It is largely agreed that social network links are formed due to either homophily or social influence. Inspired by this, we aim at understanding the generation of links via providing a novel embedding-based graph formation model. Different from existing graph representation learning, where link generation probabilities are defined as a simple function of the corresponding node embeddings, we model the link generation as a mixture model of the two factors. In addition, we model the homophily factor in spherical space and the influence factor in hyperbolic space to accommodate the fact that (1) homophily results in cycles and (2) influence results in hierarchies in networks. We also design a special projection to align these two spaces. We call this model Non-Euclidean Mixture Model, i.e., NMM. We further integrate NMM with our non-Euclidean graph variational autoencoder (VAE) framework, NMM-GNN. NMM-GNN learns embeddings through a unified framework which uses non-Euclidean GNN encoders, non-Euclidean Gaussian priors, a non-Euclidean decoder, and a novel space unification loss component to unify distinct non-Euclidean geometric spaces. Experiments on public datasets show NMM-GNN significantly outperforms state-of-the-art baselines on social network generation and classification tasks, demonstrating its ability to better explain how the social network is formed.

Graph Neural Networks (GNNs) have emerged as powerful tools for representation learning on structured data. The graph convolutional filter (GCF) for aggregating neighbor information is shown to be the key factor that leads to GNNs' success. Various GCFs are designed but how to select the proper filter that can best benefit the data and the task remains an open problem. In this paper, we introduce the Adaptive Filter Selection (AdaFS) framework that addresses two critical issues: (1) defining a criterion to establish a strong base filter set; and (2) adaptively selecting filters for a specific task, even when labeled data is limited, by employing Laplacian score regularization. We further connect this multiple GCF learning process and the well-developed multiple kernel learning problem to provide a solid rationale for filter selection. With experiments on 9 datasets, AdaFS gets the best average performance.

Graph convolutional networks (GCNs) have recently received wide attentions, due to their successful applications in different graph tasks and different domains. Training GCNs for a large graph, however, is still a challenge. Original full-batch GCN training requires calculating the representation of all the nodes in the graph per GCN layer, which brings in high computation and memory costs. To alleviate this issue, several sampling-based methods are proposed to train GCNs on a subset of nodes. Among them, the node-wise neighbor-sampling method recursively samples a fixed number of neighbor nodes, and thus its computation cost suffers from exponential growing neighbor size across layers; while the layer-wise importance-sampling method discards the neighbor-dependent constraints, and thus the nodes sampled across layer suffer from sparse connection problem. To deal with the above two problems, we propose a new effective sampling algorithm called LAyer-Dependent ImportancE Sampling (LADIES). Based on the sampled nodes in the upper layer, LADIES selects nodes that are in the neighborhood of these nodes and uses the constructed bipartite graph to compute the importance probability. Then, it samples a fixed number of nodes according to the probability for the whole layer, and recursively conducts such procedure per layer to construct the whole computation graph. We prove theoretically and experimentally, that our proposed sampling algorithm outperforms the previous sampling methods regarding both time and memory. Furthermore, LADIES is shown to have better generalization accuracy than original full-batch GCN, due to its stochastic nature.