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Register a new userInvestigating Extensions to Random Walk Based Graph Embedding
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Graph embedding has recently gained momentum in the research community, in particular after the introduction of random walk and neural network based approaches. However, most of the embedding approaches focus on representing the local neighborhood of nodes and fail to capture the global graph structure, i.e. to retain the relations to distant nodes. To counter that problem, we propose a novel extension to random walk based graph embedding, which removes a percentage of least frequent nodes from the walks at different levels. By this removal, we simulate farther distant nodes to reside in the close neighborhood of a node and hence explicitly represent their connection. Besides the common evaluation tasks for graph embeddings, such as node classification and link prediction, we evaluate and compare our approach against related methods on shortest path approximation. The results indicate, that extensions to random walk based methods (including our own) improve the predictive performance only slightly - if at all.
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Graph kernels are widely used for measuring the similarity between graphs. Many existing graph kernels, which focus on local patterns within graphs rather than their global properties, suffer from significant structure information loss when representing graphs. Some recent global graph kernels, which utilizes the alignment of geometric node embeddings of graphs, yield state-of-the-art performance. However, these graph kernels are not necessarily positive-definite. More importantly, computing the graph kernel matrix will have at least quadratic {time} complexity in terms of the number and the size of the graphs. In this paper, we propose a new family of global alignment graph kernels, which take into account the global properties of graphs by using geometric node embeddings and an associated node transportation based on earth movers distance. Compared to existing global kernels, the proposed kernel is positive-definite. Our graph kernel is obtained by defining a distribution over emph{random graphs}, which can naturally yield random feature approximations. The random feature approximations lead to our graph embeddings, which is named as random graph embeddings (RGE). In particular, RGE is shown to achieve emph{(quasi-)linear scalability} with respect to the number and the size of the graphs. The experimental results on nine benchmark datasets demonstrate that RGE outperforms or matches twelve state-of-the-art graph classification algorithms.
Higher-order proximity preserved network embedding has attracted increasing attention. In particular, due to the superior scalability, random-walk-based network embedding has also been well developed, which could efficiently explore higher-order neighborhoods via multi-hop random walks. However, despite the success of current random-walk-based methods, most of them are usually not expressive enough to preserve the personalized higher-order proximity and lack a straightforward objective to theoretically articulate what and how network proximity is preserved. In this paper, to address the above issues, we present a general scalable random-walk-based network embedding framework, in which random walk is explicitly incorporated into a sound objective designed theoretically to preserve arbitrary higher-order proximity. Further, we introduce the random walk with restart process into the framework to naturally and effectively achieve personalized-weighted preservation of proximities of different orders. We conduct extensive experiments on several real-world networks and demonstrate that our proposed method consistently and substantially outperforms the state-of-the-art network embedding methods.
Recently, a considerable literature has grown up around the theme of Graph Convolutional Network (GCN). How to effectively leverage the rich structural information in complex graphs, such as knowledge graphs with heterogeneous types of entities and relations, is a primary open challenge in the field. Most GCN methods are either restricted to graphs with a homogeneous type of edges (e.g., citation links only), or focusing on representation learning for nodes only instead of jointly propagating and updating the embeddings of both nodes and edges for target-driven objectives. This paper addresses these limitations by proposing a novel framework, namely the Knowledge Embedding based Graph Convolutional Network (KE-GCN), which combines the power of GCNs in graph-based belief propagation and the strengths of advanced knowledge embedding (a.k.a. knowledge graph embedding) methods, and goes beyond. Our theoretical analysis shows that KE-GCN offers an elegant unification of several well-known GCN methods as specific cases, with a new perspective of graph convolution. Experimental results on benchmark datasets show the advantageous performance of KE-GCN over strong baseline methods in the tasks of knowledge graph alignment and entity classification.
Random-walk based network embedding algorithms like node2vec and DeepWalk are widely used to obtain Euclidean representation of the nodes in a network prior to performing down-stream network inference tasks. Nevertheless, despite their impressive empirical performance, there is a lack of theoretical results explaining their behavior. In this paper we studied the node2vec and DeepWalk algorithms through the perspective of matrix factorization. We analyze these algorithms in the setting of community detection for stochastic blockmodel graphs; in particular we established large-sample error bounds and prove consistent community recovery of node2vec/DeepWalk embedding followed by k-means clustering. Our theoretical results indicate a subtle interplay between the sparsity of the observed networks, the window sizes of the random walks, and the convergence rates of the node2vec/DeepWalk embedding toward the embedding of the true but unknown edge probabilities matrix. More specifically, as the network becomes sparser, our results suggest using larger window sizes, or equivalently, taking longer random walks, in order to attain better convergence rate for the resulting embeddings. The paper includes numerical experiments corroborating these observations.
Representation learning of static and more recently dynamically evolving graphs has gained noticeable attention. Existing approaches for modelling graph dynamics focus extensively on the evolution of individual nodes independently of the evolution of mesoscale community structures. As a result, current methods do not provide useful tools to study and cannot explicitly capture temporal community dynamics. To address this challenge, we propose GRADE - a probabilistic model that learns to generate evolving node and community representations by imposing a random walk prior over their trajectories. Our model also learns node community membership which is updated between time steps via a transition matrix. At each time step link generation is performed by first assigning node membership from a distribution over the communities, and then sampling a neighbor from a distribution over the nodes for the assigned community. We parametrize the node and community distributions with neural networks and learn their parameters via variational inference. Experiments demonstrate GRADE outperforms baselines in dynamic link prediction, shows favourable performance on dynamic community detection, and identifies coherent and interpretable evolving communities.
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