In Proceedings of the 29th ACM International Conference on Information and Knowledge Management (CIKM '20), October 19-23, 2020, Virtual Event, Ireland
Recently, there has been an interest in embedding networks in hyperbolic space, since hyperbolic space has been shown to work well in capturing graph/network structure as it can naturally reflect some properties of complex networks. However, the work on network embedding in hyperbolic space has been focused on microscopic node embedding. In this work, we are the first to present a framework to embed the structural roles of nodes into hyperbolic space. Our framework extends struct2vec, a well-known structural role preserving embedding method, by moving it to a hyperboloid model. We evaluated our method on four real-world and one synthetic network. Our results show that hyperbolic space is more effective than euclidean space in learning latent representations for the structural role of nodes.
Structural identity is a concept of symmetry in which network nodes are identified according to the network structure and their relationship to other nodes. Structural identity has been studied in theory and practice over the past decades, but only recently has it been addressed with representational learning techniques. This work presents struc2vec, a novel and flexible framework for learning latent representations for the structural identity of nodes. struc2vec uses a hierarchy to measure node similarity at different scales, and constructs a multilayer graph to encode structural similarities…
Nodes in networks may have one or more functions that determine their role in the system. As opposed to local proximity, which captures the local context of nodes, the role identity captures the functional "role" that nodes play in a network, such as being the center of a group, or the bridge between two groups. This means that nodes far apart in a network can have similar structural role identities. Several recent works have explored methods for embedding the roles of nodes in networks. However, these methods all rely on either approximating or indirect modeling of structural equivalence. In …
Recent research on network embedding in hyperbolic space have proven successful in several applications. However, nodes in real world networks tend to interact through several distinct channels. Simple aggregation or ignorance of this multiplexity will lead to misleading results. On the other hand, there exists redundant information between different interaction patterns between nodes. Recent research reveals the analogy between the community structure and the hyperbolic coordinate. To learn each node's effective embedding representation while reducing the redundancy of multiplex network, we t…
Message passing Graph Neural Networks (GNNs) provide a powerful modeling framework for relational data. However, the expressive power of existing GNNs is upper-bounded by the 1-Weisfeiler-Lehman (1-WL) graph isomorphism test, which means GNNs that are not able to predict node clustering coefficients and shortest path distances, and cannot differentiate between different d-regular graphs. Here we develop a class of message passing GNNs, named Identity-aware Graph Neural Networks (ID-GNNs), with greater expressive power than the 1-WL test. ID-GNN offers a minimal but powerful solution to limitat…
Jilin University（吉林大学）；University of Technology Sydney（悉尼科技大学）；Nanjing Forestry University（南京林业大学）
Signed network embedding methods aim to learn vector representations of nodes in signed networks. However, existing algorithms only managed to embed networks into low-dimensional Euclidean spaces whereas many intrinsic features of signed networks are reported more suitable for non-Euclidean spaces. For instance, previous works did not consider the hierarchical structures of networks, which is widely witnessed in real-world networks. In this work, we answer an open question that whether the hyperbolic space is a better choice to accommodate signed networks and learn embeddings that can preserve…
Beijing University of Posts and Telecommunications（北京邮电大学）；Florida State University（佛罗里达州立大学）；Beihang University（北京航空航天大学）；University of Illinois at Chicago（伊利诺伊大学芝加哥分校）
Learning representations for graphs plays a critical role in a wide spectrum of downstream applications. In this paper, we summarize the limitations of the prior works in three folds: representation space, modeling dynamics and modeling uncertainty. To bridge this gap, we propose to learn dynamic graph representation in hyperbolic space, for the first time, which aims to infer stochastic node representations. Working with hyperbolic space, we present a novel Hyperbolic Variational Graph Neural Network, referred to as HVGNN. In particular, to model the dynamics, we introduce a Temporal GNN (TGN…
Finding a low dimensional representation of hierarchical, structured data described by a network remains a challenging problem in the machine learning community. An emerging approach is embedding these networks into hyperbolic space because it can naturally represent a network's hierarchical structure. However, existing hyperbolic embedding approaches cannot deal with attributed networks, in which nodes are annotated with additional attributes. These attributes might provide additional proximity information to constrain the representations of the nodes, which is important to learn high quality…
Recent advances in the field of network embedding have shown that low-dimensional network representation is playing a critical role in network analysis. Most existing network embedding methods encode the local proximity of a node, such as the first- and second-order proximities. While being efficient, these methods are short of leveraging the global structural information between nodes distant from each other. In addition, most existing methods learn embeddings on one single fixed network, and thus cannot be generalized to unseen nodes or networks without retraining. In this paper we present S…
Beihang University（北京航空航天大学）；Macquarie University（麦考瑞大学）；Central South University（中南大学）；University of Illinois at Chicago（伊利诺伊大学芝加哥分校）
