{"type":"ScholarlyArticle","title":"Sampling for Approximate Bipartite Network Projection","authors":[{"name":"Nesreen Ahmed","slug":"nesreen-ahmed","given":"Nesreen","family":"Ahmed","affiliation":"Intel Labs , CA"},{"name":"Nick Duffield","slug":"nick-duffield","given":"Nick","family":"Duffield","affiliation":"Texas A&M University"},{"name":"Liangzhen Xia","slug":"liangzhen-xia","given":"Liangzhen","family":"Xia","affiliation":"Texas A&M University"}],"abstract":"Bipartite graphs manifest as a stream of edges that represent transactions, e.g., purchases by retail customers. Recommender systems employ neighborhood-based measures of node similarity, such as the pairwise number of common neighbors (CN) and related metrics. While the number of node pairs that share neighbors is potentially enormous, only a relatively small proportion of them have many common neighbors. This motivates finding a weighted sampling approach to preferentially sample these node pairs. This paper presents a new sampling algorithm that provides a fixed size unbiased estimate of the similarity matrix resulting from a bipartite edge stream projection. The algorithm has two components. First, it maintains a reservoir of sampled bipartite edges with sampling weights that favor selection of high similarity nodes. Second, arriving edges generate a stream of similarity updates, based on their adjacency with the current sample. These updates are aggregated in a second reservoir sample-based stream aggregator to yield the final unbiased estimate. Experiments on real world graphs show that a 10% sample at each stage yields estimates of high similarity edges with weighted relative errors of about 1%.","doi":"10.24963/ijcai.2018/456","url":"https://ijcai.org/proceedings/2018/456","pdf":"https://ijcai.org/proceedings/2018/0456.pdf","markdown":"https://ijcai.org/proceedings/2018/456.md","bibtex":"https://ijcai.org/proceedings/2018/bibtex/456","volume":{"slug":"2018","title":"Proceedings of the Twenty-Seventh International Joint Conference on Artificial Intelligence","short_title":"IJCAI 2018","url":"https://ijcai.org/proceedings/2018/","year":2018,"location":"Stockholm","dates":"13-19 July 2018","editors":"Jérôme Lang","isbn":"978-0-9992411-2-7","publisher":"International Joint Conferences on Artificial Intelligence Organization","doi_prefix":"10.24963/ijcai.2018"},"section":"Machine Learning Applications","track":"Main track","number":456,"pages":{"first":3286,"last":3292},"keywords":["Machine Learning: Data Mining","Machine Learning Applications: Networks","Machine Learning: Time-series;Data Streams","Machine Learning: Relational Learning"],"videos":[],"references":[{"position":1,"raw":"[Ahmed et al., 2014a] Nesreen K. Ahmed, Nick Duffield, Jennifer Neville, and Ramana Kompella. Graph sam- ple and hold: A framework for big-graph analytics. In SIGKDD, 2014.","title":"Graph sample and hold: A framework for big-graph analytics","authors":"Ahmed","year":"2014","venue":"SIGKDD","doi":null,"url":null,"internal_url":null},{"position":2,"raw":"[Ahmed et al., 2014b] Nesreen K. Ahmed, Jennifer Neville, and Ramana Kompella. Network sampling: From static to streaming graphs. In TKDD, 8(2):1-56, 2014.","title":"Network sampling: From static to streaming graphs","authors":"Ahmed","year":"2014","venue":"TKDD","doi":null,"url":null,"internal_url":null},{"position":3,"raw":"[Ahmed et al., 2017] Nesreen K. Ahmed, Nick Duffield, Theodore L. Willke, and Ryan A. Rossi. On sampling from massive graph streams. Proc. VLDB, 10(11):1430-1441, August 