Arbitrary-Order Proximity Preserved Network Embedding

Zhang, Ziwei; Cui, Peng; Wang, Xiao; Pei, Jian; Yao, Xuanrong; Zhu, Wenwu

doi:10.1145/3219819.3219969

Cited by 179 publications

(141 citation statements)

References 28 publications

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“…Link prediction aims to predict which node pairs are likely to form edges. Following previous work [59], we first remove 30% randomly selected edges from the input graph G, and then construct embeddings on the modified graph G . After that, we form a testing set Etest consisting of (i) the node pairs corresponding to the 30% removed edges, and (ii) an equal number of node pairs that are not connected by any edge in G. Note that on directed graphs, each node pair (u, v) is ordered, i.e., we aim to predict whether there is a directed edge from u to v.…”

Section: Link Predictionmentioning

confidence: 99%

“…However, the number of possible random walks grows exponentially with the length of the walk; thus, for longer walks on a large graph, it is infeasible for the training process to cover even a considerable portion of the random walk space. Another popular methodology is to construct node embeddings by factorizing a proximity matrix, e.g., in [59]. The effectiveness of such methods depends on the proximity measure between node pairs.…”

Section: Introductionmentioning

confidence: 99%

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Homogeneous network embedding for massive graphs via reweighted personalized PageRank

et al. 2020

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Given an input graph G and a node v ∈ G, homogeneous network embedding (HNE) maps the graph structure in the vicinity of v to a compact, fixed-dimensional feature vector. This paper focuses on HNE for massive graphs, e.g., with billions of edges. On this scale, most existing approaches fail, as they incur either prohibitively high costs, or severely compromised result utility.Our proposed solution, called Node-Reweighted PageRank (NRP), is based on a classic idea of deriving embedding vectors from pairwise personalized PageRank (PPR) values. Our contributions are twofold: first, we design a simple and efficient baseline HNE method based on PPR that is capable of handling billion-edge graphs on commodity hardware; second and more importantly, we identify an inherent drawback of vanilla PPR, and address it in our main proposal NRP. Specifically, PPR was designed for a very different purpose, i.e., ranking nodes in G based on their relative importance from a source node's perspective. In contrast, HNE aims to build node embeddings considering the whole graph. Consequently, node embeddings derived directly from PPR are of suboptimal utility.The proposed NRP approach overcomes the above deficiency through an effective and efficient node reweighting algorithm, which augments PPR values with node degree information, and iteratively adjusts embedding vectors accordingly. Overall, NRP takes O(m log n) time and O(m) space to compute all node embeddings for a graph with m edges and n nodes. Our extensive experiments that compare NRP against 18 existing solutions over 6 real graphs demonstrate that NRP achieves higher result utility than all the solutions for link prediction, graph reconstruction and node classification, while being up to orders of magnitude faster. In particular, on a billion-edge Twitter graph, NRP terminates within 4 hours, using a single CPU core.

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Section: Link Predictionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Homogeneous network embedding for massive graphs via reweighted personalized PageRank

et al. 2020

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“…However, GraRep is not scalable due to the high time complexity of both raising the transition matrix A to higher powers and taking the element-wise logarithm of A k , which is a dense n × n matrix. A few recent work thus propose to speed up the construction of such a node similarity matrix [25,26,39], which are inspired by the spectral graph theory. The basic idea is that if the top-h eigendecomposition of A is given by A = U h Λ h U ⊤ h , then A k can be approximated with U h Λ k h U ⊤ h [26,39].…”

Section: Related Workmentioning

confidence: 99%

Fast and Accurate Network Embeddings via Very Sparse Random Projection

Chen

Sultan

Tian

et al. 2019

Proceedings of the 28th ACM International Conference on Information and Knowledge Management

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We present FastRP, a scalable and performant algorithm for learning distributed node representations in a graph. FastRP is over 4,000 times faster than state-of-the-art methods such as DeepWalk and node2vec, while achieving comparable or even better performance as evaluated on several real-world networks on various downstream tasks. We observe that most network embedding methods consist of two components: construct a node similarity matrix and then apply dimension reduction techniques to this matrix. We show that the success of these methods should be attributed to the proper construction of this similarity matrix, rather than the dimension reduction method employed.FastRP is proposed as a scalable algorithm for network embeddings. Two key features of FastRP are: 1) it explicitly constructs a node similarity matrix that captures transitive relationships in a graph and normalizes matrix entries based on node degrees; 2) it utilizes very sparse random projection, which is a scalable optimization-free method for dimension reduction. An extra benefit from combining these two design choices is that it allows the iterative computation of node embeddings so that the similarity matrix need not be explicitly constructed, which further speeds up FastRP. FastRP is also advantageous for its ease of implementation, parallelization and hyperparameter tuning. The source code is available at https://github.com/GTmac/FastRP.

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“…Besides, LINE [23] designs and optimizes the objective function to preserve both the first order and second order proximities of networks. Beyond first order and second order proximities, AROPE [34] is a model that supports shifts across arbitrary order proximities based on SVD framework. In addition, there are some deep neural network based methods such as SDNE [27], SDAE [6], and SiNE [30], which introduce deep models to fit network data.…”

Section: Related Workmentioning

confidence: 99%

Hyper-Path-Based Representation Learning for Hyper-Networks

Huang

Liu

Song

2019

Proceedings of the 28th ACM International Conference on Information and Knowledge Management

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Network representation learning has aroused widespread interests in recent years. While most of the existing methods deal with edges as pairwise relationships, only a few studies have been proposed for hyper-networks to capture more complicated tuplewise relationships among multiple nodes. A hyper-network is a network where each edge, called hyperedge, connects an arbitrary number of nodes. Different from conventional networks, hyper-networks have certain degrees of indecomposability such that the nodes in a subset of a hyperedge may not possess a strong relationship. That is the main reason why traditional algorithms fail in learning representations in hyper-networks by simply decomposing hyperedges into pairwise relationships. In this paper, we firstly define a metric to depict the degrees of indecomposability for hyper-networks. Then we propose a new concept called hyper-path and design hyperpath-based random walks to preserve the structural information of hyper-networks according to the analysis of the indecomposability. Then a carefully designed algorithm, Hyper-gram, utilizes these random walks to capture both pairwise relationships and tuplewise relationships in the whole hyper-networks. Finally, we conduct extensive experiments on several real-world datasets covering the tasks of link prediction and hyper-network reconstruction, and results demonstrate the rationality, validity, and effectiveness of our methods compared with those existing state-of-the-art models designed for conventional networks or hyper-networks.

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Arbitrary-Order Proximity Preserved Network Embedding

Cited by 179 publications

References 28 publications

Homogeneous network embedding for massive graphs via reweighted personalized PageRank

Homogeneous network embedding for massive graphs via reweighted personalized PageRank

Fast and Accurate Network Embeddings via Very Sparse Random Projection

Hyper-Path-Based Representation Learning for Hyper-Networks

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