Generalized latent space model for one-mode networks with awareness of two-mode networks

Latent space models have been widely studied for one-mode networks, in which the same type of nodes connect with each other. In many applications, one-mode networks are often observed along with two-mode networks, which reflect connections between different types of nodes and provide important information for understanding the one-mode network structure. However, the classical one-mode latent space models have several limitations in incorporating two-mode networks. To address this gap, a generalized latent space model is proposed to capture common structures and heterogeneous connecting patterns across one-mode and two-mode networks. Specifically, each node is embedded with a latent vector and network-specific degree parameters that determine the connection probabilities between nodes. A projected gradient descent algorithm is developed to estimate the latent vectors and degree parameters. Moreover, the theoretical properties of the estimators are established and it has been proven that the estimation accuracy of the shared latent vectors can be improved through incorporating two-mode networks. Finally, simulation studies and applications on two real-world datasets demonstrate the usefulness of the proposed model.