2017.","title":"On sampling from massive graph streams","authors":"K Nesreen, Nick Ahmed, Theodore L Duffield, Ryan A Willke, Rossi","year":"2017","venue":"Proc. VLDB","doi":null,"url":null,"internal_url":null},{"position":4,"raw":"[Andoni et al., 2011] Alexandr Andoni, Robert Krauthgamer, and Krzysztof Onak. Streaming algo- rithms via precision sampling. In IEEE FOCS, pages 363-372, Oct 2011.","title":"Streaming algorithms via precision sampling","authors":"Alexandr Andoni, Robert Krauthgamer, Krzysztof Onak","year":"2011","venue":"IEEE FOCS","doi":null,"url":null,"internal_url":null},{"position":5,"raw":"[Cohen et al., 2011] Edith Cohen, Nick Duffield, Haim Ka- plan, Carsten Lund, and Mikkel Thorup. Efficient stream sampling for variance-optimal estimation of subset sums. SIAM J. Comput., 40(5):1402-1431, September 2011.","title":"Efficient stream sampling for variance-optimal estimation of subset sums","authors":"Cohen","year":"2011","venue":"SIAM J. Comput","doi":null,"url":null,"internal_url":null},{"position":6,"raw":"[Cormen et al., 2001] Thomas H. Cormen, Clifford Stein, Ronald L. Rivest, and Charles E. Leiserson. Introduction to Algorithms. 2nd edition, 2001.","title":"Introduction to Algorithms","authors":"H Thomas, Clifford Cormen, Ronald L Stein, Charles E Rivest, Leiserson","year":"2001","venue":null,"doi":null,"url":null,"internal_url":null},{"position":7,"raw":"[Duffield et al., 2017] Nick Duffield, Yunhong Xu, Liangzhen Xia, Nesreen K. Ahmed, and Minlan Yu. Stream aggregation through order sampling. In CIKM, 2017.","title":"Stream aggregation through order sampling","authors":"Nick Duffield, Yunhong Xu, Liangzhen Xia, Nesreen K Ahmed, Minlan Yu","year":"2017","venue":"CIKM","doi":null,"url":null,"internal_url":null},{"position":8,"raw":"[Eggert et al., 2012] Sebastian Eggert, Lasse Kliemann, Pe- ter Munstermann, and Anand Srivastav. Bipartite matching in the semi-streaming model. Algorithmica, 63:490-508, 2012.","title":"Bipartite matching in the semi-streaming model","authors":"Sebastian Eggert, Lasse Kliemann, Peter Munstermann, Anand Srivastav","year":"2012","venue":"Algorithmica","doi":null,"url":null,"internal_url":null},{"position":9,"raw":"[Estan and Varghese, 2002] Cristian Estan and George Varghese. New directions in traffic measurement and accounting. In SIGCOMM, 2002.","title":"New directions in traffic measurement and accounting","authors":"Cristian Estan, George Varghese","year":"2002","venue":"SIGCOMM","doi":null,"url":null,"internal_url":null},{"position":10,"raw":"[Fouss et al., 2007] Francois Fouss, Alain Pirotte, Jean- Michel Renders, and Marco Saerens. Random-walk com- putation of similarities between nodes of a graph with ap- plication to collaborative recommendation. IEEE TKDE, 19(3):355-369, 2007.","title":"Random-walk computation of similarities between nodes of a graph with application to collaborative recommendation","authors":"Francois Fouss, Alain Pirotte, Jean-Michel Renders, Marco Saerens","year":"2007","venue":"IEEE TKDE","doi":null,"url":null,"internal_url":null},{"position":11,"raw":"[Goel et al., 2012] Ashish Goel, Michael Kapralov, and San- jeev Khanna. On the communication and streaming com- plexity of maximum bipartite matching. In Proc. SODA '12, pages 468-485, Philadelphia, PA, USA, 2012.","title":"On the communication and streaming complexity of maximum bipartite matching","authors":"Ashish Goel, Michael Kapralov, Sanjeev Khanna","year":"2012","venue":"Proc. SODA '12","doi":null,"url":null,"internal_url":null},{"position":12,"raw":"[Gunawardana