SMGRL: Scalable Multi-resolution Graph Representation Learning

Graph convolutional networks (GCNs) allow us to learn topologically-aware node embeddings, which can be useful for classification or link prediction. However, they are unable to capture long-range dependencies between nodes without adding additional layers -- which in turn leads to over-smoothing and increased time and space complexity. Further, the complex dependencies between nodes make mini-batching challenging, limiting their applicability to large graphs. We propose a Scalable Multi-resolution Graph Representation Learning (SMGRL) framework that enables us to learn multi-resolution node embeddings efficiently. Our framework is model-agnostic and can be applied to any existing GCN model. We dramatically reduce training costs by training only on a reduced-dimension coarsening of the original graph, then exploit self-similarity to apply the resulting algorithm at multiple resolutions. The resulting multi-resolution embeddings can be aggregated to yield high-quality node embeddings that capture both long- and short-range dependencies. Our experiments show that this leads to improved classification accuracy, without incurring high computational costs.Comment: 22 page

Extracting Implicit Social Relation for Social Recommendation Techniques in User Rating Prediction

Recommendation plays an increasingly important role in our daily lives. Recommender systems automatically suggest items to users that might be interesting for them. Recent studies illustrate that incorporating social trust in Matrix Factorization methods demonstrably improves accuracy of rating prediction. Such approaches mainly use the trust scores explicitly expressed by users. However, it is often challenging to have users provide explicit trust scores of each other. There exist quite a few works, which propose Trust Metrics to compute and predict trust scores between users based on their interactions. In this paper, first we present how social relation can be extracted from users' ratings to items by describing Hellinger distance between users in recommender systems. Then, we propose to incorporate the predicted trust scores into social matrix factorization models. By analyzing social relation extraction from three well-known real-world datasets, which both: trust and recommendation data available, we conclude that using the implicit social relation in social recommendation techniques has almost the same performance compared to the actual trust scores explicitly expressed by users. Hence, we build our method, called Hell-TrustSVD, on top of the state-of-the-art social recommendation technique to incorporate both the extracted implicit social relations and ratings given by users on the prediction of items for an active user. To the best of our knowledge, this is the first work to extend TrustSVD with extracted social trust information. The experimental results support the idea of employing implicit trust into matrix factorization whenever explicit trust is not available, can perform much better than the state-of-the-art approaches in user rating prediction

Modeling and analysis of time-evolving sparse networks

An important problem that arises in many applications of large networks is using observational data to infer the interactions (i.e., edges) between individuals (or vertices) which leads to complex collective behavior. In our work, we focus on time-evolving networks where basic assumptions about the shape or size of the underlying network topology do not hold. As the availability and importance of temporal interaction data such as email communication increases, it becomes increasingly important to not only analyze their data structure but also to generate a model to capture their properties. When analyzing these kinds of networks, we observe interactions between a set of entities and we wish to extract informative representations that are useful for making predictions about the entities and their relationships. We then develop generative models that explain the probabilistic distributions governing the dynamic networks, fit such models to real networks, and use them to generate realistic graphs. A central focus of this thesis is on applications where the edges of their dynamic network might not be observed, but instead we can observe the dynamics of stochastic cascading processes (e.g., information diffusion, virus propagation) occurring over the unobserved network. Further, we assume that the inferred edges construct a multigraph there might be multiple edges between two entities in a multigraph. We generate a probabilistic model for such data, where a tree construction phase is proposed to extract the most probable edges of the network. Using such a model allows us to infer the network given observations from the stochastic cascading process. Another important aspect of our research is the study of sparse real networks. most realworld multigraphs, such as email interaction datasets, are typically sparse in practice and they exhibit a modular structure with the distributions that evolve over time. We take the advantage of nonparametric models for interaction multigraphs which combines the sparsity of edge-exchangeable multigraphs coupled with the dynamic clustering patterns that tend to reinforce recent behavioral patterns. Finally, the problem of identifying central entities from the information point of view in a network is addressed by considering a prominent centrality measure in the networks. In addition to providing algorithms and theoretical analyses, we present extensive empirical evaluation of our approaches on several synthetic and real-world graphs.12