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Bandyopadhyay, Sambaran, N. Lokesh, and M. N. Murty. "Outlier Aware Network Embedding for Attributed Networks." Proceedings of the AAAI Conference on Artificial Intelligence 33 (July 17, 2019): 12–19. http://dx.doi.org/10.1609/aaai.v33i01.330112.
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Attributed network embedding has received much interest from the research community as most of the networks come with some content in each node, which is also known as node attributes. Existing attributed network approaches work well when the network is consistent in structure and attributes, and nodes behave as expected. But real world networks often have anomalous nodes. Typically these outliers, being relatively unexplainable, affect the embeddings of other nodes in the network. Thus all the downstream network mining tasks fail miserably in the presence of such outliers. Hence an integrated approach to detect anomalies and reduce their overall effect on the network embedding is required.Towards this end, we propose an unsupervised outlier aware network embedding algorithm (ONE) for attributed networks, which minimizes the effect of the outlier nodes, and hence generates robust network embeddings. We align and jointly optimize the loss functions coming from structure and attributes of the network. To the best of our knowledge, this is the first generic network embedding approach which incorporates the effect of outliers for an attributed network without any supervision. We experimented on publicly available real networks and manually planted different types of outliers to check the performance of the proposed algorithm. Results demonstrate the superiority of our approach to detect the network outliers compared to the state-of-the-art approaches. We also consider different downstream machine learning applications on networks to show the efficiency of ONE as a generic network embedding technique. The source code is made available at https://github.com/sambaranban/ONE.
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Armandpour, Mohammadreza, Patrick Ding, Jianhua Huang, and Xia Hu. "Robust Negative Sampling for Network Embedding." Proceedings of the AAAI Conference on Artificial Intelligence 33 (July 17, 2019): 3191–98. http://dx.doi.org/10.1609/aaai.v33i01.33013191.
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Many recent network embedding algorithms use negative sampling (NS) to approximate a variant of the computationally expensive Skip-Gram neural network architecture (SGA) objective. In this paper, we provide theoretical arguments that reveal how NS can fail to properly estimate the SGA objective, and why it is not a suitable candidate for the network embedding problem as a distinct objective. We show NS can learn undesirable embeddings, as the result of the “Popular Neighbor Problem.” We use the theory to develop a new method “R-NS” that alleviates the problems of NS by using a more intelligent negative sampling scheme and careful penalization of the embeddings. R-NS is scalable to large-scale networks, and we empirically demonstrate the superiority of R-NS over NS for multi-label classification on a variety of real-world networks including social networks and language networks.
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He, Tao, Lianli Gao, Jingkuan Song, Xin Wang, Kejie Huang, and Yuanfang Li. "SNEQ: Semi-Supervised Attributed Network Embedding with Attention-Based Quantisation." Proceedings of the AAAI Conference on Artificial Intelligence 34, no. 04 (April 3, 2020): 4091–98. http://dx.doi.org/10.1609/aaai.v34i04.5832.
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Learning accurate low-dimensional embeddings for a network is a crucial task as it facilitates many network analytics tasks. Moreover, the trained embeddings often require a significant amount of space to store, making storage and processing a challenge, especially as large-scale networks become more prevalent. In this paper, we present a novel semi-supervised network embedding and compression method, SNEQ, that is competitive with state-of-art embedding methods while being far more space- and time-efficient. SNEQ incorporates a novel quantisation method based on a self-attention layer that is trained in an end-to-end fashion, which is able to dramatically compress the size of the trained embeddings, thus reduces storage footprint and accelerates retrieval speed. Our evaluation on four real-world networks of diverse characteristics shows that SNEQ outperforms a number of state-of-the-art embedding methods in link prediction, node classification and node recommendation. Moreover, the quantised embedding shows a great advantage in terms of storage and time compared with continuous embeddings as well as hashing methods.
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Li, Yu, Yuan Tian, Jiawei Zhang, and Yi Chang. "Learning Signed Network Embedding via Graph Attention." Proceedings of the AAAI Conference on Artificial Intelligence 34, no. 04 (April 3, 2020): 4772–79. http://dx.doi.org/10.1609/aaai.v34i04.5911.
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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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Wang, Yueyang, Ziheng Duan, Binbing Liao, Fei Wu, and Yueting Zhuang. "Heterogeneous Attributed Network Embedding with Graph Convolutional Networks." Proceedings of the AAAI Conference on Artificial Intelligence 33 (July 17, 2019): 10061–62. http://dx.doi.org/10.1609/aaai.v33i01.330110061.
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Network embedding which assigns nodes in networks to lowdimensional representations has received increasing attention in recent years. However, most existing approaches, especially the spectral-based methods, only consider the attributes in homogeneous networks. They are weak for heterogeneous attributed networks that involve different node types as well as rich node attributes and are common in real-world scenarios. In this paper, we propose HANE, a novel network embedding method based on Graph Convolutional Networks, that leverages both the heterogeneity and the node attributes to generate high-quality embeddings. The experiments on the real-world dataset show the effectiveness of our method.
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Zhong, Jianan, Hongjun Qiu, and Benyun Shi. "Dynamics-Preserving Graph Embedding for Community Mining and Network Immunization." Information 11, no. 5 (May 2, 2020): 250. http://dx.doi.org/10.3390/info11050250.
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In recent years, the graph embedding approach has drawn a lot of attention in the field of network representation and analytics, the purpose of which is to automatically encode network elements into a low-dimensional vector space by preserving certain structural properties. On this basis, downstream machine learning methods can be implemented to solve static network analytic tasks, for example, node clustering based on community-preserving embeddings. However, by focusing only on structural properties, it would be difficult to characterize and manipulate various dynamics operating on the network. In the field of complex networks, epidemic spreading is one of the most typical dynamics in networks, while network immunization is one of the effective methods to suppress the epidemics. Accordingly, in this paper, we present a dynamics-preserving graph embedding method (EpiEm) to preserve the property of epidemic dynamics on networks, i.e., the infectiousness and vulnerability of network nodes. Specifically, we first generate a set of propagation sequences through simulating the Susceptible-Infectious process on a network. Then, we learn node embeddings from an influence matrix using a singular value decomposition method. Finally, we show that the node embeddings can be used to solve epidemics-related community mining and network immunization problems. The experimental results in real-world networks show that the proposed embedding method outperforms several benchmark methods with respect to both community mining and network immunization. The proposed method offers new insights into the exploration of other collective dynamics in complex networks using the graph embedding approach, such as opinion formation in social networks.
