Random Walks in Hypergraph

Random walks on graphs have been extensively used for a variety of graph-based problems such as ranking vertices, predicting links, recommendations, and clustering. However, many complex problems mandate a high-order graph representation to accurately capture the relationship structure inherent in them. Hypergraphs are particularly useful for such models due to the density of information stored in their structure. In this paper, we propose a novel extension to defining random walks on hypergraphs. Our proposed approach combines the weights of destination vertices and hyperedges in a probabilistic manner to accurately capture transition probabilities. We study and analyze our generalized form of random walks suitable for the structure of hypergraphs. We show the effectiveness of our model by conducting a text ranking experiment on a real world data set with a 9% to 33% improvement in precision and a range of 7% to 50% improvement in Bpref over other random walk approaches.

[1]  Gerard Salton,et al.  Research and Development in Information Retrieval , 1982, Lecture Notes in Computer Science.

[2]  Claude Berge,et al.  Hypergraphs - combinatorics of finite sets , 1989, North-Holland mathematical library.

[3]  David J. Aldous,et al.  Lower bounds for covering times for reversible Markov chains and random walks on graphs , 1989 .

[4]  Sergey Brin,et al.  The Anatomy of a Large-Scale Hypertextual Web Search Engine , 1998, Comput. Networks.

[5]  Douglas R. Shier,et al.  Applied Mathematical Modeling : A Multidisciplinary Approach , 1999 .

[6]  László Lovász,et al.  Random Walks on Graphs: A Survey , 1993 .

[7]  D. R. Shier,et al.  Graph-Theoretic Analysis of Finite Markov Chains , 2003 .

[8]  Ellen M. Voorhees,et al.  Retrieval evaluation with incomplete information , 2004, SIGIR '04.

[9]  Marco Gori,et al.  Learning Web Page Scores by Error Back-Propagation , 2005, IJCAI.

[10]  Bernhard Schölkopf,et al.  Beyond pairwise classification and clustering using hypergraphs , 2005, NIPS 2005.

[11]  Soumen Chakrabarti,et al.  Learning to rank networked entities , 2006, KDD '06.

[12]  Christos Faloutsos,et al.  Fast Random Walk with Restart and Its Applications , 2006, Sixth International Conference on Data Mining (ICDM'06).

[13]  Serge J. Belongie,et al.  Higher order learning with graphs , 2006, ICML.

[14]  Bernhard Schölkopf,et al.  Learning with Hypergraphs: Clustering, Classification, and Embedding , 2006, NIPS.

[15]  Hongyuan Zha,et al.  Co-ranking Authors and Documents in a Heterogeneous Network , 2007, Seventh IEEE International Conference on Data Mining (ICDM 2007).

[16]  William W. Cohen,et al.  Learning to rank typed graph walks: local and global approaches , 2007, WebKDD/SNA-KDD '07.

[17]  Soumen Chakrabarti,et al.  Learning random walks to rank nodes in graphs , 2007, ICML '07.

[18]  S. Vempala.  Geometric Random Walks: a Survey , 2007 .

[19]  Hung-Khoon Tan,et al.  Modeling video hyperlinks with hypergraph for web video reranking , 2008, ACM Multimedia.

[20]  Martin Ester,et al.  TrustWalker: a random walk model for combining trust-based and item-based recommendation , 2009, KDD.

[21]  Furu Wei,et al.  HyperSum: hypergraph based semi-supervised sentence ranking for query-oriented summarization , 2009, CIKM.

[22]  Yizhou Sun,et al.  Ranking-based clustering of heterogeneous information networks with star network schema , 2009, KDD.

[23]  Chun Chen,et al.  Music recommendation by unified hypergraph: combining social media information and music content , 2010, ACM Multimedia.

[24]  Chen Avin,et al.  Radio cover time in hyper-graphs , 2010, DIALM-POMC '10.

[25]  Minsu Cho,et al.  Hyper-graph matching via reweighted random walks , 2011, CVPR 2011.

[26]  Jure Leskovec,et al.  Supervised random walks: predicting and recommending links in social networks , 2010, WSDM '11.

[27]  Linyuan Lu,et al.  High-Ordered Random Walks and Generalized Laplacians on Hypergraphs , 2011, WAW.

[28]  Bo Zhao,et al.  Probabilistic topic models with biased propagation on heterogeneous information networks , 2011, KDD.

[29]  Ruoming Jin,et al.  A Hypergraph-based Method for Discovering Semantically Associated Itemsets , 2011, 2011 IEEE 11th International Conference on Data Mining.

[30]  Martin Ester,et al.  CrimeWalker: a recommendation model for suspect investigation , 2011, RecSys '11.

[31]  Xin Su,et al.  Social network-based recommendation: a graph random walk kernel approach , 2012, JCDL '12.

[32]  Abdelghani Bellaachia,et al.  NE-Rank: A Novel Graph-Based Keyphrase Extraction in Twitter , 2012, 2012 IEEE/WIC/ACM International Conferences on Web Intelligence and Intelligent Agent Technology.

[33]  Abdelghani Bellaachia,et al.  Learning from Twitter Hashtags: Leveraging Proximate Tags to Enhance Graph-Based Keyphrase Extraction , 2012, 2012 IEEE International Conference on Green Computing and Communications.

[34]  Alan M. Frieze,et al.  The cover times of random walks on random uniform hypergraphs , 2013, Theor. Comput. Sci..

[35]  Tao Li,et al.  News recommendation via hypergraph learning: encapsulation of user behavior and news content , 2013, WSDM.

[36]  Wahiba Bahsoun,et al.  On ranking relevant entities in heterogeneous networks using a language-based model , 2013, J. Assoc. Inf. Sci. Technol..

[37]  L. Asz.  Random Walks on Graphs: a Survey , 2022 .