{"about":{"site":"https://codewithpapers.app","non_affiliation":"Code with Papers and Syntology are not affiliated with, endorsed by, or sponsored by Papers with Code, Meta, or the pwc-archive mirror.","licence":"CC BY-SA 4.0","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","attribution":"https://codewithpapers.app/attribution","modified":"archive material modified by Syntology; see the attribution page"},"url":"/paper/mercator-uncovering-faithful-hyperbolic","title":"Mercator: uncovering faithful hyperbolic embeddings of complex networks","arxiv_id":"1904.10814","date":"2019-04-24","proceeding":null,"authors":["Guillermo García-Pérez","Antoine Allard","M. Ángeles Serrano","Marián Boguñá"],"abstract":"We introduce Mercator, a reliable embedding method to map real complex\nnetworks into their hyperbolic latent geometry. The method assumes that the\nstructure of networks is well described by the Popularity$\\times$Similarity\n$\\mathbb{S}^1/\\mathbb{H}^2$ static geometric network model, which can\naccommodate arbitrary degree distributions and reproduces many pivotal\nproperties of real networks, including self-similarity patterns. The algorithm\nmixes machine learning and maximum likelihood approaches to infer the\ncoordinates of the nodes in the underlying hyperbolic disk with the best\nmatching between the observed network topology and the geometric model. In its\nfast mode, Mercator uses a model-adjusted machine learning technique performing\ndimensional reduction to produce a fast and accurate map, whose quality already\noutperform other embedding algorithms in the literature. In the refined\nMercator mode, the fast-mode embedding result is taken as an initial condition\nin a Maximum Likelihood estimation, which significantly improves the quality of\nthe final embedding. Apart from its accuracy as an embedding tool, Mercator has\nthe clear advantage of systematically inferring not only node orderings, or\nangular positions, but also the hidden degrees and global model parameters, and\nhas the ability to embed networks with arbitrary degree distributions. Overall,\nour results suggest that mixing machine learning and maximum likelihood\ntechniques in a model-dependent framework can boost the meaningful mapping of\ncomplex networks.","url_abs":"http://arxiv.org/abs/1904.10814v1","url_pdf":"http://arxiv.org/pdf/1904.10814v1.pdf","source":{"archive":"pwc-archive (Hugging Face), CC BY-SA 4.0","snapshot":"2025-07-28","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","row_kind":"abstracts"},"code_links":[{"paper_slug":"mercator-uncovering-faithful-hyperbolic","repo_url":"https://github.com/networkgeometry/mercator","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":1,"framework":"none","reach":null},{"paper_slug":"mercator-uncovering-faithful-hyperbolic","repo_url":"https://github.com/DynamicaLab/code-dynalearn","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"pytorch","reach":null},{"paper_slug":"mercator-uncovering-faithful-hyperbolic","repo_url":"https://github.com/networkgeometry/d-mercator","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"none","reach":null}],"tasks":[{"task_slug":"machine-learning","task_name":"BIG-bench Machine Learning"}],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"syntology_url":null,"atlas_url":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}