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Zhuo, Wei, Qianyi Zhan, Yuan Liu, Zhenping Xie, and Jing Lu. "Context Attention Heterogeneous Network Embedding." Computational Intelligence and Neuroscience 2019 (August 21, 2019): 1–15. http://dx.doi.org/10.1155/2019/8106073.
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Network embedding (NE), which maps nodes into a low-dimensional latent Euclidean space to represent effective features of each node in the network, has obtained considerable attention in recent years. Many popular NE methods, such as DeepWalk, Node2vec, and LINE, are capable of handling homogeneous networks. However, nodes are always fully accompanied by heterogeneous information (e.g., text descriptions, node properties, and hashtags) in the real-world network, which remains a great challenge to jointly project the topological structure and different types of information into the fixed-dimensional embedding space due to heterogeneity. Besides, in the unweighted network, how to quantify the strength of edges (tightness of connections between nodes) accurately is also a difficulty faced by existing methods. To bridge the gap, in this paper, we propose CAHNE (context attention heterogeneous network embedding), a novel network embedding method, to accurately determine the learning result. Specifically, we propose the concept of node importance to measure the strength of edges, which can better preserve the context relations of a node in unweighted networks. Moreover, text information is a widely ubiquitous feature in real-world networks, e.g., online social networks and citation networks. On account of the sophisticated interactions between the network structure and text features of nodes, CAHNE learns context embeddings for nodes by introducing the context node sequence, and the attention mechanism is also integrated into our model to better reflect the impact of context nodes on the current node. To corroborate the efficacy of CAHNE, we apply our method and various baseline methods on several real-world datasets. The experimental results show that CAHNE achieves higher quality compared to a number of state-of-the-art network embedding methods on the tasks of network reconstruction, link prediction, node classification, and visualization.
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Lu, Ruili, Pengfei Jiao, Yinghui Wang, Huaming Wu, and Xue Chen. "Layer Information Similarity Concerned Network Embedding." Complexity 2021 (August 26, 2021): 1–10. http://dx.doi.org/10.1155/2021/2260488.
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Great achievements have been made in network embedding based on single-layer networks. However, there are a variety of scenarios and systems that can be presented as multiplex networks, which can reveal more interesting patterns hidden in the data compared to single-layer networks. In the field of network embedding, in order to project the multiplex network into the latent space, it is necessary to consider richer structural information among network layers. However, current methods for multiplex network embedding mostly focus on the similarity of nodes in each layer of the network, while ignoring the similarity between different layers. In this paper, for multiplex network embedding, we propose a Layer Information Similarity Concerned Network Embedding (LISCNE) model considering the similarities between layers. Firstly, we introduce the common vector for each node shared by all layers and layer vectors for each layer where common vectors obtain the overall structure of the multiplex network and layer vectors learn semantics for each layer. We get the node embeddings in each layer by concatenating the common vectors and layer vectors with the consideration that the node embedding is related not only to the surrounding neighbors but also to the overall semantics. Furthermore, we define an index to formalize the similarity between different layers and the cross-network association. Constrained by layer similarity, the layer vectors with greater similarity are closer to each other and the aligned node embedding in these layers is also closer. To evaluate our proposed model, we conduct node classification and link prediction tasks to verify the effectiveness of our model, and the results show that LISCNE can achieve better or comparable performance compared to existing baseline methods.
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Makarov, Ilya, Mikhail Makarov, and Dmitrii Kiselev. "Fusion of text and graph information for machine learning problems on networks." PeerJ Computer Science 7 (May 11, 2021): e526. http://dx.doi.org/10.7717/peerj-cs.526.
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Today, increased attention is drawn towards network representation learning, a technique that maps nodes of a network into vectors of a low-dimensional embedding space. A network embedding constructed this way aims to preserve nodes similarity and other specific network properties. Embedding vectors can later be used for downstream machine learning problems, such as node classification, link prediction and network visualization. Naturally, some networks have text information associated with them. For instance, in a citation network, each node is a scientific paper associated with its abstract or title; in a social network, all users may be viewed as nodes of a network and posts of each user as textual attributes. In this work, we explore how combining existing methods of text and network embeddings can increase accuracy for downstream tasks and propose modifications to popular architectures to better capture textual information in network embedding and fusion frameworks.
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Ji, Fujiao, Zhongying Zhao, Hui Zhou, Heng Chi, and Chao Li. "A comparative study on heterogeneous information network embeddings." Journal of Intelligent & Fuzzy Systems 39, no. 3 (October 7, 2020): 3463–73. http://dx.doi.org/10.3233/jifs-191796.
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Heterogeneous information networks are widely used to represent real world applications in forms of social networks, word co-occurrence networks, and communication networks, etc. However, It is difficult for traditional machine learning methods to analyze these networks effectively. Heterogeneous information network embedding aims to convert the network into low dimensional vectors, which facilitates the following tasks. Thus it is receiving tremendous attention from the research community due to its effectiveness and efficiency. Although numerous methods have been present and applied successfully, there are few works to make a comparative study on heterogeneous information network embedding, which is very important for developers and researchers to select an appropriate method. To address the above problem, we make a comparative study on the heterogeneous information network embeddings. Specifically, we first give the problem definition of heterogeneous information network embedding. Then the heterogeneous information networks are classified into four categories from the perspective of network type. The state-of-the-art methods for each category are also compared and reviewed. Finally, we make a conclusion and suggest some potential future research directions.
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Park, Chanyoung, Donghyun Kim, Jiawei Han, and Hwanjo Yu. "Unsupervised Attributed Multiplex Network Embedding." Proceedings of the AAAI Conference on Artificial Intelligence 34, no. 04 (April 3, 2020): 5371–78. http://dx.doi.org/10.1609/aaai.v34i04.5985.
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Nodes in a multiplex network are connected by multiple types of relations. However, most existing network embedding methods assume that only a single type of relation exists between nodes. Even for those that consider the multiplexity of a network, they overlook node attributes, resort to node labels for training, and fail to model the global properties of a graph. We present a simple yet effective unsupervised network embedding method for attributed multiplex network called DMGI, inspired by Deep Graph Infomax (DGI) that maximizes the mutual information between local patches of a graph, and the global representation of the entire graph. We devise a systematic way to jointly integrate the node embeddings from multiple graphs by introducing 1) the consensus regularization framework that minimizes the disagreements among the relation-type specific node embeddings, and 2) the universal discriminator that discriminates true samples regardless of the relation types. We also show that the attention mechanism infers the importance of each relation type, and thus can be useful for filtering unnecessary relation types as a preprocessing step. Extensive experiments on various downstream tasks demonstrate that DMGI outperforms the state-of-the-art methods, even though DMGI is fully unsupervised.
