{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T12:42:53Z","timestamp":1760186573749,"version":"build-2065373602"},"reference-count":39,"publisher":"MDPI AG","issue":"1","license":[{"start":{"date-parts":[[2019,1,2]],"date-time":"2019-01-02T00:00:00Z","timestamp":1546387200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Algorithms"],"abstract":"<jats:p>Link prediction is a task predicting whether there is a link between two nodes in a network. Traditional link prediction methods that assume handcrafted features (such as common neighbors) as the link\u2019s formation mechanism are not universal. Other popular methods tend to learn the link\u2019s representation, but they cannot represent the link fully. In this paper, we propose Edge-Nodes Representation Neural Machine (ENRNM), a novel method which can learn abundant topological features from the network as the link\u2019s representation to promote the formation of the link. The ENRNM learns the link\u2019s formation mechanism by combining the representation of edge and the representations of nodes on the two sides of the edge as link\u2019s full representation. To predict the link\u2019s existence, we train a fully connected neural network which can learn meaningful and abundant patterns. We prove that the features of edge and two nodes have the same importance in link\u2019s formation. Comprehensive experiments are conducted on eight networks, experiment results demonstrate that the method ENRNM not only exceeds plenty of state-of-the-art link prediction methods but also performs very well on diverse networks with different structures and characteristics.<\/jats:p>","DOI":"10.3390\/a12010012","type":"journal-article","created":{"date-parts":[[2019,1,3]],"date-time":"2019-01-03T03:36:30Z","timestamp":1546486590000},"page":"12","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":3,"title":["Edge-Nodes Representation Neural Machine for Link Prediction"],"prefix":"10.3390","volume":"12","author":[{"given":"Guangluan","family":"Xu","sequence":"first","affiliation":[{"name":"Institute of Electronics, Chinese Academy of Sciences, Beijing 100190, China"},{"name":"Key Laboratory of Technology in Geo-Spatial Information Processing and Application System, Chinese Academy of Sciences, Beijing 100190, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-0121-7995","authenticated-orcid":false,"given":"Xiaoke","family":"Wang","sequence":"additional","affiliation":[{"name":"Institute of Electronics, Chinese Academy of Sciences, Beijing 100190, China"},{"name":"Key Laboratory of Technology in Geo-Spatial Information Processing and Application System, Chinese Academy of Sciences, Beijing 100190, China"},{"name":"School of Electronic, Electrical and Communication Engineering, University of Chinese Academy of Sciences, Beijing 100049, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Yang","family":"Wang","sequence":"additional","affiliation":[{"name":"Institute of Electronics, Chinese Academy of Sciences, Beijing 100190, China"},{"name":"Key Laboratory of Technology in Geo-Spatial Information Processing and Application System, Chinese Academy of Sciences, Beijing 100190, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-8352-0081","authenticated-orcid":false,"given":"Daoyu","family":"Lin","sequence":"additional","affiliation":[{"name":"Institute of Electronics, Chinese Academy of Sciences, Beijing 100190, China"},{"name":"Key Laboratory of Technology in Geo-Spatial Information Processing and Application System, Chinese Academy of Sciences, Beijing 100190, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Xian","family":"Sun","sequence":"additional","affiliation":[{"name":"Institute of Electronics, Chinese Academy of Sciences, Beijing 100190, China"},{"name":"Key Laboratory of Technology in Geo-Spatial Information Processing and Application System, Chinese Academy of Sciences, Beijing 100190, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Kun","family":"Fu","sequence":"additional","affiliation":[{"name":"Institute of Electronics, Chinese Academy of Sciences, Beijing 100190, China"},{"name":"Key Laboratory of Technology in Geo-Spatial Information Processing and Application System, Chinese Academy of Sciences, Beijing 100190, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2019,1,2]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"1019","DOI":"10.1002\/asi.20591","article-title":"The link-prediction problem for social networks","volume":"58","author":"Kleinberg","year":"2007","journal-title":"J. Am. Soc. Inf. Sci. Technol."},{"key":"ref_2","unstructured":"Kipf, T.N., and Welling, M. (arXiv, 2016). Semi-supervised classification with graph convolutional networks, arXiv."