Random-walk computation of similarities between nodes of a graph with application to collaborative recommendation

IEEE Transactions on Knowledge and Data Engineering

Volumn 19, Issue 3, 2007, Pages 355-369

  Fouss, François ^b   Pirotte, Alain ^a,b   Renders, Jean Michel ^c   Saerens, Marco ^a,b  

^a IEEE   (Belgium)

^b UNIVERSITÉ CATHOLIQUE DE LOUVAIN   (Belgium)

^c XEROX RESEARCH CENTRE EUROPE   (France)

Author keywords

Collaborative recommendation; Fiedler vector; Graph analysis; Graph and database mining; Graph kernels; Proximity measures; Spectral clustering; Statistical relational learning

Indexed keywords

COLLABORATIVE RECOMMENDATION; FIEDLER VECTORS; GRAPH ANALYSIS; GRAPH AND DATABASE MINING; GRAPH KERNELS; PROXIMITY MEASURES; RANDOM-WALK COMPUTATION; SPECTRAL CLUSTERING; STATISTICAL RELATIONAL LEARNING;

COMPUTER SUPPORTED COOPERATIVE WORK; DATA MINING; LAPLACE TRANSFORMS; MARKOV PROCESSES; MATHEMATICAL MODELS; MATRIX ALGEBRA;

GRAPH THEORY;

EID: 33847766633     PISSN: 10414347     EISSN: None     Source Type: Journal    
DOI: 10.1109/TKDE.2007.46     Document Type: Article

References (67)