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Wang, Zheng, Yuexin Wu, Yang Bao, Jing Yu, and Xiaohui Wang. "Fusing Node Embeddings and Incomplete Attributes by Complement-Based Concatenation." Wireless Communications and Mobile Computing 2021 (February 25, 2021): 1–10. http://dx.doi.org/10.1155/2021/6654349.
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Network embedding that learns representations of network nodes plays a critical role in network analysis, since it enables many downstream learning tasks. Although various network embedding methods have been proposed, they are mainly designed for a single network scenario. This paper considers a “multiple network” scenario by studying the problem of fusing the node embeddings and incomplete attributes from two different networks. To address this problem, we propose to complement the incomplete attributes, so as to conduct data fusion via concatenation. Specifically, we first propose a simple inductive method, in which attributes are defined as a parametric function of the given node embedding vectors. We then propose its transductive variant by adaptively learning an adjacency graph to approximate the original network structure. Additionally, we also provide a light version of this transductive variant. Experimental results on four datasets demonstrate the superiority of our methods.
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Škrlj, Blaž, Jan Kralj, and Nada Lavrač. "Embedding-based Silhouette community detection." Machine Learning 109, no. 11 (July 27, 2020): 2161–93. http://dx.doi.org/10.1007/s10994-020-05882-8.
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AbstractMining complex data in the form of networks is of increasing interest in many scientific disciplines. Network communities correspond to densely connected subnetworks, and often represent key functional parts of real-world systems. This paper proposes the embedding-based Silhouette community detection (SCD), an approach for detecting communities, based on clustering of network node embeddings, i.e. real valued representations of nodes derived from their neighborhoods. We investigate the performance of the proposed SCD approach on 234 synthetic networks, as well as on a real-life social network. Even though SCD is not based on any form of modularity optimization, it performs comparably or better than state-of-the-art community detection algorithms, such as the InfoMap and Louvain. Further, we demonstrate that SCD’s outputs can be used along with domain ontologies in semantic subgroup discovery, yielding human-understandable explanations of communities detected in a real-life protein interaction network. Being embedding-based, SCD is widely applicable and can be tested out-of-the-box as part of many existing network learning and exploration pipelines.
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Guo, Lei, Haoran Jiang, Xiyu Liu, and Changming Xing. "Network Embedding-Aware Point-of-Interest Recommendation in Location-Based Social Networks." Complexity 2019 (November 4, 2019): 1–18. http://dx.doi.org/10.1155/2019/3574194.
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As one of the important techniques to explore unknown places for users, the methods that are proposed for point-of-interest (POI) recommendation have been widely studied in recent years. Compared with traditional recommendation problems, POI recommendations are suffering from more challenges, such as the cold-start and one-class collaborative filtering problems. Many existing studies have focused on how to overcome these challenges by exploiting different types of contexts (e.g., social and geographical information). However, most of these methods only model these contexts as regularization terms, and the deep information hidden in the network structure has not been fully exploited. On the other hand, neural network-based embedding methods have shown its power in many recommendation tasks with its ability to extract high-level representations from raw data. According to the above observations, to well utilize the network information, a neural network-based embedding method (node2vec) is first exploited to learn the user and POI representations from a social network and a predefined location network, respectively. To deal with the implicit feedback, a pair-wise ranking-based method is then introduced. Finally, by regarding the pretrained network representations as the priors of the latent feature factors, an embedding-based POI recommendation method is proposed. As this method consists of an embedding model and a collaborative filtering model, when the training data are absent, the predictions will mainly be generated by the extracted embeddings. In other cases, this method will learn the user and POI factors from these two components. Experiments on two real-world datasets demonstrate the importance of the network embeddings and the effectiveness of our proposed method.
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Nguyen, Van Quan, Tien Nguyen Anh, and Hyung-Jeong Yang. "Real-time event detection using recurrent neural network in social sensors." International Journal of Distributed Sensor Networks 15, no. 6 (June 2019): 155014771985649. http://dx.doi.org/10.1177/1550147719856492.
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We proposed an approach for temporal event detection using deep learning and multi-embedding on a set of text data from social media. First, a convolutional neural network augmented with multiple word-embedding architectures is used as a text classifier for the pre-processing of the input textual data. Second, an event detection model using a recurrent neural network is employed to learn time series data features by extracting temporal information. Recently, convolutional neural networks have been used in natural language processing problems and have obtained excellent results as performing on available embedding vector. In this article, word-embedding features at the embedding layer are combined and fed to convolutional neural network. The proposed method shows no size limitation, supplementation of more embeddings than standard multichannel based approaches, and obtained similar performance (accuracy score) on some benchmark data sets, especially in an imbalanced data set. For event detection, a long short-term memory network is used as a predictor that learns higher level temporal features so as to predict future values. An error distribution estimation model is built to calculate the anomaly score of observation. Events are detected using a window-based method on the anomaly scores.
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Shi, Yong, Minglong Lei, Hong Yang, and Lingfeng Niu. "Diffusion network embedding." Pattern Recognition 88 (April 2019): 518–31. http://dx.doi.org/10.1016/j.patcog.2018.12.004.
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Gaur, Utkarsh, and B. S. Manjunath. "Superpixel Embedding Network." IEEE Transactions on Image Processing 29 (2020): 3199–212. http://dx.doi.org/10.1109/tip.2019.2957937.
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Shi, Min, Yufei Tang, Xingquan Zhu, Jianxun Liu, and Haibo He. "Topical network embedding." Data Mining and Knowledge Discovery 34, no. 1 (October 24, 2019): 75–100. http://dx.doi.org/10.1007/s10618-019-00659-7.
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Zhan, Junjian, Feng Li, Yang Wang, Daoyu Lin, and Guangluan Xu. "Structural Adversarial Variational Auto-Encoder for Attributed Network Embedding." Applied Sciences 11, no. 5 (March 7, 2021): 2371. http://dx.doi.org/10.3390/app11052371.
