{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T03:39:44Z","timestamp":1760240384780,"version":"build-2065373602"},"reference-count":37,"publisher":"MDPI AG","issue":"2","license":[{"start":{"date-parts":[[2019,5,24]],"date-time":"2019-05-24T00:00:00Z","timestamp":1558656000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["MAKE"],"abstract":"<jats:p>Graph-embedding algorithms map a graph into a vector space with the aim of preserving its structure and its intrinsic properties. Unfortunately, many of them are not able to encode the neighborhood information of the nodes well, especially from a topological prospective. To address this limitation, we propose a novel graph-embedding method called Deep-Order Proximity and Structural Information Embedding (DOPSIE). It provides topology and depth information at the same time through the analysis of the graph structure. Topological information is provided through clustering coefficients (CCs), which is connected to other structural properties, such as transitivity, density, characteristic path length, and efficiency, useful for representation in the vector space. The combination of individual node properties and neighborhood information constitutes an optimal network representation. Our experimental results show that DOPSIE outperforms state-of-the-art embedding methodologies in different classification problems.<\/jats:p>","DOI":"10.3390\/make1020040","type":"journal-article","created":{"date-parts":[[2019,5,24]],"date-time":"2019-05-24T11:20:46Z","timestamp":1558696846000},"page":"684-697","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":4,"title":["DOPSIE: Deep-Order Proximity and Structural Information Embedding"],"prefix":"10.3390","volume":"1","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-8727-9865","authenticated-orcid":false,"given":"Mario","family":"Manzo","sequence":"first","affiliation":[{"name":"Information Technology Services, University of Naples \u201cL\u2019Orientale\u201d, 80121 Naples, Italy"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-6269-1351","authenticated-orcid":false,"given":"Alessandro","family":"Rozza","sequence":"additional","affiliation":[{"name":"lastminute.com group, 6830 Chiasso, Switzerland"}]}],"member":"1968","published-online":{"date-parts":[[2019,5,24]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"1535","DOI":"10.1038\/nprot.2009.177","article-title":"Network visualization and analysis of gene expression data using BioLayout Express3D","volume":"4","author":"Theocharidis","year":"2009","journal-title":"Nat. Protoc."},{"key":"ref_2","doi-asserted-by":"crossref","unstructured":"Scott, J. (2017). Social Network Analysis, SAGE Publications Ltd.","DOI":"10.4135\/9781529716597"},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"1020","DOI":"10.1016\/j.patcog.2012.09.015","article-title":"A Survey of Graph Theoretical Approaches to Image Segmentation","volume":"46","author":"Peng","year":"2013","journal-title":"Pattern Recogn."},{"key":"ref_4","unstructured":"Manzo, M., Pellino, S., Petrosino, A., and Rozza, A. (2014, January 6\u201312). A novel graph embedding framework for object recognition. Proceedings of the European Conference on Computer Vision, Zurich, Switzerland."},{"key":"ref_5","doi-asserted-by":"crossref","unstructured":"Collobert, R., and Weston, J. (2008). A unified architecture for natural language processing: Deep neural networks with multitask learning. Proceedings of the 25th International Conference on Machine Learning;, ACM.","DOI":"10.1145\/1390156.1390177"},{"key":"ref_6","doi-asserted-by":"crossref","unstructured":"Aggarwal, C.C. (2011). An introduction to social network data analytics. Social Network Data Analytics, Springer.","DOI":"10.1007\/978-1-4419-8462-3_1"},{"key":"ref_7","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. Assoc. Inf. Sci. Tech."},{"key":"ref_8","unstructured":"Ding, C.H., He, X., Zha, H., Gu, M., and Simon, H.D. (December, January 29). A min-max cut algorithm for graph partitioning and data clustering. Proceedings of the IEEE International Conference on Data Mining, San Jose, CA, USA."},{"key":"ref_9","first-page":"2579","article-title":"Visualizing data using t-SNE","volume":"9","author":"Maaten","year":"2008","journal-title":"J. Mach. Learn. Res."