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Register a new userBidirectional group random walk based network embedding for asymmetric proximity
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Added by
Shu Xincheng
Publication date
2021
fields
Informatics Engineering
and research's language is
English
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Network embedding aims to represent a network into a low dimensional space where the network structural information and inherent properties are maximumly preserved. Random walk based network embedding methods such as DeepWalk and node2vec have shown outstanding performance in the aspect of preserving the network topological structure. However, these approaches either predict the distribution of a nodes neighbors in both direction together, which makes them unable to capture any asymmetric relationship in a network; or preserve asymmetric relationship in only one direction and hence lose the one in another direction. To address these limitations, we propose bidirectional group random walk based network embedding method (BiGRW), which treats the distributions of a nodes neighbors in the forward and backward direction in random walks as two different asymmetric network structural information. The basic idea of BiGRW is to learn a representation for each node that is useful to predict its distribution of neighbors in the forward and backward direction separately. Apart from that, a novel random walk sampling strategy is proposed with a parameter {alpha} to flexibly control the trade-off between breadth-first sampling (BFS) and depth-first sampling (DFS). To learn representations from node attributes, we design an attributed version of BiGRW (BiGRW-AT). Experimental results on several benchmark datasets demonstrate that the proposed methods significantly outperform the state-of-the-art plain and attributed network embedding methods on tasks of node classification and clustering.
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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.
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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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