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As most networks come with some content in each node, attributed network embedding has aroused much research interest. Most existing attributed network embedding methods aim at learning a fixed representation for each node encoding its local proximity. However, those methods usually neglect the global information between nodes distant from each other and distribution of the latent codes. We propose Structural Adversarial Variational Graph Auto-Encoder (SAVGAE), a novel framework which encodes the network structure and node content into low-dimensional embeddings. On one hand, our model captures the local proximity and proximities at any distance of a network by exploiting a high-order proximity indicator named Rooted Pagerank. On the other hand, our method learns the data distribution of each node representation while circumvents the side effect its sampling process causes on learning a robust embedding through adversarial training. On benchmark datasets, we demonstrate that our method performs competitively compared with state-of-the-art models.
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Wang, Xiao, Yiding Zhang, and Chuan Shi. "Hyperbolic Heterogeneous Information Network Embedding." Proceedings of the AAAI Conference on Artificial Intelligence 33 (July 17, 2019): 5337–44. http://dx.doi.org/10.1609/aaai.v33i01.33015337.
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Heterogeneous information network (HIN) embedding, aiming to project HIN into a low-dimensional space, has attracted considerable research attention. Most of the exiting HIN embedding methods focus on preserving the inherent network structure and semantic correlations in Euclidean spaces. However, one fundamental problem is that whether the Euclidean spaces are the appropriate or intrinsic isometric spaces of HIN? Recent researches argue that the complex network may have the hyperbolic geometry underneath, because the underlying hyperbolic geometry can naturally reflect some properties of complex network, e.g., hierarchical and power-law structure. In this paper, we make the first effort toward HIN embedding in hyperbolic spaces. We analyze the structures of two real-world HINs and discover some properties, e.g., the power-law distribution, also exist in HIN. Therefore, we propose a novel hyperbolic heterogeneous information network embedding model. Specifically, to capture the structure and semantic relations between nodes, we employ the meta-path guided random walk to sample the sequences for each node. Then we exploit the distance in hyperbolic spaces as the proximity measurement. The hyperbolic distance is able to meet the triangle inequality and well preserve the transitivity in HIN. Our model enables the nodes and their neighborhoods have small hyperbolic distances. We further derive the effective optimization strategy to update the hyperbolic embeddings iteratively. The experimental results, in comparison with the state-of-the-art, demonstrate that our proposed model not only has superior performance on network reconstruction and link prediction tasks but also shows its ability of capture hierarchy structure in HIN via visualization.
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Yochum, Phatpicha, Liang Chang, Tianlong Gu, and Manli Zhu. "Learning Sentiment over Network Embedding for Recommendation System." International Journal of Machine Learning and Computing 11, no. 1 (January 2021): 12–20. http://dx.doi.org/10.18178/ijmlc.2021.11.1.1008.
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With the rapid development of Internet, various unstructured information, such as user-generated content, textual reviews, and implicit or explicit feedbacks have grown continuously. Though structured knowledge bases (KBs) which consist of a large number of triples exhibit great advantages in recommendation field recently. In this paper, we propose a novel approach to learn sentiment over network embedding for recommendation system based on the knowledge graph which we have been built, that is, we integrate the network embedding method with the sentiment of user reviews. Specifically, we use the typical network embedding method node2vec to embed the large-scale structured data into a low-dimensional vector space to capture the internal semantic information of users and attractions and apply the user weight scoring which is the combination of user review ratings and textual reviews to get similar attractions among users. Experimental results on real-world dataset verified the superior recommendation performance on precision, recall, and F-measure of our approach compared with state-of-the-art baselines.
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Qin, Xiaorui, Yanghui Rao, Haoran Xie, Jian Yin, and Fu Lee Wang. "Extractive convolutional adversarial networks for network embedding." World Wide Web 23, no. 3 (November 23, 2019): 1925–44. http://dx.doi.org/10.1007/s11280-019-00740-7.
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Lai, Yi-Yu, Jennifer Neville, and Dan Goldwasser. "TransConv: Relationship Embedding in Social Networks." Proceedings of the AAAI Conference on Artificial Intelligence 33 (July 17, 2019): 4130–38. http://dx.doi.org/10.1609/aaai.v33i01.33014130.
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Representation learning (RL) for social networks facilitates real-world tasks such as visualization, link prediction and friend recommendation. Traditional knowledge graph embedding models learn continuous low-dimensional embedding of entities and relations. However, when applied to social networks, existing approaches do not consider the rich textual communications between users, which contains valuable information to describe social relationships. In this paper, we propose TransConv, a novel approach that incorporates textual interactions between pair of users to improve representation learning of both users and relationships. Our experiments on real social network data show TransConv learns better user and relationship embeddings compared to other state-of-theart knowledge graph embedding models. Moreover, the results illustrate that our model is more robust for sparse relationships where there are fewer examples.
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Su, Chang, Jie Tong, Yongjun Zhu, Peng Cui, and Fei Wang. "Network embedding in biomedical data science." Briefings in Bioinformatics 21, no. 1 (December 10, 2018): 182–97. http://dx.doi.org/10.1093/bib/bby117.
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AbstractOwning to the rapid development of computer technologies, an increasing number of relational data have been emerging in modern biomedical research. Many network-based learning methods have been proposed to perform analysis on such data, which provide people a deep understanding of topology and knowledge behind the biomedical networks and benefit a lot of applications for human healthcare. However, most network-based methods suffer from high computational and space cost. There remain challenges on handling high dimensionality and sparsity of the biomedical networks. The latest advances in network embedding technologies provide new effective paradigms to solve the network analysis problem. It converts network into a low-dimensional space while maximally preserves structural properties. In this way, downstream tasks such as link prediction and node classification can be done by traditional machine learning methods. In this survey, we conduct a comprehensive review of the literature on applying network embedding to advance the biomedical domain. We first briefly introduce the widely used network embedding models. After that, we carefully discuss how the network embedding approaches were performed on biomedical networks as well as how they accelerated the downstream tasks in biomedical science. Finally, we discuss challenges the existing network embedding applications in biomedical domains are faced with and suggest several promising future directions for a better improvement in human healthcare.
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Cape, Joshua, Minh Tang, and Carey E. Priebe. "On spectral embedding performance and elucidating network structure in stochastic blockmodel graphs." Network Science 7, no. 3 (September 2019): 269–91. http://dx.doi.org/10.1017/nws.2019.23.
