Dyadic data contains co-occurrences of objects, which is often modeled by finite mixture model which in turn is learned by expectation maximization (EM) algorithm. Objects in traditional dyadic data are identified by names, causing the drawback which is that it is impossible to extract implicit valuable knowledge under objects. In this research, I propose the so-called attributed dyadic data (ADD) in which each object has an informative attribute and each co-occurrence of two objects is associated with a value. ADD is flexible and covers most of structures / forms of dyadic data. Conditional mixture model (CMM), which is a variant of finite mixture model, is applied into learning ADD. Moreover, a significant feature of CMM is that any co-occurrence of two objects is based on some conditional variable. As a result, CMM can predict or estimate co-occurrent values based on regression model, which extends applications of ADD and CMM.

Being able to express broad families of equivariant or invariant attributed graph functions is a popular measuring stick of whether graph neural networks should be employed in practical applications. However, it is equally important to learn deep local minima of losses (i.e., with much smaller loss values than other minima), even when architectures cannot express global minima. In this work we introduce the architectural property of attracting GNN optimization trajectories to local minima as a means of achieving smaller losses. We take first steps in satisfying this property for losses defined over attributed undirected unweighted graphs with a novel architecture, called Universal Local Attractor (ULA). The latter refines each dimension of end-to-end trained node feature embeddings based on graph structure to track the optimization trajectories of losses satisfying some mild conditions. The refined dimensions are then linearly pooled to create predictions. We experiment on 10 tasks, from node classification to clique detection, on which ULA is comparable with or significantly outperforms popular alternatives of similar or greater theoretical expressive power.

Nowadays, we use social networks such as Twitter, Facebook, WeChat and Weibo as means to communicate with each other and get to know others. Gradually social networks has become indispensable in our everyday life, and we cannot absolutely imagine what the daily life would be like without social networks. Through social networks, we can access friends' opinions and behaviors easily and are influenced by them in turn. Thus, an effective algorithm to find the top-K influential nodes (the problem of influence maximization) in the social network is critical for various downstream tasks such as viral marketing, anticipating natural hazards, reducing gang violence, public opinion supervision etc. Solving the problem of influence maximization in real-world propagation scenarios often involves estimating influence strength (influence probability between two nodes), which cannot directly observed. To estimate influence strength, conventional approaches propose various humanly-devised rules to extract features of user interactions, the effectiveness of which heavily depends on domain expert knowledge. Besides, they are often applicable for special scenarios or specific diffusion models. Consequently, they are difficult to be generalized into different scenarios, diffusion models and even domains. Inspired by the powerful ability of neural networks in the field of representation learning, we design a deep hierarchical network embedding model HGE to map nodes (with attributes) into latent space automatically. In general, HGE takes an attributed social network as the input for learning latent network representation of each node, incorporating hierarchical community structure, node attributes and general network structure into a unified deep generative framework. Then, with the leaned latent representation of each node, we propose a HGE-GA algorithm to predict influence strength and compute the top-K influential nodes through a greedy-based maximization algorithm. Extensive experiments on real-world attributed networks demonstrate the outstanding superiority of the proposed HGE model and HGE-GA algorithm compared with the state-of-the-art methods, verifying the effectiveness of the proposed model and algorithm.