and Shani, 2009] Asela Gunawardana and Guy Shani. A survey of accuracy evaluation metrics of recommendation tasks. J. Mach. Learn. Res., 10, 2009.","title":"A survey of accuracy evaluation metrics of recommendation tasks","authors":"Asela Gunawardana, Guy Shani","year":"2009","venue":"J. Mach. Learn. Res","doi":null,"url":null,"internal_url":null},{"position":13,"raw":"[Herlocker et al., 2004] Jonathan L Herlocker, Joseph A Konstan, Loren G Terveen, and John T Riedl. Evaluating collaborative filtering recommender systems. ACM Trans- actions on Information Systems (TOIS), 22(1):5-53, 2004.","title":"Evaluating collaborative filtering recommender systems","authors":"Jonathan L Herlocker, Joseph A Konstan, Loren G Terveen, John T Riedl","year":"2004","venue":"ACM Transactions on Information Systems (TOIS)","doi":null,"url":null,"internal_url":null},{"position":14,"raw":"[Horvitz and Thompson, 1952] Daniel Horvitz and Donovan Thompson. A generalization of sampling without replace- ment from a finite universe. J. of the American Stat. Assoc., 47(260):663-685, 1952.","title":"A generalization of sampling without replacement from a finite universe","authors":"Daniel Horvitz, Donovan Thompson","year":"1952","venue":"J. of the American Stat. Assoc","doi":null,"url":null,"internal_url":null},{"position":15,"raw":"[Jha et al., 2015] Madhav Jha, C. Seshadhri, and Ali Pinar. A space-efficient streaming algorithm for estimating transi- tivity and triangle counts using the birthday paradox. ACM Trans. Knowl. Discov. Data, 9(3):15:1-15:21, 2015.","title":"A space-efficient streaming algorithm for estimating transitivity and triangle counts using the birthday paradox","authors":"C Madhav Jha, Ali Seshadhri, Pinar","year":"2015","venue":"ACM Trans. Knowl. Discov. Data","doi":null,"url":null,"internal_url":null},{"position":16,"raw":"[Kliemann, 2011] Lasse Kliemann. Matching in Bipartite Graph Streams in a Small Number of Passes, pages 254- 266. Springer, Berlin, Heidelberg, 2011.","title":"Matching in Bipartite Graph Streams in a Small Number of Passes","authors":"Lasse Kliemann, Kliemann","year":"2011","venue":null,"doi":null,"url":null,"internal_url":null},{"position":17,"raw":"[Koren, 2008] Yehuda Koren. Factorization meets the neigh- borhood: a multifaceted collaborative filtering model. In SIGKDD, pages 426-434, 2008.","title":"Factorization meets the neighborhood: a multifaceted collaborative filtering model","authors":"Koren ;, Yehuda Koren","year":"2008","venue":"SIGKDD","doi":null,"url":null,"internal_url":null},{"position":18,"raw":"[Liben-Nowell and Kleinberg, 2007] David Liben-Nowell and Jon Kleinberg. The link-prediction problem for social networks. J. Am. Soc. Inf. Sci. Technol., 58(7):1019-1031, 2007.","title":"The link-prediction problem for social networks","authors":"Liben-Nowell, Kleinberg, David Liben-Nowell, Jon Kleinberg","year":"2007","venue":"J. Am. Soc. Inf. Sci. Technol","doi":null,"url":null,"internal_url":null},{"position":19,"raw":"[Monemizadeh and Woodruff, 2010] Morteza Monem- izadeh and David Woodruff. 