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AbstractStatistical inference on graphs often proceeds via spectral methods involving low-dimensional embeddings of matrix-valued graph representations such as the graph Laplacian or adjacency matrix. In this paper, we analyze the asymptotic information-theoretic relative performance of Laplacian spectral embedding and adjacency spectral embedding for block assignment recovery in stochastic blockmodel graphs by way of Chernoff information. We investigate the relationship between spectral embedding performance and underlying network structure (e.g., homogeneity, affinity, core-periphery, and (un)balancedness) via a comprehensive treatment of the two-block stochastic blockmodel and the class of K-blockmodels exhibiting homogeneous balanced affinity structure. Our findings support the claim that, for a particular notion of sparsity, loosely speaking, “Laplacian spectral embedding favors relatively sparse graphs, whereas adjacency spectral embedding favors not-too-sparse graphs.” We also provide evidence in support of the claim that “adjacency spectral embedding favors core-periphery network structure.”
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Mao, Yuqing, and Kin Wah Fung. "Use of word and graph embedding to measure semantic relatedness between Unified Medical Language System concepts." Journal of the American Medical Informatics Association 27, no. 10 (October 1, 2020): 1538–46. http://dx.doi.org/10.1093/jamia/ocaa136.
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Abstract Objective The study sought to explore the use of deep learning techniques to measure the semantic relatedness between Unified Medical Language System (UMLS) concepts. Materials and Methods Concept sentence embeddings were generated for UMLS concepts by applying the word embedding models BioWordVec and various flavors of BERT to concept sentences formed by concatenating UMLS terms. Graph embeddings were generated by the graph convolutional networks and 4 knowledge graph embedding models, using graphs built from UMLS hierarchical relations. Semantic relatedness was measured by the cosine between the concepts’ embedding vectors. Performance was compared with 2 traditional path-based (shortest path and Leacock-Chodorow) measurements and the publicly available concept embeddings, cui2vec, generated from large biomedical corpora. The concept sentence embeddings were also evaluated on a word sense disambiguation (WSD) task. Reference standards used included the semantic relatedness and semantic similarity datasets from the University of Minnesota, concept pairs generated from the Standardized MedDRA Queries and the MeSH (Medical Subject Headings) WSD corpus. Results Sentence embeddings generated by BioWordVec outperformed all other methods used individually in semantic relatedness measurements. Graph convolutional network graph embedding uniformly outperformed path-based measurements and was better than some word embeddings for the Standardized MedDRA Queries dataset. When used together, combined word and graph embedding achieved the best performance in all datasets. For WSD, the enhanced versions of BERT outperformed BioWordVec. Conclusions Word and graph embedding techniques can be used to harness terms and relations in the UMLS to measure semantic relatedness between concepts. Concept sentence embedding outperforms path-based measurements and cui2vec, and can be further enhanced by combining with graph embedding.
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Yu, Liqun, Hongqi Wang, and Haoran Mo. "Estimating Network Flowing over Edges by Recursive Network Embedding." Shock and Vibration 2020 (November 26, 2020): 1–7. http://dx.doi.org/10.1155/2020/8893381.
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In this paper, we propose a novel semisupervised learning framework to learn the flows of edges over a graph. Given the flow values of the labeled edges, the task of this paper is to learn the unknown flow values of the remaining unlabeled edges. To this end, we introduce a value amount hold by each node and impose that the amount of values flowing from the conjunctive edges of each node to be consistent with the node’s own value. We propose to embed the nodes to a continuous vector space so that the embedding vector of each node can be reconstructed from its neighbors by a recursive neural network model, linear normalized long short-term memory. Moreover, we argue that the value of each node is also embedded in the embedding vectors of its neighbors, thus propose to approximate the node value from the output of the neighborhood recursive network. We build a unified learning framework by formulating a minimization problem. To construct the learning problem, we build three subproblems of minimization: (1) the embedding error of each node from the recursive network, (2) the loss of the construction for the amount of value of each node, and (3) the difference between the value amount of each node and the estimated value from the edge flows. We develop an iterative algorithm to learn the node embeddings, edge flows, and node values jointly. We perform experiments based on the datasets of some network data, including the transportation network and innovation. The experimental results indicate that our algorithm is more effective than the state-of-the-arts.
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Ata, Sezin Kircali, Yuan Fang, Min Wu, Jiaqi Shi, Chee Keong Kwoh, and Xiaoli Li. "Multi-View Collaborative Network Embedding." ACM Transactions on Knowledge Discovery from Data 15, no. 3 (April 12, 2021): 1–18. http://dx.doi.org/10.1145/3441450.
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Real-world networks often exist with multiple views, where each view describes one type of interaction among a common set of nodes. For example, on a video-sharing network, while two user nodes are linked, if they have common favorite videos in one view, then they can also be linked in another view if they share common subscribers. Unlike traditional single-view networks, multiple views maintain different semantics to complement each other. In this article, we propose M ulti-view coll A borative N etwork E mbedding (MANE), a multi-view network embedding approach to learn low-dimensional representations. Similar to existing studies, MANE hinges on diversity and collaboration—while diversity enables views to maintain their individual semantics, collaboration enables views to work together. However, we also discover a novel form of second-order collaboration that has not been explored previously, and further unify it into our framework to attain superior node representations. Furthermore, as each view often has varying importance w.r.t. different nodes, we propose MANE , an attention -based extension of MANE, to model node-wise view importance. Finally, we conduct comprehensive experiments on three public, real-world multi-view networks, and the results demonstrate that our models consistently outperform state-of-the-art approaches.
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Qi, Yiyan, Jiefeng Cheng, Xiaojun Chen, Reynold Cheng, Albert Bifet, and Pinghui Wang. "Discriminative Streaming Network Embedding." Knowledge-Based Systems 190 (February 2020): 105138. http://dx.doi.org/10.1016/j.knosys.2019.105138.
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Liao, Lizi, Xiangnan He, Hanwang Zhang, and Tat-Seng Chua. "Attributed Social Network Embedding." IEEE Transactions on Knowledge and Data Engineering 30, no. 12 (December 1, 2018): 2257–70. http://dx.doi.org/10.1109/tkde.2018.2819980.
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Yu, Minlan, Yung Yi, Jennifer Rexford, and Mung Chiang. "Rethinking virtual network embedding." ACM SIGCOMM Computer Communication Review 38, no. 2 (March 31, 2008): 17–29. http://dx.doi.org/10.1145/1355734.1355737.
