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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. Disentangled Network Alignment with Matching Explainability

   https://doi.org/10.1109/INFOCOM.2019.8737411  

   Zhou, Fan; Wen, Zijing; Trajcevski, Goce; Zhang, Kunpeng; Zhong, Ting; Liu, Fang (April 2019, 2019 {IEEE} Conference on Computer Communications, {INFOCOM} 2019, Paris, France, April 29 - May 2, 2019)

   Network alignment (NA) is a fundamental problem in many application domains – from social networks, through biology and communications, to neuroscience. The main objective is to identify common nodes and most similar connections across multiple networks (resp. graphs). Many of the existing efforts focus on efficient anchor node linkage by leveraging various features and optimizing network mapping functions with the pairwise similarity between anchor nodes. Despite the recent advances, there still exist two kinds of challenges: (1) entangled node embeddings, arising from the contradictory goals of NA: embedding proximal nodes in a closed form for representation in a single network vs. discriminating among them when mapping the nodes across networks; and (2) lack of interpretability about the node matching and alignment, essential for understanding prediction tasks. We propose dNAME (disentangled Network Alignment with Matching Explainability) – a novel solution for NA in heterogeneous networks settings, based on a matching technique that embeds nodes in a disentangled and faithful manner. The NA task is cast as an adversarial optimization problem which learns a proximity-preserving model locally around the anchor nodes, while still being discriminative. We also introduce a method to explain our semi-supervised model with the theory of robust statistics, by tracing the importance of each anchor node and its explanations on the NA performance. This is extensible to many other NA methods, as it provides model interpretability. Experiments conducted on several public datasets show that dNAME outperforms the state-of-the-art methods in terms of both network alignment precision and node matching ranking. 

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3. GAGE: Geometry Preserving Attributed Graph Embeddings

   https://doi.org/10.1145/3488560.3498467  

   Kanatsoulis, Charilaos I.; Sidiropoulos, Nicholas D. (February 2022, 15th ACM Conference on Web Search and Data Mining (WSDM))

   Node embedding is the task of extracting concise and informative representations of certain entities that are connected in a network. Various real-world networks include information about both node connectivity and certain node attributes, in the form of features or time-series data. Modern representation learning techniques employ both the connectivity and attribute information of the nodes to produce embeddings in an unsupervised manner. In this context, deriving embeddings that preserve the geometry of the network and the attribute vectors would be highly desirable, as they would reflect both the topological neighborhood structure and proximity in feature space. While this is fairly straightforward to maintain when only observing the connectivity or attribute information of the network, preserving the geometry of both types of information is challenging. A novel tensor factorization approach for node embedding in attributed networks is proposed in this paper, that preserves the distances of both the connections and the attributes. Furthermore, an effective and lightweight algorithm is developed to tackle the learning task and judicious experiments with multiple state-of-the-art baselines suggest that the proposed algorithm offers significant performance improvements in downstream tasks. 

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4. SINE: Scalable Incomplete Network Embedding

   https://doi.org/10.1109/ICDM.2018.00089  

   Zhang, Daokun; Yin, Jie; Zhu, Xingquan; Zhang, Chengqi (November 2018, Proc. of the 18th IEEE International Conference on Data Mining (ICDM-2018))

   Attributed network embedding aims to learn lowdimensional vector representations for nodes in a network, where each node contains rich attributes/features describing node content. Because network topology structure and node attributes often exhibit high correlation, incorporating node attribute proximity into network embedding is beneficial for learning good vector representations. In reality, large-scale networks often have incomplete/missing node content or linkages, yet existing attributed network embedding algorithms all operate under the assumption that networks are complete. Thus, their performance is vulnerable to missing data and suffers from poor scalability. In this paper, we propose a Scalable Incomplete Network Embedding (SINE) algorithm for learning node representations from incomplete graphs. SINE formulates a probabilistic learning framework that separately models pairs of node-context and node-attribute relationships. Different from existing attributed network embedding algorithms, SINE provides greater flexibility to make the best of useful information and mitigate negative effects of missing information on representation learning. A stochastic gradient descent based online algorithm is derived to learn node representations, allowing SINE to scale up to large-scale networks with high learning efficiency. We evaluate the effectiveness and efficiency of SINE through extensive experiments on real-world networks. Experimental results confirm that SINE outperforms state-of-the-art baselines in various tasks, including node classification, node clustering, and link prediction, under settings with missing links and node attributes. SINE is also shown to be scalable and efficient on large-scale networks with millions of nodes/edges and high-dimensional node features. 

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5. Learning Signed Network Embedding via Graph Attention

   https://doi.org/10.1609/aaai.v34i04.5911  

   Li, Yu; Tian, Yuan; Zhang, Jiawei; Chang, Yi (June 2020, Proceedings of the AAAI Conference on Artificial Intelligence)

   null (Ed.)

   Learning the low-dimensional representations of graphs (i.e., network embedding) plays a critical role in network analysis and facilitates many downstream tasks. Recently graph convolutional networks (GCNs) have revolutionized the field of network embedding, and led to state-of-the-art performance in network analysis tasks such as link prediction and node classification. Nevertheless, most of the existing GCN-based network embedding methods are proposed for unsigned networks. However, in the real world, some of the networks are signed, where the links are annotated with different polarities, e.g., positive vs. negative. Since negative links may have different properties from the positive ones and can also significantly affect the quality of network embedding. Thus in this paper, we propose a novel network embedding framework SNEA to learn Signed Network Embedding via graph Attention. In particular, we propose a masked self-attentional layer, which leverages self-attention mechanism to estimate the importance coefficient for pair of nodes connected by different type of links during the embedding aggregation process. Then SNEA utilizes the masked self-attentional layers to aggregate more important information from neighboring nodes to generate the node embeddings based on balance theory. Experimental results demonstrate the effectiveness of the proposed framework through signed link prediction task on several real-world signed network datasets. 

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