{"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/learning-networks-from-random-walk-based-node","title":"Learning Networks from Random Walk-Based Node Similarities","arxiv_id":"1801.07386","date":"2018-01-23","proceeding":null,"authors":["Jeremy G. Hoskins","Cameron Musco","Christopher Musco","Charalampos E. Tsourakakis"],"abstract":"Digital presence in the world of online social media entails significant\nprivacy risks. In this work we consider a privacy threat to a social network in\nwhich an attacker has access to a subset of random walk-based node\nsimilarities, such as effective resistances (i.e., commute times) or\npersonalized PageRank scores. Using these similarities, the attacker's goal is\nto infer as much information as possible about the underlying network,\nincluding any remaining unknown pairwise node similarities and edges.\n  For the effective resistance metric, we show that with just a small subset of\nmeasurements, the attacker can learn a large fraction of edges in a social\nnetwork, even when the measurements are noisy. We also show that it is possible\nto learn a graph which accurately matches the underlying network on all other\neffective resistances. This second observation is interesting from a data\nmining perspective, since it can be expensive to accurately compute all\neffective resistances. As an alternative, our graphs learned from just a subset\nof approximate effective resistances can be used as surrogates in a wide range\nof applications that use effective resistances to probe graph structure,\nincluding for graph clustering, node centrality evaluation, and anomaly\ndetection.\n  We obtain our results by formalizing the graph learning objective\nmathematically, using two optimization problems. One formulation is convex and\ncan be solved provably in polynomial time. The other is not, but we solve it\nefficiently with projected gradient and coordinate descent. We demonstrate the\neffectiveness of these methods on a number of social networks obtained from\nFacebook. We also discuss how our methods can be generalized to other random\nwalk-based similarities, such as personalized PageRank. Our code is available\nat https://github.com/cnmusco/graph-similarity-learning.","url_abs":"http://arxiv.org/abs/1801.07386v1","url_pdf":"http://arxiv.org/pdf/1801.07386v1.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":"learning-networks-from-random-walk-based-node","repo_url":"https://github.com/cnmusco/graph-similarity-learning","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":0,"framework":"none","reach":null}],"tasks":[{"task_slug":"anomaly-detection","task_name":"Anomaly Detection"},{"task_slug":"clustering","task_name":"Clustering"},{"task_slug":"graph-clustering","task_name":"Graph Clustering"},{"task_slug":"graph-learning","task_name":"Graph Learning"},{"task_slug":"graph-similarity","task_name":"Graph Similarity"}],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}