Estimating Network Flowing over Edges by Recursive Network Embedding

Abstract

In this paper, we propose a novel semisupervised learning framework to learn the flows of edges over a graph. Given the flow values of the labeled edges, the task of this paper is to learn the unknown flow values of the remaining unlabeled edges. To this end, we introduce a value amount hold by each node and impose that the amount of values flowing from the conjunctive edges of each node to be consistent with the node’s own value. We propose to embed the nodes to a continuous vector space so that the embedding vector of each node can be reconstructed from its neighbors by a recursive neural network model, linear normalized long short-term memory. Moreover, we argue that the value of each node is also embedded in the embedding vectors of its neighbors, thus propose to approximate the node value from the output of the neighborhood recursive network. We build a unified learning framework by formulating a minimization problem. To construct the learning problem, we build three subproblems of minimization: (1) the embedding error of each node from the recursive network, (2) the loss of the construction for the amount of value of each node, and (3) the difference between the value amount of each node and the estimated value from the edge flows. We develop an iterative algorithm to learn the node embeddings, edge flows, and node values jointly. We perform experiments based on the datasets of some network data, including the transportation network and innovation. The experimental results indicate that our algorithm is more effective than the state-of-the-arts.