Graph Neural Networks (GNNs) have been widely studied in various graph data mining tasks. Most existingGNNs embed graph data into Euclidean space and thus are less effective to capture the ubiquitous hierarchical structures in real-world networks. Hyperbolic Graph Neural Networks(HGNNs) extend GNNs to hyperbolic space and thus are more effective to capture the hierarchical structures of graphs in node representation learning. In hyperbolic geometry, the graph hierarchical structure can be reflected by the curvatures of the hyperbolic space, and different curvatures can model different hierarch…
Link prediction is a paradigmatic problem in network science with a variety of applications. In latent space network models this problem boils down to ranking pairs of nodes in the order of increasing latent distances between them. The network model with hyperbolic latent spaces has a number of attractive properties suggesting it must be a powerful tool to predict links, but the past work in this direction reported mixed results. Here we perform systematic investigation of the utility of latent hyperbolic geometry for link prediction in networks. We first show that some measures of link predic…
Heterogeneous networks, which connect informative nodes containing text with different edge types, are routinely used to store and process information in various real-world applications. Graph Neural Networks (GNNs) and their hyperbolic variants provide a promising approach to encode such networks in a low-dimensional latent space through neighborhood aggregation and hierarchical feature extraction, respectively. However, these approaches typically ignore metapath structures and the available semantic information. Furthermore, these approaches are sensitive to the noise present in the training…
The idea of minimum curvilinearity (MC) is that the hidden geometry of complex networks, in particular when they are sufficiently sparse, clustered, small-world and heterogeneous, can be efficiently navigated using the minimum spanning tree (MST), which is a greedy navigator. The local topological information drives the global geometrical navigation and the MST can be interpreted as a growing path that greedily maximizes local similarity between the nodes attached at each step by globally minimizing their overall distances in the network. This is also valid in absence of the network structure …
Technische Universität Dresden（德累斯顿工业大学）；Tsinghua University（清华大学）
Analysis of 'big data' characterized by high-dimensionality such as word vectors and complex networks requires often their representation in a geometrical space by embedding. Recent developments in machine learning and network geometry have pointed out the hyperbolic space as a useful framework for the representation of this data derived by real complex physical systems. In the hyperbolic space, the radial coordinate of the nodes characterizes their hierarchy, whereas the angular distance between them represents their similarity. Several studies have highlighted the relationship between the an…
Several observations indicate the existence of a latent hyperbolic space behind real networks that makes their structure very intuitive in the sense that the probability for a connection is decreasing with the hyperbolic distance between the nodes. A remarkable network model generating random graphs along this line is the popularity-similarity optimisation (PSO) model, offering a scale-free degree distribution, high clustering and the small world property at the same time. These results provide a strong motivation for the development of hyperbolic embedding algorithms, that tackle the problem …
The University of Queensland（昆士兰大学）；University of Technology Sydney（悉尼科技大学）；University of Electronic Science and Technology of China（电子科技大学）
Signed link prediction in social networks aims to reveal the underlying relationships (i.e. links) among users (i.e. nodes) given their existing positive and negative interactions observed. Most of the prior efforts are devoted to learning node embeddings with graph neural networks (GNNs), which preserve the signed network topology by message-passing along edges to facilitate the downstream link prediction task. Nevertheless, the existing graph-based approaches could hardly provide human-intelligible explanations for the following three questions: (1) which neighbors to aggregate, (2) which pa…
User identity linkage across social networks is an essential problem for cross-network data mining. Since network structure, profile and content information describe different aspects of users, it is critical to learn effective user representations that integrate heterogeneous information. This paper proposes a novel framework with INformation FUsion and Neighborhood Enhancement (INFUNE) for user identity linkage. The information fusion component adopts a group of encoders and decoders to fuse heterogeneous information and generate discriminative node embeddings for preliminary matching. Then,…
Hyperbolic geometry offers a natural focus + context for data visualization and has been shown to underlie real-world complex networks. However, current hyperbolic network visualization approaches are limited to special types of networks and do not scale to large datasets. With this in mind, we designed, implemented, and analyzed three methods for hyperbolic visualization of networks in the browser based on inverse projections, generalized force-directed algorithms, and hyperbolic multi-dimensional scaling (H-MDS). A comparison with Euclidean MDS shows that H-MDS produces embeddings with lower…
Information routing is one of the main tasks in many complex networks with a communication function. Maps produced by embedding the networks in hyperbolic space can assist this task enabling the implementation of efficient navigation strategies. However, only static maps have been considered so far, while navigation in more realistic situations, where the network structure may vary in time, remain largely unexplored. Here, we analyze the navigability of real networks by using greedy routing in hyperbolic space, where the nodes are subject to a stochastic activation-inactivation dynamics. We fi…