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"78","DOI":"10.1016\/j.knosys.2018.03.022","article-title":"Graph Embedding Techniques, Applications, and Performance: A Survey","volume":"151","author":"Goyal","year":"2018","journal-title":"Knowl.-Based Syst."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"1616","DOI":"10.1109\/TKDE.2018.2807452","article-title":"A comprehensive survey of graph embedding: Problems, techniques and applications","volume":"30","author":"Cai","year":"2018","journal-title":"IEEE Trans. Knowl. Data Eng."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"82","DOI":"10.1016\/j.amc.2007.12.010","article-title":"Information Processing in Complex Networks: Graph Entropy and Information Functionals","volume":"201","author":"Dehmer","year":"2008","journal-title":"Appl. Math. Comput."},{"key":"ref_13","doi-asserted-by":"crossref","unstructured":"Holzinger, A., H\u00f6rtenhuber, M., Mayer, C., Bachler, M., Wassertheurer, S., Pinho, A.J., and Koslicki, D. (2014). On entropy-based data mining. Interactive Knowledge Discovery and Data Mining in Biomedical Informatics, Springer.","DOI":"10.1007\/978-3-662-43968-5_12"},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"185","DOI":"10.1049\/iet-syb.2010.0025","article-title":"Networks for systems biology: conceptual connection of data and function","volume":"5","author":"Dehmer","year":"2011","journal-title":"IET Syst. Biol."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"55","DOI":"10.1016\/j.socnet.2004.11.008","article-title":"Centrality and network flow","volume":"27","author":"Borgatti","year":"2005","journal-title":"Soc. Netw."},{"key":"ref_16","doi-asserted-by":"crossref","unstructured":"Junker, B.H., Kosch\u00fctzki, D., and Schreiber, F. (2006). Exploration of biological network centralities with CentiBiN. BMC Bioinform., 7.","DOI":"10.1186\/1471-2105-7-219"},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"EBO-S12012","DOI":"10.4137\/EBO.S12012","article-title":"SBEToolbox: A Matlab toolbox for biological network analysis","volume":"9","author":"Konganti","year":"2013","journal-title":"Evol. Bioinform."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"1059","DOI":"10.1016\/j.neuroimage.2009.10.003","article-title":"Complex network measures of brain connectivity: uses and interpretations","volume":"52","author":"Rubinov","year":"2010","journal-title":"Neuroimage"},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"016117","DOI":"10.1103\/PhysRevE.85.016117","article-title":"Overview of metrics and their correlation patterns for multiple-metric topology analysis on heterogeneous graph ensembles","volume":"85","author":"Bounova","year":"2012","journal-title":"Phys. Rev. E"},{"key":"ref_20","doi-asserted-by":"crossref","unstructured":"Perozzi, B., Al-Rfou, R., and Skiena, S. (2014, January 24\u201327). Deepwalk: Online learning of social representations. Proceedings of the 20th ACM SIGKDD International Conference on Knowledge Discovery and Data Mining, New York, NY, USA.","DOI":"10.1145\/2623330.2623732"},{"key":"ref_21","doi-asserted-by":"crossref","unstructured":"Grover, A., and Leskovec, J. (2016, January 13\u201317). node2vec: Scalable feature learning for networks. Proceedings of the 22nd ACM SIGKDD International Conference on Knowledge Discovery and Data Mining, San Francisco, CA, USA.","DOI":"10.1145\/2939672.2939754"},{"key":"ref_22","doi-asserted-by":"crossref","unstructured":"Ou, M., Cui, P., Pei, J., Zhang, Z., and Zhu, W. (2016, January 13\u201317). Asymmetric Transitivity Preserving Graph Embedding. Proceedings of the 22nd ACM SIGKDD International Conference on Knowledge Discovery and Data Mining, San Francisco, CA, USA.","DOI":"10.1145\/2939672.2939751"},{"key":"ref_23","doi-asserted-by":"crossref","unstructured":"Ahmed, A., Shervashidze, N., Narayanamurthy, S., Josifovski, V., and Smola, A.J. (2013, January 13\u201317). Distributed large-scale natural graph factorization. Proceedings of the 22nd international conference on World Wide Web, Rio de Janeiro, Brazil.","DOI":"10.1145\/2488388.2488393"},{"key":"ref_24","doi-asserted-by":"crossref","unstructured":"Wang, D., Cui, P., and Zhu, W. (2016, January 13\u201317). Structural deep network embedding. Proceedings