1-pass relative-error l p -sampling with applications. In SODA, 2010.","title":"1-pass relative-error l p -sampling with applications","authors":"Morteza Monemizadeh, David Woodruff","year":"2010","venue":"SODA","doi":null,"url":null,"internal_url":null},{"position":20,"raw":"[Muthukrishnan, 2005] S. Muthukrishnan. Data streams: Algorithms and applications. Now Publishers Inc, 2005.","title":"Data streams: Algorithms and applications","authors":"S Muthukrishnan","year":"2005","venue":null,"doi":null,"url":null,"internal_url":null},{"position":21,"raw":"[Ning et al., 2015] Xia Ning, Christian Desrosiers, and George Karypis. A Comprehensive Survey of Neighborhood-Based Recommendation Methods, pages 37-76. Springer US, Boston, MA, 2015.","title":"A Comprehensive Survey of Neighborhood-Based Recommendation Methods","authors":"Xia Ning, Christian Desrosiers, George Karypis","year":"2015","venue":null,"doi":null,"url":null,"internal_url":null},{"position":22,"raw":"[Pan and Zhu, 2012] Shirui Pan and Xingquan Zhu. Contin- uous top-k query for graph streams. In Proc. CIKM '12, pages 2659-2662, New York, NY, USA, 2012.","title":"Continuous top-k query for graph streams","authors":"Zhu Pan, Shirui Pan, Xingquan Zhu","year":"2012","venue":"Proc. CIKM '12","doi":null,"url":null,"internal_url":null},{"position":23,"raw":"[Rossi and Ahmed, 2015] Ryan A. Rossi and Nesreen K. Ahmed. The network data repository with interactive graph analytics and visualization. In AAAI, 2015. http: //networkrepository.com.","title":"The network data repository with interactive graph analytics and visualization","authors":"Ryan A Rossi, Nesreen K Ahmed","year":"2015","venue":"AAAI","doi":null,"url":"http://networkrepository.com","internal_url":null},{"position":24,"raw":"[Salton et al., 1993] Gerard Salton, James Allan, and Chris Buckley. Approaches to passage retrieval in full text infor- mation systems. In ACM SIGIR, pages 49-58, 1993.","title":"Approaches to passage retrieval in full text information systems","authors":"Gerard Salton, James Allan, Chris Buckley","year":"1993","venue":"ACM SIGIR","doi":null,"url":null,"internal_url":null},{"position":25,"raw":"[Stefani et al., 2017] Lorenzo De Stefani, Alessandro Epasto, Matteo Riondato, and Eli Upfal. Tri Èst: Counting local and global triangles in fully dynamic streams with fixed memory size. ACM TKDD, 11(4):43:1-43:50, 2017.","title":"Tri Èst: Counting local and global triangles in fully dynamic streams with fixed memory size","authors":"Lorenzo De, Stefani, Alessandro Epasto, Matteo Riondato, Eli Upfal","year":"2017","venue":"ACM TKDD","doi":null,"url":null,"internal_url":null},{"position":26,"raw":"[Tillé, 2006] Yyes Tillé. Sampling Algorithms. Springer- Verlag, 2006.","title":"Yyes Tillé. Sampling Algorithms","authors":"Tillé","year":"2006","venue":null,"doi":null,"url":null,"internal_url":null},{"position":27,"raw":"[Zakrzewska and Bader, 2017] Anita Zakrzewska and David A Bader. Streaming graph sampling with size restrictions. In IEEE/ACM ASONAM, 2017.","title":"Streaming graph sampling with size restrictions","authors":"Anita Zakrzewska, David A Bader","year":"2017","venue":"IEEE/ACM ASONAM","doi":null,"url":null,"internal_url":null},{"position":28,"raw":"[Zhao et al., 2016] Peixiang Zhao, Charu Aggarwal, and Gewen He. Link prediction in graph streams. In ICDE, pages 553-564, 2016.","title":"Link prediction in graph streams","authors":"Zhao","year":"2016","venue":"ICDE","doi":null,"url":null,"internal_url":null},{"position":29,"raw":"[Zhou et al., 2007] Tao Zhou, Jie Ren, Matúš Medo, and Yi- Cheng Zhang. Bipartite network projection and personal recommendation. Physical Review E, 76(4):046115, 2007.","title":"Bipartite network projection and personal recommendation","authors":"Tao Zhou, Jie Ren, Matúš Medo, Yi-Cheng Zhang","year":"2007","venue":"Physical Review E","doi":null,"url":null,"internal_url":null}],"license_note":"Copyright International Joint Conferences on Artificial Intelligence."}