A unifying framework of rating users and data items in peer-to-peer and social networks Article First Online: 05 June 2008 Received: 21 October 2007 Accepted: 11 April 2008 DOI:
10.1007/s12083-008-0008-4 Cite this article as: Bickson, D. & Malkhi, D. Peer-to-Peer Netw. Appl. (2008) 1: 93. doi:10.1007/s12083-008-0008-4 Abstract
We propose a unifying family of quadratic cost functions to be used in Peer-to-Peer ratings. We show that our approach is general since it captures many of the existing algorithms in the fields of visual layout, collaborative filtering and Peer-to-Peer rating, among them Koren spectral layout algorithm, Katz method, Spatial ranking, Personalized PageRank and Information Centrality. Besides of the theoretical interest in finding common basis of algorithms that where not linked before, we allow a single efficient implementation for computing those various rating methods. We introduce a distributed solver based on the Gaussian Belief Propagation algorithm which is able to efficiently and distributively compute a solution to any single cost function drawn from our family of quadratic cost functions. By implementing our algorithm once, and choosing the computed cost function dynamically on the run we allow a high flexibility in the selection of the rating method deployed in the Peer-to-Peer network. Using simulations over real social network topologies obtained from various sources, including the MSN Messenger social network, we demonstrate the applicability of our approach. We report simulation results using networks of millions of nodes.
Keywords Peer-to-peer Social networks Collaborative filtering Gaussian belief propagation Katz method Spatial ranking
Danny Bickson was partially supported by Microsoft Research Internship and by EVERGROW IP 1935 of the EU Sixth Framework.
Moallemi CC, Van Roy B (2006) Consensus propagation. IEEE Trans Inf Theory 52(11):4753–4766
CrossRef Google Scholar
Johnson J, Malioutov D, Willsky A (2005) Walk-sum interpretation and analysis of Gaussian Belief Propagation. In: NIPS 05’, Vancouver, 5–10 December 2005
Grinstead CM, Laurie Snell J (1997) Introduction to probability. The CHANCE Project. Chapter 11 - Markov chains.
Brin S, Page L (1998) The anatomy of a large-scale hypertextual Web search engine. In: Proceedings of the seventh international conference on World Wide Web, vol 7. Elsevier, Amsterdam, pp 107–117
Weiss Y, Freeman WT (1999) Correctness of belief propagation in Gaussian graphical models of arbitrary topology. In: NIPS-12, Denver, 30 November–2 December 1999
Malioutov DM, Johnson JK, Willsky AS (2006) Walk-sums and belief propagation in Gaussian graphical models. J Mach Learn Res 7:2031–2064 (October)
MathSciNet Google Scholar
Crammer K, Singer Y (2001) Pranking with ranking. In: Proceedings of the conference on neural information processing systems (NIPS)
Doyle PG, Snell JL (1984) Random walks and electrical networks. The mathematical association of America.
Brandes U, Fleisch D (2005) Centrality measures based on current flow. In: STACS 2005, LNCS 3404, Stuttgart, 24–26 February 2005, pp 533–544
Benczur A, Csalogany K, Sarlos T (2005) On the feasibility of low-rank approximation for personalized PageRank. In: Poster proceedings of the 14th international World Wide Web conference (WWW), Chiba, 10–14 May 2005, pp 972–973
Bickson D, Dolev D, Shental O, Siegel PH, Wolf JK (2007) Linear detection via belief propagation. In: The 45th annual allerton conference on communication, control, and computing, Allerton House, Illinois, September 2007
Koren Y (2003) On spectral graph drawing. In: Proceedings of the 9th international computing and combinatorics conference (COCOON’03). Lecture notes in computer science, vol 2697. Springer, Berlin Heidelberg New York, pp 496–508
Bickson D, Malkhi D, Zhou L (2007) Peer to peer rating. In: The 7th IEEE Peer-to-Peer Computing, Galway, Ireland, September 2007
Katz L (1953) A new status index derived from sociometric analysis. Psychometrika 18:39–43
MATH CrossRef Google Scholar
Hall KM (1970) An r-dimensional quadratic placement algorithm. Manage Sci 17:219–229
MATH CrossRef Google Scholar
DellAmico M (2007) Mapping small worlds. In: The 7th IEEE Peer-to-Peer computing, Galway, Ireland, September 2007
Johnson JK, Malioutov D, Willsky AS (2007) Lagrangian relaxation for MAP estimation in graphical models. In: The 45th annual Allerton conference on communication, control and computing, Monticello, September 2007.
Bell R, Koren Y (2007) Scalable collaborative filtering with jointly derived neighborhood interpolation weights. In: IEEE international conference on data mining (ICDM’07). IEEE, Piscataway
Elidan G, McGraw I, Koller D (2006) Residual belief propagation: informed scheduling for asynchronous message passing. In: Proceedings of the twenty-second conference on uncertainty in AI (UAI), Cambridge, 13 July 2006
DIMES (2006) The DIMES project.
Pajek - A program for large network analysis.
Bickson D, Shental O, Dolev D, Siegel PH, Wolf JK (2008) Gaussian belief propagation based multiuser detection. In: IEEE Int. Symp. Inform. Theory (ISIT), July 2008, Toronto, Canada (to appear)
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