep models, inside the deep loopy
neural network, there exist a large number of loops created by the extensive
connections among nodes in the input graph data, which makes model learning an
infeasible task. To resolve such a problem, in this paper, we will introduce a
new learning algorithm for the deep loopy neural network specifically. Instead
of learning the model variables based on the original model, in the proposed
learning algorithm, errors will be back-propagated through the edges in a group
of extracted spanning trees. Extensive numerical experiments have been done on
several real-world graph datasets, and the experimental results demonstrate the
effectiveness of both the proposed model and the learning algorithm in handling
graph data.
