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The underlying idea is that two nodes are considered as similar when they often appear together on (preferably short) paths of the network. The different expressions are obtained for both regular and hitting paths and serve as a basis for computing new covariance and correlation measures between nodes, which are valid positive semi-definite kernels on a graph. Experiments on semi-supervised classification problems show that the introduced similarity measures provide competitive results compared to other state-of-the-art distance and similarity measures between nodes.<\/jats:p>","DOI":"10.1093\/comnet\/cnaa026","type":"journal-article","created":{"date-parts":[[2020,7,22]],"date-time":"2020-07-22T19:22:42Z","timestamp":1595445762000},"source":"Crossref","is-referenced-by-count":5,"title":["Covariance and correlation measures on a graph in a generalized bag-of-paths formalism"],"prefix":"10.1093","volume":"8","author":[{"given":"Guillaume","family":"Guex","sequence":"first","affiliation":[{"name":"SLI, Universit\u00e9 de Lausanne, Lausanne 1002, Switzerland"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Sylvain","family":"Courtain","sequence":"additional","affiliation":[{"name":"LOURIM, Universit\u00e9 catholique de Louvain, Louvain-la-neuve 1348, Belgium"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Marco","family":"Saerens","sequence":"additional","affiliation":[{"name":"ICTEAM, Universit\u00e9 catholique de Louvain, Louvain-la-neuve 1348, Belgium"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"286","published-online":{"date-parts":[[2021,3,7]]},"reference":[{"volume-title":"Network Science","year":"2016","author":"Barab\u00e1si,","key":"2021031105082788000_B1"},{"key":"2021031105082788000_B2","doi-asserted-by":"crossref","DOI":"10.1017\/CBO9781139176200","volume-title":"Networked Life","author":"Chiang,","year":"2012"},{"key":"2021031105082788000_B3","doi-asserted-by":"crossref","DOI":"10.1090\/cbms\/107","volume-title":"Complex Graphs and Networks","author":"Chung,","year":"2006"},{"volume-title":"The Structure of Complex Networks","year":"2012","author":"Estrada,","key":"2021031105082788000_B4"},{"key":"2021031105082788000_B5","doi-asserted-by":"crossref","DOI":"10.1017\/CBO9781316418321","volume-title":"Algorithms and Models for Network Data and Link Analysis","author":"Fouss,","year":"2016"},{"key":"2021031105082788000_B6","doi-asserted-by":"crossref","DOI":"10.1007\/978-0-387-88146-1","volume-title":"Statistical Analysis of Network Data: Methods and Models","author":"Kolaczyk,","year":"2009"},{"key":"2021031105082788000_B7","doi-asserted-by":"crossref","DOI":"10.1002\/9780470400791","volume-title":"Network Science","author":"Lewis,","year":"2009"},{"volume-title":"Graph-based Natural Language Processing and Information Retrieval","year":"2011","author":"Chung,","key":"2021031105082788000_B8"},{"key":"2021031105082788000_B9","doi-asserted-by":"crossref","DOI":"10.1093\/oso\/9780198805090.001.0001","volume-title":"Networks","author":"Newman,","year":"2018","edition":"2nd edn"},{"volume-title":"Machine Learning in Complex Networks","year":"2016","author":"Chung,","key":"2021031105082788000_B10"},{"key":"2021031105082788000_B11","doi-asserted-by":"crossref","DOI":"10.1108\/S1876-0562(2004)04","volume-title":"Link Analysis: An Information Science Approach","author":"Thelwall,","year":"2004"},{"volume-title":"Social Network Analysis: Methods and Applications","year":"1994","author":"Chung,","key":"2021031105082788000_B12"},{"key":"2021031105082788000_B13","first-page":"68","article-title":"Interpolating between random walks and shortest paths: a path functional approach","volume-title":"International Conference on Social Informatics","author":"Chung,","year":"2012"},{"key":"2021031105082788000_B14","doi-asserted-by":"crossref","first-page":"90","DOI":"10.1016\/j.neunet.2017.03.010","article-title":"A bag-of-paths framework for network data analysis","volume":"90","author":"Fran\u00e7oisse,","year":"2017","journal-title":"Neural Netw."},{"key":"2021031105082788000_B15","doi-asserted-by":"crossref","first-page":"600","DOI":"10.1016\/j.physa.2013.09.016","article-title":"Developments in the theory of randomized shortest paths with a comparison of graph node distances","volume":"393","author":"Kivim\u00e4ki,","year":"2014","journal-title":"Physica A"},{"key":"2021031105082788000_B16","doi-asserted-by":"crossref","first-page":"2363","DOI":"10.1162\/neco.2009.11-07-643","article-title":"Randomized shortest-path problems: two related models","volume":"21","author":"Saerens,","year":"2009","journal-title":"Neural Comput."},{"key":"2021031105082788000_B17","doi-asserted-by":"crossref","first-page":"785","DOI":"10.1145\/1401890.1401984","article-title":"A family of dissimilarity measures between nodes generalizing both the shortest-path and the commute-time distances","volume-title":"Proceedings of the 14th SIGKDD International Conference on Knowledge Discovery and Data Mining (KDD 2008)","author":"Yen,","year":"2008"},{"key":"2021031105082788000_B18","doi-asserted-by":"crossref","first-page":"1112","DOI":"10.1109\/TPAMI.2009.78","article-title":"The sum-over-paths covariance kernel: a novel covariance between nodes of a directed graph","volume":"32","author":"Mantrach,","year":"2010","journal-title":"IEEE Trans. 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