An Automorphic Distance Metric and Its Application to Node Embedding for Role Mining Martínez, Víctor Berzal Galiano, Fernando Cubero Talavera, Juan Carlos This work was partially supported by the Spanish Ministry of Economy and the European Regional Development Fund (FEDER), under grant TIN2012-36951, and the program "Ayudas para contratos predoctorales para la formacion de doc 2013," under grant BES-2013-064699. This work was also partially supported by the project "BIGDATAMED: Analisis de datos en Medicina, de las historias clinicas al BIGDATA" with references B-TIC-145-UGR18 and P18RT-1765. Role is a fundamental concept in the analysis of the behavior and function of interacting entities in complex networks. Role discovery is the task of uncovering the hidden roles of nodes within a network. Node roles are commonly defined in terms of equivalence classes. Two nodes have the same role if they fall within the same equivalence class. Automorphic equivalence, where two nodes are equivalent when they can swap their labels to form an isomorphic graph, captures this notion of role. )e binary concept of equivalence is too restrictive, and nodes in real-world networks rarely belong to the same equivalence class. Instead, a relaxed definition in terms of similarity or distance is commonly used to compute the degree to which two nodes are equivalent. In this paper, we propose a novel distance metric called automorphic distance, which measures how far two nodes are from being automorphically equivalent. We also study its application to node embedding, showing how our metric can be used to generate role-preserving vector representations of nodes. Our experiments confirm that the proposed automorphic distance metric outperforms a state-of-the-art automorphic equivalence-based metric and different state-of-the-art techniques for the generation of node embeddings in different role-related tasks. 2022-02-03T08:17:02Z 2022-02-03T08:17:02Z 2021-10-13 info:eu-repo/semantics/article Víctor Martínez, Fernando Berzal, Juan-Carlos Cubero, "An Automorphic Distance Metric and Its Application to Node Embedding for Role Mining", Complexity, vol. 2021, Article ID 5571006, 17 pages, 2021. [https://doi.org/10.1155/2021/5571006] http://hdl.handle.net/10481/72630 10.1155/2021/5571006 eng http://creativecommons.org/licenses/by/3.0/es/ info:eu-repo/semantics/openAccess Atribución 3.0 España Hindawi