Structural Factorization of Latent Adjacency Matrix, with an application to Auto Industry Networks

There is substantial interest in the current literature -spanning finance, economics, engineering and medical imaging - on the relationship structure between several nodes in a complex system. In this paper, we extend the literature by developing model and inference for complex networks in terms of latent factors, by extracting the hidden factors that plays significant role in the configuration of inter node relationships. Together, we extend inferences to applications where the underlying network structure is also latent; that is, the adjacency matrix is unobserved. Here, we consider a Bayesian variant of the matrix factorization technique to develop a structural model of the latent adjacency matrix. There are many potential applications. For illustration,
we consider a latent network of firms in the in the US automotive sector, where the central object is to understand the impact of an economic shock on firms (or nodes of the network). An important question centers around the factors that affect the stability and resilience of inter node relationships in a network. In the automotive sector application, we would like to know whether these relationship structures are driven by collaborative or competitive environments? What are the effects of a collaborative or competitive role played by a specific firm on the configuration of the relationship network? Using accounting data on firm sales and costs, we use our proposed object oriented factorization methodology to provide explanation of the estimated network links between 3 major US auto manufacturers and their intermediate suppliers.