Node Embedding over Temporal Graphs

In this work, we present a method for node embedding in temporal graphs. We propose an algorithm that learns the evolution of a temporal graph's nodes and edges over time and incorporates this dynamics in a temporal node embedding framework for different graph prediction tasks. We present a joint loss function that creates a temporal embedding of a node by learning to combine its historical temporal embeddings, such that it optimizes per given task (e.g., link prediction). The algorithm is initialized using static node embeddings, which are then aligned over the representations of a node at different time points, and eventually adapted for the given task in a joint optimization. We evaluate the effectiveness of our approach over a variety of temporal graphs for the two fundamental tasks of temporal link prediction and multi-label node classification, comparing to competitive baselines and algorithmic alternatives. Our algorithm shows performance improvements across many of the datasets and baselines and is found particularly effective for graphs that are less cohesive, with a lower clustering coefficient

Learning Edge Representations via Low-Rank Asymmetric Projections

We propose a new method for embedding graphs while preserving directed edge information. Learning such continuous-space vector representations (or embeddings) of nodes in a graph is an important first step for using network information (from social networks, user-item graphs, knowledge bases, etc.) in many machine learning tasks. Unlike previous work, we (1) explicitly model an edge as a function of node embeddings, and we (2) propose a novel objective, the "graph likelihood", which contrasts information from sampled random walks with non-existent edges. Individually, both of these contributions improve the learned representations, especially when there are memory constraints on the total size of the embeddings. When combined, our contributions enable us to significantly improve the state-of-the-art by learning more concise representations that better preserve the graph structure. We evaluate our method on a variety of link-prediction task including social networks, collaboration networks, and protein interactions, showing that our proposed method learn representations with error reductions of up to 76% and 55%, on directed and undirected graphs. In addition, we show that the representations learned by our method are quite space efficient, producing embeddings which have higher structure-preserving accuracy but are 10 times smaller

SNE: Signed Network Embedding

Several network embedding models have been developed for unsigned networks. However, these models based on skip-gram cannot be applied to signed networks because they can only deal with one type of link. In this paper, we present our signed network embedding model called SNE. Our SNE adopts the log-bilinear model, uses node representations of all nodes along a given path, and further incorporates two signed-type vectors to capture the positive or negative relationship of each edge along the path. We conduct two experiments, node classification and link prediction, on both directed and undirected signed networks and compare with four baselines including a matrix factorization method and three state-of-the-art unsigned network embedding models. The experimental results demonstrate the effectiveness of our signed network embedding.Comment: To appear in PAKDD 201

Adversarial Attack and Defense on Graph Data: A Survey

Deep neural networks (DNNs) have been widely applied to various applications including image classification, text generation, audio recognition, and graph data analysis. However, recent studies have shown that DNNs are vulnerable to adversarial attacks. Though there are several works studying adversarial attack and defense strategies on domains such as images and natural language processing, it is still difficult to directly transfer the learned knowledge to graph structure data due to its representation challenges. Given the importance of graph analysis, an increasing number of works start to analyze the robustness of machine learning models on graph data. Nevertheless, current studies considering adversarial behaviors on graph data usually focus on specific types of attacks with certain assumptions. In addition, each work proposes its own mathematical formulation which makes the comparison among different methods difficult. Therefore, in this paper, we aim to survey existing adversarial learning strategies on graph data and first provide a unified formulation for adversarial learning on graph data which covers most adversarial learning studies on graph. Moreover, we also compare different attacks and defenses on graph data and discuss their corresponding contributions and limitations. In this work, we systemically organize the considered works based on the features of each topic. This survey not only serves as a reference for the research community, but also brings a clear image researchers outside this research domain. Besides, we also create an online resource and keep updating the relevant papers during the last two years. More details of the comparisons of various studies based on this survey are open-sourced at https://github.com/YingtongDou/graph-adversarial-learning-literature.Comment: In submission to Journal. For more open-source and up-to-date information, please check our Github repository: https://github.com/YingtongDou/graph-adversarial-learning-literatur