{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,11,2]],"date-time":"2025-11-02T04:16:16Z","timestamp":1762056976573,"version":"build-2065373602"},"reference-count":37,"publisher":"MDPI AG","issue":"6","license":[{"start":{"date-parts":[[2022,6,18]],"date-time":"2022-06-18T00:00:00Z","timestamp":1655510400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>With the goal of understanding if the information contained in node metadata can help in the task of link weight prediction, we investigate herein whether incorporating it as a similarity feature (referred to as metadata similarity) between end nodes of a link improves the prediction accuracy of common supervised machine learning methods. In contrast with previous works, instead of normalizing the link weights, we treat them as count variables representing the number of interactions between end nodes, as this is a natural representation for many datasets in the literature. In this preliminary study, we find no significant evidence that metadata similarity improved the prediction accuracy of the four empirical datasets studied. To further explore the role of node metadata in weight prediction, we synthesized weights to analyze the extreme case where the weights depend solely on the metadata of the end nodes, while encoding different relationships between them using logical operators in the generation process. Under these conditions, the random forest method performed significantly better than other methods in 99.07% of cases, though the prediction accuracy was significantly degraded for the methods analyzed in comparison to the experiments with the original weights.<\/jats:p>","DOI":"10.3390\/e24060842","type":"journal-article","created":{"date-parts":[[2022,6,18]],"date-time":"2022-06-18T09:51:11Z","timestamp":1655545871000},"page":"842","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":4,"title":["Examining Supervised Machine Learning Methods for Integer Link Weight Prediction Using Node Metadata"],"prefix":"10.3390","volume":"24","author":[{"given":"Larissa","family":"Mori","sequence":"first","affiliation":[{"name":"School of Industrial Engineering, Purdue University, West Lafayette, IN 47906, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-5119-742X","authenticated-orcid":false,"given":"Kaleigh","family":"O\u2019Hara","sequence":"additional","affiliation":[{"name":"School of Industrial Engineering, Purdue University, West Lafayette, IN 47906, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-3992-2710","authenticated-orcid":false,"given":"Toyya A.","family":"Pujol","sequence":"additional","affiliation":[{"name":"RAND Corporation, Santa Monica, CA 90407-2138, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Mario","family":"Ventresca","sequence":"additional","affiliation":[{"name":"School of Industrial Engineering, Purdue University, West Lafayette, IN 47906, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2022,6,18]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"e1602548","DOI":"10.1126\/sciadv.1602548","article-title":"The ground truth about metadata and community detection in networks","volume":"3","author":"Peel","year":"2017","journal-title":"Sci. Adv."},{"key":"ref_2","doi-asserted-by":"crossref","unstructured":"Fajardo-Fontiveros, O., Sales-Pardo, M., and Guimera, R. (2021). Node metadata can produce predictability transitions in network inference problems. arXiv.","DOI":"10.1103\/PhysRevX.12.011010"},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"38080","DOI":"10.1038\/srep38080","article-title":"Weight Prediction in Complex Networks Based on Neighbor Set","volume":"6","author":"Zhu","year":"2016","journal-title":"Sci. Rep."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"67","DOI":"10.1109\/4235.585893","article-title":"No Free Lunch Theorems for Optimization","volume":"1","author":"Wolpert","year":"1997","journal-title":"IEEE Trans. Evol. Comput."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"12261","DOI":"10.1038\/srep12261","article-title":"Prediction of Links and Weights in Networks by Reliable Routes","volume":"5","author":"Zhao","year":"2015","journal-title":"Sci. Rep."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"440","DOI":"10.1038\/30918","article-title":"Collective dynamics of \u2018small-world\u2019networks","volume":"393","author":"Watts","year":"1998","journal-title":"Nature"},{"key":"ref_7","unstructured":"Batagelj, V., and Mrvar, A. (2021, July 18). Pajek Datasets. Available online: https:\/\/vlado.fmf.uni-lj.si\/pub\/networks\/data\/."},{"key":"ref_8","doi-asserted-by":"crossref","unstructured":"Kunegis, J. (2013, January 13\u201317). Konect: The koblenz network collection. Proceedings of the 22nd International Conference on World Wide Web, Rio de Janeiro, Brazil. Available online: https:\/\/konect.uni-koblenz.de\/.","DOI":"10.1145\/2487788.2488173"},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"1068","DOI":"10.1016\/j.cell.2012.08.011","article-title":"A census of human soluble protein complexes","volume":"150","author":"Havugimana","year":"2012","journal-title":"Cell"},{"key":"ref_10","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_11","doi-asserted-by":"crossref","first-page":"98","DOI":"10.1038\/nature06830","article-title":"Hierarchical Structure and the Prediction of Missing Links in Networks","volume":"453","author":"Clauset","year":"2008","journal-title":"Nature"},{"key":"ref_12","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_13","doi-asserted-by":"crossref","first-page":"22073","DOI":"10.1073\/pnas.0908366106","article-title":"Missing and Spurious Interactions and the Reconstruction of Complex Networks","volume":"106","year":"2009","journal-title":"Proc. Natl. Acad. Sci. USA"},{"key":"ref_14","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":"Lu","year":"2011","journal-title":"Phys. A Stat. Mech. Its Appl."