of the 22nd ACM SIGKDD International Conference on Knowledge Discovery and Data Mining, San Francisco, CA, USA.","DOI":"10.1145\/2939672.2939753"},{"key":"ref_25","doi-asserted-by":"crossref","unstructured":"Tang, J., Qu, M., Wang, M., Zhang, M., Yan, J., and Mei, Q. (2015, January 18\u201322). Line: Large-scale information network embedding. Proceedings of the 24th International Conference on World Wide Web, Florence, Italy.","DOI":"10.1145\/2736277.2741093"},{"key":"ref_26","doi-asserted-by":"crossref","unstructured":"Cao, S., Lu, W., and Xu, Q. (2016, January 12\u201317). Deep Neural Networks for Learning Graph Representations. Proceedings of the Thirtieth AAAI Conference on Artificial Intelligence, Phoenix, Arizona, USA.","DOI":"10.1609\/aaai.v30i1.10179"},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"159","DOI":"10.1016\/j.socnet.2011.07.001","article-title":"Triadic closure in two-mode networks: Redefining the global and local clustering coefficients","volume":"35","author":"Opsahl","year":"2013","journal-title":"Soc. Netw."},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"2566","DOI":"10.1073\/pnas.012582999","article-title":"Random graph models of social networks","volume":"99","author":"Newman","year":"2002","journal-title":"Proc. Natl. Acad. Sci. USA"},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"265","DOI":"10.7155\/jgaa.00108","article-title":"Approximating Clustering Coefficient and Transitivity","volume":"9","author":"Schank","year":"2005","journal-title":"J. Graph Algorithm. Appl."},{"key":"ref_30","unstructured":"Ne\u0161etril, J., and Ossona de Mendez, P. (2008, January 14\u201318). From sparse graphs to nowhere dense structures: Decompositions, independence, dualities and limits. Proceedings of the 8th European Congress of Mathematics, Amsterdam, The Netherlands."},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"14","DOI":"10.1007\/s13278-018-0492-3","article-title":"Generalized relationships between characteristic path length, efficiency, clustering coefficients, and density","volume":"8","author":"Strang","year":"2018","journal-title":"Soc. Netw. Anal. Min."},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"333","DOI":"10.1016\/j.socnet.2003.10.001","article-title":"Minimal and maximal characteristic path lengths in connected sociomatrices","volume":"25","author":"Lovejoy","year":"2003","journal-title":"Soc. Netw."},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"198701","DOI":"10.1103\/PhysRevLett.87.198701","article-title":"Efficient behavior of small-world networks","volume":"87","author":"Latora","year":"2001","journal-title":"Phys. Rev. Lett."},{"key":"ref_34","unstructured":"Tang, L., and Liu, H. (July, January 28). Relational learning via latent social dimensions. Proceedings of the 15th ACM SIGKDD International Conference on Knowledge Discovery and Data Mining, Paris, France."},{"key":"ref_35","doi-asserted-by":"crossref","first-page":"2","DOI":"10.1145\/1217299.1217301","article-title":"Graph evolution: Densification and shrinking diameters","volume":"1","author":"Leskovec","year":"2007","journal-title":"ACM Trans. Knowl. Discov. Data"},{"key":"ref_36","unstructured":"Candan, S., Chen, L., Pedersen, T., Chang, L., and Hua, W. (2017). Ppne: Property preserving network embedding. Database Systems for Advanced Applications, Springer."},{"key":"ref_37","doi-asserted-by":"crossref","unstructured":"Menard, S. (2010). Logistic Regression: From Introductory to Advanced Concepts and Applications, SAGE Publications.","DOI":"10.4135\/9781483348964"}],"container-title":["Machine Learning and Knowledge Extraction"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2504-4990\/1\/2\/40\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T12:54:54Z","timestamp":1760187294000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2504-4990\/1\/2\/40"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2019,5,24]]},"references-count":37,"journal-issue":{"issue":"2","published-online":{"date-parts":[[2019,6]]}},"alternative-id":["make1020040"],"URL":"https:\/\/doi.org\/10.3390\/make1020040","relation":{},"ISSN":["2504-4990"],"issn-type":[{"type":"electronic","value":"2504-4990"}],"subject":[],"published":{"date-parts":[[2019,5,24]]}}}