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1. BRIGHT: A Bridging Algorithm for Network Alignment

   Yuchen Yan, Si Zhang ( April 2021 , TheWebConf)

   null (Ed.)

   Multiple networks emerge in a wealth of high-impact applications. Network alignment, which aims to find the node correspondence across different networks, plays a fundamental role for many data mining tasks. Most of the existing methods can be divided into two categories: (1) consistency optimization based methods, which often explicitly assume the alignment to be consistent in terms of neighborhood topology and attribute across networks, and (2) network embedding based methods which learn low-dimensional node embedding vectors to infer alignment. In this paper, by analyzing certain methods of these two categories, we show that (1) the consistency optimization based methods are essentially specific random walk propagations from anchor links that might be restrictive; (2) the embedding based methods no longer explicitly assume alignment consistency but inevitably suffer from the space disparity issue. To overcome these two limitations, we bridge these methods and propose a novel family of network alignment algorithms BRIGHT to handle both non-attributed and attributed networks. Specifically, it constructs a space by random walk with restart (RWR) whose bases are one-hot encoding vectors of anchor nodes, followed by a shared linear layer. Our experiments on real-world networks show that the proposed family of algorithms BRIGHT outperform the state-of-the- arts for both non-attributed and attributed network alignment tasks. 

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2. Alignment of dynamic networks

   https://doi.org/10.1093/bioinformatics/btx246  

   Vijayan, V. ; Critchlow, D. ; Milenković, T. ( July 2017 , Bioinformatics)

   Network alignment (NA) aims to find a node mapping that conserves similar regions between compared networks. NA is applicable to many fields, including computational biology, where NA can guide the transfer of biological knowledge from well- to poorly-studied species across aligned network regions. Existing NA methods can only align static networks. However, most complex real-world systems evolve over time and should thus be modeled as dynamic networks. We hypothesize that aligning dynamic network representations of evolving systems will produce superior alignments compared to aligning the systems’ static network representations, as is currently done.

   For this purpose, we introduce the first ever dynamic NA method, DynaMAGNA ++. This proof-of-concept dynamic NA method is an extension of a state-of-the-art static NA method, MAGNA++. Even though both MAGNA++ and DynaMAGNA++ optimize edge as well as node conservation across the aligned networks, MAGNA++ conserves static edges and similarity between static node neighborhoods, while DynaMAGNA++ conserves dynamic edges (events) and similarity between evolving node neighborhoods. For this purpose, we introduce the first ever measure of dynamic edge conservation and rely on our recent measure of dynamic node conservation. Importantly, the two dynamic conservation measures can be optimized with any state-of-the-art NA method and not just MAGNA++. We confirm our hypothesis that dynamic NA is superior to static NA, on synthetic and real-world networks, in computational biology and social domains. DynaMAGNA++ is parallelized and has a user-friendly graphical interface.

   http://nd.edu/∼cone/DynaMAGNA++/.

   Supplementary data are available at Bioinformatics online.

    

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3. ATTENT: Active Attributed Network Alignment

   Qinghai Zhou, Liangyue Li ( April 2021 , TheWebConf)

   null (Ed.)

   Network alignment finds node correspondences across multiple networks, where the alignment accuracy is of crucial importance because of its profound impact on downstream applications. The vast majority of existing works focus on how to best utilize the topology and attribute information of the input networks as well as the anchor links when available. Nonetheless, it has not been well studied on how to boost the alignment performance through actively obtaining high-quality and informative anchor links, with a few exceptions. The sparse literature on active network alignment introduces the human in the loop to label some seed node correspondence (i.e., anchor links), which are informative from the perspective of querying the most uncertain node given few potential matchings. However, the direct influence of the intrinsic network attribute information on the alignment results has largely remained unknown. In this paper, we tackle this challenge and propose an active network alignment method (Attent) to identify the best nodes to query. The key idea of the proposed method is to leverage effective and efficient influence functions defined over the alignment solution to evaluate the goodness of the candidate nodes for query. Our proposed query strategy bears three distinct advantages, including (1) effectiveness, being able to accurately quantify the influence of the candidate nodes on the alignment results; (2) efficiency, scaling linearly with 15 − 17× speed-up over the straightforward implementation without any quality loss; (3) generality, consistently improving alignment performance of a variety of network alignment algorithms. 

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4. ORIGIN: Non-Rigid Network Alignment

   https://doi.org/10.1109/BigData47090.2019.9005663  

   Zhang, Si ; Tong, Hanghang ; Xu, Jiejun ; Hu, Yifan ; Maciejewski, Ross ( December 2019 , BigData)

   Network alignment is a fundamental task in many high-impact applications. Most of the existing approaches either explicitly or implicitly consider the alignment matrix as a linear transformation to map one network to another, and might overlook the complicated alignment relationship across networks. On the other hand, node representation learning based alignment methods are hampered by the incomparability among the node representations of different networks. In this paper, we propose a unified semi-supervised deep model (ORIGIN) that simultaneously finds the non-rigid network alignment and learns node representations in multiple networks in a mutually beneficial way. The key idea is to learn node representations by the effective graph convolutional networks, which subsequently enable us to formulate network alignment as a point set alignment problem. The proposed method offers two distinctive advantages. First (node representations), unlike the existing graph convolutional networks that aggregate the node information within a single network, we can effectively aggregate the auxiliary information from multiple sources, achieving far-reaching node representations. Second (network alignment), guided by the highquality node representations, our proposed non-rigid point set alignment approach overcomes the bottleneck of the linear transformation assumption. We conduct extensive experiments that demonstrate the proposed non-rigid alignment method is (1) effective, outperforming both the state-of-the-art linear transformation-based methods and node representation based methods, and (2) efficient, with a comparable computational time between the proposed multi-network representation learning component and its single-network counterpart. 

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5. FASTEN: Fast Sylvester Equation Solver for Graph Mining

   https://doi.org/10.1145/3219819.3220002  

   Du, Boxin ; Tong, Hanghang ( January 2018 , KDD '18 Proceedings of the 24th ACM SIGKDD International Conference on Knowledge Discovery & Data Mining)

   The Sylvester equation offers a powerful and unifying primitive for a variety of important graph mining tasks, including network alignment, graph kernel, node similarity, subgraph matching, etc. A major bottleneck of Sylvester equation lies in its high computational complexity. Despite tremendous effort, state-of-the-art methods still require a complexity that is at least \em quadratic in the number of nodes of graphs, even with approximations. In this paper, we propose a family of Krylov subspace based algorithms (\fasten) to speed up and scale up the computation of Sylvester equation for graph mining. The key idea of the proposed methods is to project the original equivalent linear system onto a Kronecker Krylov subspace. We further exploit (1) the implicit representation of the solution matrix as well as the associated computation, and (2) the decomposition of the original Sylvester equation into a set of inter-correlated Sylvester equations of smaller size. The proposed algorithms bear two distinctive features. First, they provide the \em exact solutions without any approximation error. Second, they significantly reduce the time and space complexity for solving Sylvester equation, with two of the proposed algorithms having a \em linear complexity in both time and space. Experimental evaluations on a diverse set of real networks, demonstrate that our methods (1) are up to $10,000\times$ faster against Conjugate Gradient method, the best known competitor that outputs the exact solution, and (2) scale up to million-node graphs. 

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