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Xu, Linchuan, Xiaokai Wei, Jiannong Cao, and Philip S. Yu. "Multi-task network embedding." International Journal of Data Science and Analytics 8, no. 2 (December 5, 2018): 183–98. http://dx.doi.org/10.1007/s41060-018-0166-2.
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Zhang, Yiding, Xiao Wang, Nian Liu, and Chuan Shi. "Embedding Heterogeneous Information Network in Hyperbolic Spaces." ACM Transactions on Knowledge Discovery from Data 16, no. 2 (April 30, 2022): 1–23. http://dx.doi.org/10.1145/3468674.
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Heterogeneous information network (HIN) embedding, aiming to project HIN into a low-dimensional space, has attracted considerable research attention. Most of the existing HIN embedding methods focus on preserving the inherent network structure and semantic correlations in Euclidean spaces. However, one fundamental problem is whether the Euclidean spaces are the intrinsic spaces of HIN? Recent researches find the complex network with hyperbolic geometry can naturally reflect some properties, e.g., hierarchical and power-law structure. In this article, we make an effort toward embedding HIN in hyperbolic spaces. We analyze the structures of three HINs and discover some properties, e.g., the power-law distribution, also exist in HINs. Therefore, we propose a novel HIN embedding model HHNE. Specifically, to capture the structure and semantic relations between nodes, HHNE employs the meta-path guided random walk to sample the sequences for each node. Then HHNE exploits the hyperbolic distance as the proximity measurement. We also derive an effective optimization strategy to update the hyperbolic embeddings iteratively. Since HHNE optimizes different relations in a single space, we further propose the extended model HHNE++. HHNE++ models different relations in different spaces, which enables it to learn complex interactions in HINs. The optimization strategy of HHNE++ is also derived to update the parameters of HHNE++ in a principle manner. The experimental results demonstrate the effectiveness of our proposed models.
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Li, Ziyao, Liang Zhang, and Guojie Song. "SepNE: Bringing Separability to Network Embedding." Proceedings of the AAAI Conference on Artificial Intelligence 33 (July 17, 2019): 4261–68. http://dx.doi.org/10.1609/aaai.v33i01.33014261.
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Many successful methods have been proposed for learning low dimensional representations on large-scale networks, while almost all existing methods are designed in inseparable processes, learning embeddings for entire networks even when only a small proportion of nodes are of interest. This leads to great inconvenience, especially on super-large or dynamic networks, where these methods become almost impossible to implement. In this paper, we formalize the problem of separated matrix factorization, based on which we elaborate a novel objective function that preserves both local and global information. We further propose SepNE, a simple and flexible network embedding algorithm which independently learns representations for different subsets of nodes in separated processes. By implementing separability, our algorithm reduces the redundant efforts to embed irrelevant nodes, yielding scalability to super-large networks, automatic implementation in distributed learning and further adaptations. We demonstrate the effectiveness of this approach on several real-world networks with different scales and subjects. With comparable accuracy, our approach significantly outperforms state-of-the-art baselines in running times on large networks.
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Zhang, H., J. J. Zhou, and R. Li. "Enhanced Unsupervised Graph Embedding via Hierarchical Graph Convolution Network." Mathematical Problems in Engineering 2020 (July 26, 2020): 1–9. http://dx.doi.org/10.1155/2020/5702519.
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Graph embedding aims to learn the low-dimensional representation of nodes in the network, which has been paid more and more attention in many graph-based tasks recently. Graph Convolution Network (GCN) is a typical deep semisupervised graph embedding model, which can acquire node representation from the complex network. However, GCN usually needs to use a lot of labeled data and additional expressive features in the graph embedding learning process, so the model cannot be effectively applied to undirected graphs with only network structure information. In this paper, we propose a novel unsupervised graph embedding method via hierarchical graph convolution network (HGCN). Firstly, HGCN builds the initial node embedding and pseudo-labels for the undirected graphs, and then further uses GCNs to learn the node embedding and update labels, finally combines HGCN output representation with the initial embedding to get the graph embedding. Furthermore, we improve the model to match the different undirected networks according to the number of network node label types. Comprehensive experiments demonstrate that our proposed HGCN and HGCN∗ can significantly enhance the performance of the node classification task.
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Liu, Xu, Zhongbao Zhang, Junning Li, and Sen Su. "Clustering-based energy-aware virtual network embedding." International Journal of Distributed Sensor Networks 13, no. 8 (August 2017): 155014771772671. http://dx.doi.org/10.1177/1550147717726714.
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Virtual network embedding has received a lot of attention from researchers. In this problem, it needs to map a sequence of virtual networks onto the physical network. Generally, the virtual networks have topology, node, and link constraints. Prior studies mainly focus on designing a solution to maximize the revenue by accepting more virtual networks while ignoring the energy cost for the physical network. In this article, to bridge this gap, we design a heuristic energy-aware virtual network embedding algorithm called EA-VNE-C, to coordinate the dynamic electricity price and energy consumption to further optimize the energy cost. Extensive simulations demonstrate that this algorithm significantly reduces the energy cost by up to 14% over the state-of-the-art algorithm while maintaining similar revenue.
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Wu, Wei, Guangmin Hu, and Fucai Yu. "An Unsupervised Learning Method for Attributed Network Based on Non-Euclidean Geometry." Symmetry 13, no. 5 (May 19, 2021): 905. http://dx.doi.org/10.3390/sym13050905.
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Many real-world networks can be modeled as attributed networks, where nodes are affiliated with attributes. When we implement attributed network embedding, we need to face two types of heterogeneous information, namely, structural information and attribute information. The structural information of undirected networks is usually expressed as a symmetric adjacency matrix. Network embedding learning is to utilize the above information to learn the vector representations of nodes in the network. How to integrate these two types of heterogeneous information to improve the performance of network embedding is a challenge. Most of the current approaches embed the networks in Euclidean spaces, but the networks themselves are non-Euclidean. As a consequence, the geometric differences between the embedded space and the underlying space of the network will affect the performance of the network embedding. According to the non-Euclidean geometry of networks, this paper proposes an attributed network embedding framework based on hyperbolic geometry and the Ricci curvature, namely, RHAE. Our method consists of two modules: (1) the first module is an autoencoder module in which each layer is provided with a network information aggregation layer based on the Ricci curvature and an embedding layer based on hyperbolic geometry; (2) the second module is a skip-gram module in which the random walk is based on the Ricci curvature. These two modules are based on non-Euclidean geometry, but they fuse the topology information and attribute information in the network from different angles. Experimental results on some benchmark datasets show that our approach outperforms the baselines.