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"399","DOI":"10.1038\/nature750","article-title":"Comparative assessment of large-scale data sets of protein\u2013protein interactions","volume":"417","author":"Krause","year":"2002","journal-title":"Nature"},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"211","DOI":"10.1016\/S0378-8733(03)00009-1","article-title":"Friends and neighbors on the Web","volume":"25","author":"Adamic","year":"2003","journal-title":"Soc. Netw."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"30","DOI":"10.1109\/MC.2009.263","article-title":"Matrix factorization techniques for recommender systems","volume":"42","author":"Koren","year":"2009","journal-title":"Computer"},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"11","DOI":"10.1109\/JPROC.2015.2483592","article-title":"A review of relational machine learning for knowledge graphs","volume":"104","author":"Nickel","year":"2016","journal-title":"Proc. IEEE"},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"608","DOI":"10.1093\/bioinformatics\/btw684","article-title":"BoostGAPFILL: Improving the fidelity of metabolic network reconstructions through integrated constraint and pattern-based methods","volume":"33","author":"Oyetunde","year":"2016","journal-title":"Bioinformatics"},{"key":"ref_8","doi-asserted-by":"crossref","unstructured":"Salakhutdinov, R., and Mnih, A. (2008). Bayesian probabilistic matrix factorization using Markov chain Monte Carlo. Proceedings of the 25th International Conference on Machine Learning, Helsinki, Finland, 5\u20139 July 2008, ACM.","DOI":"10.1145\/1390156.1390267"},{"key":"ref_9","first-page":"1981","article-title":"Mixed membership stochastic blockmodels","volume":"9","author":"Airoldi","year":"2008","journal-title":"J. Mach. Learn. Res."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"509","DOI":"10.1126\/science.286.5439.509","article-title":"Emergence of scaling in random networks","volume":"286","author":"Albert","year":"1999","journal-title":"Science"},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"623","DOI":"10.1140\/epjb\/e2009-00335-8","article-title":"Predicting missing links via local information","volume":"71","author":"Zhou","year":"2009","journal-title":"Eur. Phys. J. B"},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"39","DOI":"10.1007\/BF02289026","article-title":"A new status index derived from sociometric analysis","volume":"18","author":"Katz","year":"1953","journal-title":"Psychometrika"},{"key":"ref_13","doi-asserted-by":"crossref","unstructured":"Jeh, G., and Widom, J. (2002). SimRank: A measure of structural-context similarity. Proceedings of the eighth ACM SIGKDD International Conference on Knowledge Discovery and Data Mining, Edmonton, AB, Canada, 23\u201326 July 2002, ACM.","DOI":"10.1145\/775047.775126"},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"81","DOI":"10.1007\/BF01164627","article-title":"Resistance distance","volume":"12","author":"Klein","year":"1993","journal-title":"J. Math. Chem."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"1150","DOI":"10.1016\/j.physa.2010.11.027","article-title":"Link prediction in complex networks: A survey","volume":"390","author":"Zhou","year":"2011","journal-title":"Phys. A Stat. Mech. Appl."},{"key":"ref_16","doi-asserted-by":"crossref","unstructured":"Zhang, M., and Chen, Y. (2017). Weisfeiler\u2013Lehman neural machine for link prediction. Proceedings of the 23rd ACM SIGKDD International Conference on Knowledge Discovery and Data Mining, Halifax, NS, Canada, 13\u201317 August 2017, ACM.","DOI":"10.1145\/3097983.3097996"},{"key":"ref_17","doi-asserted-by":"crossref","unstructured":"Perozzi, B., Al-Rfou, R., and Skiena, S. (arXiv, 2014). DeepWalk: Online Learning of Social Representations, arXiv.","DOI":"10.1145\/2623330.2623732"},{"key":"ref_18","doi-asserted-by":"crossref","unstructured":"Grover, A., and Leskovec, J. (2016). node2vec: Scalable feature learning for networks. Proceedings of the 22nd ACM SIGKDD International Conference on Knowledge Discovery and Data Mining, San Francisco, CA, USA, 13\u201317 August 2016, ACM.","DOI":"10.1145\/2939672.2939754"},{"key":"ref_19","doi-asserted-by":"crossref","unstructured":"Tang, J., Qu, M., Wang, M., Zhang, M., Yan, J., and Mei, Q. (arXiv, 2015). LINE: Large-scale Information Network Embedding, arXiv.","DOI":"10.1145\/2736277.2741093"},{"key":"ref_20","unstructured":"Cai, H., Zheng, V.W., and Chang, K.C. (arXiv, 2017). A Comprehensive Survey of Graph Embedding: Problems, Techniques and Applications, arXiv."