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"103217","DOI":"10.1016\/j.isci.2021.103217","article-title":"Progresses and Challenges in Link Prediction","volume":"24","author":"Zhou","year":"2021","journal-title":"iScience"},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"221","DOI":"10.1093\/comnet\/cnu026","article-title":"Learning Latent Block Structure in Weighted Networks","volume":"3","author":"Aicher","year":"2015","journal-title":"J. Complex Netw."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"1507","DOI":"10.1109\/TKDE.2018.2801854","article-title":"Link Weight Prediction Using Supervised Learning Methods and Its Application to Yelp Layered Network","volume":"30","author":"Fu","year":"2018","journal-title":"IEEE Trans. Knowl. Data Eng."},{"key":"ref_18","doi-asserted-by":"crossref","unstructured":"Kumar, S., Spezzano, F., Subrahmanian, V.S., and Faloutsos, C. (2016, January 12\u201315). Edge Weight Prediction in Weighted Signed Networks. Proceedings of the 2016 IEEE 16th International Conference on Data Mining (ICDM), Barcelona, Spain.","DOI":"10.1109\/ICDM.2016.0033"},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"56","DOI":"10.1007\/978-3-030-34869-4_7","article-title":"Link Weight Prediction for Directed WSN Using Features from Network and Its Dual","volume":"Volume 11941","author":"Deka","year":"2019","journal-title":"Pattern Recognition and Machine Intelligence"},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"725","DOI":"10.1080\/10618600.2017.1286243","article-title":"Link Prediction for Partially Observed Networks","volume":"26","author":"Zhao","year":"2017","journal-title":"J. Comput. Graph. Stat."},{"key":"ref_21","unstructured":"Popescul, A., and Ungar, L.H. (2003, January 9\u201311). Statistical Relational Learning for Link Prediction. Proceedings of the Workshop on Learning Statistical Models from Relational Data at IJCAI-2003, Acapulco, Mexico."},{"key":"ref_22","first-page":"8","article-title":"Link Prediction in Relational Data","volume":"16","author":"Taskar","year":"2003","journal-title":"Adv. Neural Inf. Processing Syst."},{"key":"ref_23","unstructured":"Kim, D.I., Hughes, M.C., and Sudderth, E.B. (2012). The Nonparametric Metadata Dependent Relational Model. arXiv."},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"589","DOI":"10.1109\/TCYB.2016.2521376","article-title":"Learning Nonparametric Relational Models by Conjugately Incorporating Node Information in a Network","volume":"47","author":"Fan","year":"2017","journal-title":"IEEE Trans. Cybern."},{"key":"ref_25","unstructured":"Zhao, H., Du, L., and Buntine, W. (2017). Leveraging Node Attributes for Incomplete Relational Data. arXiv."},{"key":"ref_26","first-page":"11","article-title":"Link Prediction Based on Graph Neural Networks","volume":"31","author":"Zhang","year":"2018","journal-title":"Adv. Neural Inf. Processing Syst."},{"key":"ref_27","unstructured":"Goodfellow, I., Bengio, Y., and Courville, A. (2016). Deep Learning, MIT Press. Available online: http:\/\/www.deeplearningbook.org."},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"025102","DOI":"10.1103\/PhysRevE.64.025102","article-title":"Clustering and preferential attachment in growing networks","volume":"64","author":"Newman","year":"2001","journal-title":"Phys. Rev. E"},{"key":"ref_29","first-page":"547","article-title":"\u00c9tude comparative de la distribution florale dans une portion des Alpes et des Jura","volume":"37","author":"Jaccard","year":"1901","journal-title":"Bull. Soc. Vaudoise Sci. Nat."},{"key":"ref_30","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_31","unstructured":"Salton, G., and McGill, M.J. (1983). Introduction to Modern Information Retrieval, McGraw-Hill."},{"key":"ref_32","first-page":"1","article-title":"A method of establishing groups of equal amplitude in plant sociology based on similarity of species content and its application to analyses of the vegetation on Danish commons","volume":"5","author":"Sorensen","year":"1948","journal-title":"Biol. Skar."},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"1551","DOI":"10.1126\/science.1073374","article-title":"Hierarchical organization of modularity in metabolic networks","volume":"297","author":"Ravasz","year":"2002","journal-title":"Science"},{"key":"ref_34","doi-asserted-by":"crossref","first-page":"026120","DOI":"10.1103\/PhysRevE.73.026120","article-title":"Vertex similarity in networks","volume":"73","author":"Leicht","year":"2006","journal-title":"Phys. Rev. E"},{"key":"ref_35","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_36","doi-asserted-by":"crossref","unstructured":"Ziegler, C.N., McNee, S.M., Konstan, J.A., and Lausen, G. (2005, January 10\u201314). Improving recommendation lists through topic diversification. Proceedings of the 14th International Conference on World Wide Web, Chiba, Japan.","DOI":"10.1145\/1060745.1060754"},{"key":"ref_37","doi-asserted-by":"crossref","first-page":"208701","DOI":"10.1103\/PhysRevLett.89.208701","article-title":"Assortative mixing in networks","volume":"89","author":"Newman","year":"2002","journal-title":"Phys. Rev. Lett."}],"container-title":["Entropy"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1099-4300\/24\/6\/842\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T23:34:45Z","timestamp":1760139285000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1099-4300\/24\/6\/842"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2022,6,18]]},"references-count":37,"journal-issue":{"issue":"6","published-online":{"date-parts":[[2022,6]]}},"alternative-id":["e24060842"],"URL":"https:\/\/doi.org\/10.3390\/e24060842","relation":{},"ISSN":["1099-4300"],"issn-type":[{"type":"electronic","value":"1099-4300"}],"subject":[],"published":{"date-parts":[[2022,6,18]]}}}