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Liu, Dong, Yan Ru, Qinpeng Li, Shibin Wang, and Jianwei Niu. "Semisupervised Community Preserving Network Embedding with Pairwise Constraints." Complexity 2020 (November 10, 2020): 1–14. http://dx.doi.org/10.1155/2020/7953758.
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Network embedding aims to learn the low-dimensional representations of nodes in networks. It preserves the structure and internal attributes of the networks while representing nodes as low-dimensional dense real-valued vectors. These vectors are used as inputs of machine learning algorithms for network analysis tasks such as node clustering, classification, link prediction, and network visualization. The network embedding algorithms, which considered the community structure, impose a higher level of constraint on the similarity of nodes, and they make the learned node embedding results more discriminative. However, the existing network representation learning algorithms are mostly unsupervised models; the pairwise constraint information, which represents community membership, is not effectively utilized to obtain node embedding results that are more consistent with prior knowledge. This paper proposes a semisupervised modularized nonnegative matrix factorization model, SMNMF, while preserving the community structure for network embedding; the pairwise constraints (must-link and cannot-link) information are effectively fused with the adjacency matrix and node similarity matrix of the network so that the node representations learned by the model are more interpretable. Experimental results on eight real network datasets show that, comparing with the representative network embedding methods, the node representations learned after incorporating the pairwise constraints can obtain higher accuracy in node clustering task and the results of link prediction, and network visualization tasks indicate that the semisupervised model SMNMF is more discriminative than unsupervised ones.
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Song, Guojie, Yun Wang, Lun Du, Yi Li, and Junshan Wang. "Network Embedding on Hierarchical Community Structure Network." ACM Transactions on Knowledge Discovery from Data 15, no. 4 (June 2021): 1–23. http://dx.doi.org/10.1145/3434747.
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Network embedding is a method of learning a low-dimensional vector representation of network vertices under the condition of preserving different types of network properties. Previous studies mainly focus on preserving structural information of vertices at a particular scale, like neighbor information or community information, but cannot preserve the hierarchical community structure, which would enable the network to be easily analyzed at various scales. Inspired by the hierarchical structure of galaxies, we propose the Galaxy Network Embedding (GNE) model, which formulates an optimization problem with spherical constraints to describe the hierarchical community structure preserving network embedding. More specifically, we present an approach of embedding communities into a low-dimensional spherical surface, the center of which represents the parent community they belong to. Our experiments reveal that the representations from GNE preserve the hierarchical community structure and show advantages in several applications such as vertex multi-class classification, network visualization, and link prediction. The source code of GNE is available online.
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Razzaq, Adil, Markus Hidell, and Peter Sjödin. "Virtual Network Embedding: A Hybrid Vertex Mapping Solution for Dynamic Resource Allocation." Journal of Electrical and Computer Engineering 2012 (2012): 1–17. http://dx.doi.org/10.1155/2012/358647.
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Virtual network embedding (VNE) is a key area in network virtualization, and the overall purpose of VNE is to map virtual networks onto an underlying physical network referred to as a substrate. Typically, the virtual networks have certain demands, such as resource requirements, that need to be satisfied by the mapping process. A virtual network (VN) can be described in terms of vertices (nodes) and edges (links) with certain resource requirements, and, to embed a VN, substrate resources are assigned to these vertices and edges. Substrate networks have finite resources and utilizing them efficiently is an important objective for a VNE method. This paper analyzes two existing vertex mapping approaches—one which only considers if enough node resources are available for the current VN mapping and one which considers to what degree a node already is utilized by existing VN embeddings before doing the vertex mapping. The paper also proposes a new vertex mapping approach which minimizes complete exhaustion of substrate nodes while still providing good overall resource utilization. Experimental results are presented to show under what circumstances the proposed vertex mapping approach can provide superior VN embedding properties compared to the other approaches.
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Makarov, Ilya, Dmitrii Kiselev, Nikita Nikitinsky, and Lovro Subelj. "Survey on graph embeddings and their applications to machine learning problems on graphs." PeerJ Computer Science 7 (February 4, 2021): e357. http://dx.doi.org/10.7717/peerj-cs.357.
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Dealing with relational data always required significant computational resources, domain expertise and task-dependent feature engineering to incorporate structural information into a predictive model. Nowadays, a family of automated graph feature engineering techniques has been proposed in different streams of literature. So-called graph embeddings provide a powerful tool to construct vectorized feature spaces for graphs and their components, such as nodes, edges and subgraphs under preserving inner graph properties. Using the constructed feature spaces, many machine learning problems on graphs can be solved via standard frameworks suitable for vectorized feature representation. Our survey aims to describe the core concepts of graph embeddings and provide several taxonomies for their description. First, we start with the methodological approach and extract three types of graph embedding models based on matrix factorization, random-walks and deep learning approaches. Next, we describe how different types of networks impact the ability of models to incorporate structural and attributed data into a unified embedding. Going further, we perform a thorough evaluation of graph embedding applications to machine learning problems on graphs, among which are node classification, link prediction, clustering, visualization, compression, and a family of the whole graph embedding algorithms suitable for graph classification, similarity and alignment problems. Finally, we overview the existing applications of graph embeddings to computer science domains, formulate open problems and provide experiment results, explaining how different networks properties result in graph embeddings quality in the four classic machine learning problems on graphs, such as node classification, link prediction, clustering and graph visualization. As a result, our survey covers a new rapidly growing field of network feature engineering, presents an in-depth analysis of models based on network types, and overviews a wide range of applications to machine learning problems on graphs.
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Cheng, Pengyu, Yitong Li, Xinyuan Zhang, Liqun Chen, David Carlson, and Lawrence Carin. "Dynamic Embedding on Textual Networks via a Gaussian Process." Proceedings of the AAAI Conference on Artificial Intelligence 34, no. 05 (April 3, 2020): 7562–69. http://dx.doi.org/10.1609/aaai.v34i05.6255.