},{"key":"ref_21","first-page":"547","article-title":"Etude de la distribution florale dans une portion des Alpes et du Jura","volume":"37","author":"Jaccard","year":"1901","journal-title":"Bulletin De La Societe Vaudoise Des Sciences Naturelles"},{"key":"ref_22","doi-asserted-by":"crossref","unstructured":"Cukierski, W., Hamner, B., and Yang, B. (August, January 31). Graph-based features for supervised link prediction. Proceedings of the 2011 IEEE International Joint Conference on Neural Networks (IJCNN), San Jose, CA, USA.","DOI":"10.1109\/IJCNN.2011.6033365"},{"key":"ref_23","unstructured":"Miller, K., Jordan, M.I., and Griffiths, T.L. (2009, January 7\u201310). Nonparametric latent feature models for link prediction. Proceedings of the Advances in Neural Information Processing Systems, Vancouver, BC, Canada."},{"key":"ref_24","unstructured":"Zhang, M., and Chen, Y. (arXiv, 2018). Link Prediction Based on Graph Neural Networks, arXiv."},{"key":"ref_25","unstructured":"Mikolov, T., Sutskever, I., Chen, K., Corrado, G., and Dean, J. (arXiv, 2013). Distributed Representations of Words and Phrases and their Compositionality, arXiv."},{"key":"ref_26","first-page":"12","article-title":"A reduction of a graph to a canonical form and an algebra arising during this reduction","volume":"2","author":"Weisfeiler","year":"1968","journal-title":"Nauchno-Technicheskaya Informatsia"},{"key":"ref_27","unstructured":"(2019, January 02). USAir Dataset. Available online: http:\/\/web.mit.edu\/airlinedata\/www\/default.html."},{"key":"ref_28","unstructured":"Ackland, R. (2019, January 02). Mapping the Us Political Blogosphere: Are Conservative Bloggers More Prominent? BlogTalk Downunder 2005 Conference, Sydney. Available online: https:\/\/core.ac.uk\/download\/pdf\/156616040.pdf."},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"036104","DOI":"10.1103\/PhysRevE.74.036104","article-title":"Finding community structure in networks using the eigenvectors of matrices","volume":"74","author":"Newman","year":"2006","journal-title":"Phys. Rev. E"},{"key":"ref_30","unstructured":"Zhang, M., Cui, Z., Oyetunde, T., Tang, Y., and Chen, Y. (arXiv, 2016). Recovering Metabolic Networks using A Novel Hyperlink Prediction Method, arXiv."},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"133","DOI":"10.1145\/964725.633039","article-title":"Measuring ISP topologies with Rocketfuel","volume":"32","author":"Spring","year":"2002","journal-title":"ACM SIGCOMM Comput. Commun. Rev."},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"1373","DOI":"10.1016\/S0895-4356(96)00236-3","article-title":"A simulation study of the number of events per variable in logistic regression analysis","volume":"49","author":"Peduzzi","year":"1996","journal-title":"J. Clin. Epidemiol."},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"660","DOI":"10.1109\/21.97458","article-title":"A survey of decision tree classifier methodology","volume":"21","author":"Safavian","year":"1991","journal-title":"IEEE Trans. Syst. Man Cybern."},{"key":"ref_34","first-page":"18","article-title":"Classification and regression by randomForest","volume":"2","author":"Liaw","year":"2002","journal-title":"R News"},{"key":"ref_35","first-page":"1612","article-title":"A short introduction to boosting","volume":"14","author":"Freund","year":"1999","journal-title":"J. Jpn. Soc. Artif. Intell."},{"key":"ref_36","doi-asserted-by":"crossref","unstructured":"Bengio, Y., Louradour, J., Collobert, R., and Weston, J. (2009). Curriculum learning. Proceedings of the 26th Annual International Conference on Machine Learning, Montreal, QC, Canada, 14\u201318 June 2009, ACM.","DOI":"10.1145\/1553374.1553380"},{"key":"ref_37","first-page":"1929","article-title":"Dropout: A Simple Way to Prevent Neural Networks from Overfitting","volume":"15","author":"Srivastava","year":"2014","journal-title":"J. Mach. Learn. Res."},{"key":"ref_38","doi-asserted-by":"crossref","unstructured":"Chen, Y.Y., Gan, Q., and Suel, T. (2004). Local methods for estimating pagerank values. Proceedings of the thirteenth ACM International Conference on Information and Knowledge Management, Washington, DC, USA, 8\u201313 November 2004, ACM.","DOI":"10.1145\/1031171.1031248"},{"key":"ref_39","first-page":"57","article-title":"Factorization machines with libfm","volume":"3","author":"Rendle","year":"2012","journal-title":"ACM Trans. Intell. Syst. Technol. (TIST)"}],"container-title":["Algorithms"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1999-4893\/12\/1\/12\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T12:23:09Z","timestamp":1760185389000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1999-4893\/12\/1\/12"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2019,1,2]]},"references-count":39,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2019,1]]}},"alternative-id":["a12010012"],"URL":"https:\/\/doi.org\/10.3390\/a12010012","relation":{},"ISSN":["1999-4893"],"issn-type":[{"type":"electronic","value":"1999-4893"}],"subject":[],"published":{"date-parts":[[2019,1,2]]}}}