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Textual network embedding aims to learn low-dimensional representations of text-annotated nodes in a graph. Prior work in this area has typically focused on fixed graph structures; however, real-world networks are often dynamic. We address this challenge with a novel end-to-end node-embedding model, called Dynamic Embedding for Textual Networks with a Gaussian Process (DetGP). After training, DetGP can be applied efficiently to dynamic graphs without re-training or backpropagation. The learned representation of each node is a combination of textual and structural embeddings. Because the structure is allowed to be dynamic, our method uses the Gaussian process to take advantage of its non-parametric properties. To use both local and global graph structures, diffusion is used to model multiple hops between neighbors. The relative importance of global versus local structure for the embeddings is learned automatically. With the non-parametric nature of the Gaussian process, updating the embeddings for a changed graph structure requires only a forward pass through the learned model. Considering link prediction and node classification, experiments demonstrate the empirical effectiveness of our method compared to baseline approaches. We further show that DetGP can be straightforwardly and efficiently applied to dynamic textual networks.
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Nonde, Leonard, Taisir E. H. El-Gorashi, and Jaafar M. H. Elmirghani. "Energy Efficient Virtual Network Embedding for Cloud Networks." Journal of Lightwave Technology 33, no. 9 (May 1, 2015): 1828–49. http://dx.doi.org/10.1109/jlt.2014.2380777.
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NERURKAR, Pranav, Madhav CHANDANE, and Sunil BHIRUD. "Survey of network embedding techniques for social networks." TURKISH JOURNAL OF ELECTRICAL ENGINEERING & COMPUTER SCIENCES 27, no. 6 (November 26, 2019): 4768–82. http://dx.doi.org/10.3906/elk-1807-333.
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Sun, Heli, Fang He, Jianbin Huang, Yizhou Sun, Yang Li, Chenyu Wang, Liang He, Zhongbin Sun, and Xiaolin Jia. "Network Embedding for Community Detection in Attributed Networks." ACM Transactions on Knowledge Discovery from Data 14, no. 3 (May 14, 2020): 1–25. http://dx.doi.org/10.1145/3385415.
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Zhang, Jiawei, Yuefeng Ji, Mei Song, Hui Li, Rentao Gu, Yongli Zhao, and Jie Zhang. "Dynamic Virtual Network Embedding Over Multilayer Optical Networks." Journal of Optical Communications and Networking 7, no. 9 (August 27, 2015): 918. http://dx.doi.org/10.1364/jocn.7.000918.
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Lv, Pin, Xudong Wang, and Ming Xu. "Virtual access network embedding in wireless mesh networks." Ad Hoc Networks 10, no. 7 (September 2012): 1362–78. http://dx.doi.org/10.1016/j.adhoc.2012.03.016.
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He, Mengyang, Lei Zhuang, Sijin Yang, Jianhui Zhang, and Huiping Meng. "Energy-Efficient Virtual Network Embedding Algorithm Based on Hopfield Neural Network." Wireless Communications and Mobile Computing 2021 (January 28, 2021): 1–13. http://dx.doi.org/10.1155/2021/8889923.
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To solve the energy-efficient virtual network embedding problem, this study proposes an embedding algorithm based on Hopfield neural network. An energy-efficient virtual network embedding model was established. Wavelet diffusion was performed to take the structural feature value into consideration and provide a candidate set for virtual network embedding. In addition, the Hopfield network was used in the candidate set to solve the virtual network energy-efficient embedding problem. The augmented Lagrangian multiplier method was used to transform the energy-efficient virtual network embedding constraint problem into an unconstrained problem. The resulting unconstrained problem was used as the energy function of the Hopfield network, and the network weight was iteratively trained. The energy-efficient virtual network embedding scheme was obtained when the energy function was balanced. To prove the effectiveness of the proposed algorithm, we designed two experimental environments, namely, a medium-sized scenario and a small-sized scenario. Simulation results show that the proposed algorithm achieved a superior performance and effectively decreased the energy consumption relative to the other methods in both scenarios. Furthermore, the proposed algorithm reduced the number of open nodes and open links leading to a reduction in the overall power consumption of the virtual network embedding process, while ensuring the average acceptance ratio and the average ratio of the revenue and cost.
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Jin, Di, Xinxin You, Weihao Li, Dongxiao He, Peng Cui, Françoise Fogelman-Soulié, and Tanmoy Chakraborty. "Incorporating Network Embedding into Markov Random Field for Better Community Detection." Proceedings of the AAAI Conference on Artificial Intelligence 33 (July 17, 2019): 160–67. http://dx.doi.org/10.1609/aaai.v33i01.3301160.
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Recent research on community detection focuses on learning representations of nodes using different network embedding methods, and then feeding them as normal features to clustering algorithms. However, we find that though one may have good results by direct clustering based on such network embedding features, there is ample room for improvement. More seriously, in many real networks, some statisticallysignificant nodes which play pivotal roles are often divided into incorrect communities using network embedding methods. This is because while some distance measures are used to capture the spatial relationship between nodes by embedding, the nodes after mapping to feature vectors are essentially not coupled any more, losing important structural information. To address this problem, we propose a general Markov Random Field (MRF) framework to incorporate coupling in network embedding which allows better detecting network communities. By smartly utilizing properties of MRF, the new framework not only preserves the advantages of network embedding (e.g. low complexity, high parallelizability and applicability for traditional machine learning), but also alleviates its core drawback of inadequate representations of dependencies via making up the missing coupling relationships. Experiments on real networks show that our new approach improves the accuracy of existing embedding methods (e.g. Node2Vec, DeepWalk and MNMF), and corrects most wrongly-divided statistically-significant nodes, which makes network embedding essentially suitable for real community detection applications. The new approach also outperforms other state-of-the-art conventional community detection methods.
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Wu, Zongning, Zengru Di, and Ying Fan. "An Asymmetric Popularity-Similarity Optimization Method for Embedding Directed Networks into Hyperbolic Space." Complexity 2020 (April 22, 2020): 1–16. http://dx.doi.org/10.1155/2020/8372928.
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Network embedding is a frontier topic in current network science. The scale-free property of complex networks can emerge as a consequence of the exponential expansion of hyperbolic space. Some embedding models have recently been developed to explore hyperbolic geometric properties of complex networks—in particular, symmetric networks. Here, we propose a model for embedding directed networks into hyperbolic space. In accordance with the bipartite structure of directed networks and multiplex node information, the method replays the generation law of asymmetric networks in hyperbolic space, estimating the hyperbolic coordinates of each node in a directed network by the asymmetric popularity-similarity optimization method in the model. Additionally, the experiments in several real networks show that our embedding algorithm has stability and that the model enlarges the application scope of existing methods.