1. R. Agaev and P. Chebotarev, "The Matrix of Maximum Out Forests of a Digraph and Its Applications," Automation and Remote Control, vol. 61, no. 9, pp. 1424-1450, 2000.
2. R. Agaev and P. Chebotarev, "Spanning Forests of a Digraph and Their Applications," Automation and Remote Control, vol. 62, no. 3, pp. 443-466, 2001.
3. R. Baeza-Yates and B. Ribeiro-Neto, Modern Information Retrieval. Addison-Wesley, 1999.
4. P. Baldi, P. Frasconi, and P. Smyth, Modeling the Internet and the Web: Probabilistic Methods and Algorithms. John Wiley and Sons, 2003.
5. S. Barnett, Matrices: Methods and Applications. Oxford Univ. Press, 1992.
6. M. Belkin and P. Niyogi, "Laplacian Eigenmaps and Spectral Techniques for Embedding and Clustering," Advances in Neural Information Processing Systems, T.G. Dietterich, S. Becker, and Z. Ghahramani, eds., vol. 14, pp. 585-591, MIT Press, 2001.
7. M. Belkin and P. Niyogi, "Laplacian Eigenmaps for Dimensionality Reduction and Data Representation," Neural Computation, vol. 15, pp. 1373-1396, 2003.
8. A. Ben-Israel and T. Greville, Generalized Inverses: Theory and Applications, second ed. Springer-Verlag, 2003.
9. I. Borg and P. Groenen, Modern Multidimensional Scaling: Theory and Applications. Springer, 1997.
10. M. Brand, "A Random Walks Perspective on Maximizing Satisfaction and Profit," Proc. 2005 SIAM Int'l Conf. Data Mining, 2005.
11. F. Buckley and F. Harary, Distance in Graphs. Addison-Wesley Publishing Company, 1990.
12. S. Campbell and C. Meyer, Generalized Inverses of Linear Transformations. Pitman Publishing Company, 1979.
13. T. Chan, P. Ciarlet, and W. Szeto, "On the Optimality of the Median Cut Spectral Bisection Graph Partitioning Method," SIAM J. Scientific Computing, vol. 18, no. 3, pp. 943-948, 1997.
14. A.K. Chandra, P. Raghavan, W.L. Ruzzo, R. Smolensky, and P. Tiwari, "The Electrical Resistance of a Graph Captures Its Commute and Cover Times," Proc. Ann. ACM Symp. Theory of Computing, pp. 574-586, 1989.
15. P. Chebotarev and E. Shamis, "The Matrix-Forest Theorem and Measuring Relations in Small Social Groups," Automation and Remote Control, vol. 58, no. 9, pp. 1505-1514, 1997.
16. P. Chebotarev and E. Shamis, "On a Duality between Metrics and S-Proximities," Automation and Remote Control, vol. 59, no. 4, pp. 608-612, 1998.
17. P. Chebotarev and E. Shamis, "On Proximity Measures for Graph Vertices," Automation and Remote Control, vol. 59, no. 10, pp. 1443-1459, 1998.
18. K. Cheung, K. Tsui, and J. Liu, "Extended Latent Class Models for Collaborative Recommendation," IEEE Trans. Systems, Man, and Cybernatics. Part A: Systems and Humans, vol. 34, pp. 143-148, 2004.
19. F.R. Chung, Spectral Graph Theory, Am. Math. Soc., 1997.
20. C. Ding, "Spectral Clustering," Tutorial presented at the 16th European Conf. Machine Learning (ECML '05), 2005.
21. P.G. Doyle and J.L. Snell, Random Walks and Electric Networks. The Math. Assoc. of Am., 1984.
22. S. Dzeroski, "Multi-Relational Data Mining: An Introduction," ACM SIGKDD Explorations Newsletter, vol. 5, no. 1, pp. 1-16, 2003.
23. C. Faloutsos, K. McCurley, and A. Tomkins, "Fast Discovery of Connection Subgraphs," Proc. 10th ACM SIGKDD Int'l Conf. Knowledge Discovery and Data Mining, pp. 118-127, 2004.
24. M. Fiedler, "A Property of Eigenvectors of Nonnegative Symmetric Matrices and its Applications to Graph Theory," Czechoslovak Math. J., vol. 25, no. 100, pp. 619-633, 1975.
25. F. Fouss, A. Pirotte, J.-M. Renders, and M. Saerens, "A Novel Way of Computing Similarities between Nodes of a Graph, with Application to Collaborative Recommendation," Proc. 2005 IEEE/WIC/ACM Int'l Joint Conf. Web Intelligence, pp. 550-556, 2005.
26. F. Fouss, L. Yen, A. Pirotte, and M. Saerens, "An Experimental Investigation of Graph Kernels on Two Collaborative Recommendation Tasks," submitted for publication.
27. F. Gobel and A. Jagers, "Random Walks on Graphs," Stochastic Processes and Their Applications, vol. 2, pp. 311-336, 1974.
28. J. Gower and P. Legendre, "Metric and Euclidean Properties of Dissimilarities Coefficients," J. Classification, vol. 3, pp. 5-48, 1986.
29. F.A. Graybill, Matrices with Applications in Statistics. Wadsworth Int'l Group, 1983.
30. A. Greenbaum, Iterative Methods for Solving Linear Systems. Soc. for Industrial and Applied Math., 1997.
31. D. Harel and Y. Koren, "On Clustering Using Random Walks," Proc. Conf. Foundations of Software Technology and Theoretical Computer Science, pp. 18-41, 2001.
32. J. Herlocker, J. Konstan, L. Terveen, and J. Riedl, "Evaluating Collaborative Filtering Recommender Systems," ACM Trans. Information Systems, vol. 22, no. 1, pp. 5-53, 2004.
33. I. Herstein and D. Winter, Matrix Theory and Linear Algebra. Maxwell Macmillan International Editions, 1988.
34. N.-D. Ho and P.V. Dooren, "On the Pseudo-Inverse of the Laplacian of a Bipartite Graph," Applied Math. Letters, vol. 18, no. 8, pp. 917-922, 2005.
35. Z. Huang, H. Chen, and D. Zeng, "Applying Associative Retrieval Techniques to Alleviate the Sparsity Problem in Collaborative Filtering," ACM Trans. Information Systems, vol. 22, no. 1, pp. 116-142, 2004.
36. D. Isaacson and R. Madsen, Markov Chains Theory and Applications. John Wiley and Sons, 1976.
37. T. Ito, M. Shimbo, T. Kudo, and Y. Matsumoto, "Application of Kernels to Link Analysis: First Results," Proc. Second Workshop Mining Graphs, Trees, and Sequences, ECML/PKDD, pp. 13-24, 2004.
38. R. Johnson and D. Wichern, Applied Multivariate Statistical Analysis, fifth ed. Prentice Hall, 2002.
39. G. Karypis, "Evaluation of Item-Based Top-N Recommendation Algorithms," Proc. 10th Int'l Conf. Information and Knowledge Management, pp. 247-254, 2001.
40. L. Katz, "A New Status Index Derived from Sociometric Analysis," Psychmetrika, vol. 18, no. 1, pp. 39-43, 1953.
41. J.G. Kemeny and J.L. Snell, Finite Markov Chains. Springer-Verlag, 1976.
42. D.J. Klein and M. Randic, "Resistance Distance," J. Math. Chemistry, vol. 12, pp. 81-95, 1993.
43. J.M. Kleinberg, "Authoritative Sources in a Hyperlinked Environment," J. ACM, vol. 46, no. 5, pp. 604-632, 1999.
44. R.I. Kondor and J. Lafferty, "Diffusion Kernels on Graphs and Other Discrete Structures," Proc. 19th Int'l Conf. Machine Learning, pp. 315-322, 2002.
45. C.D. Meyer, "The Role of the Group Generalized Inverse in the Theory of Finite Markov Chains," SIAM Rev., vol. 17, pp. 443-464, 1975.
46. B. Mohar, "Laplace Eigenvalues of Graphs - A Survey," Discrete Math., vol. 109, pp. 171-183, 1992.
47. B. Nadler, S. Lafon, R. Coifman, and I. Kevrekidis, "Diffusion Maps, Spectral Clustering and Eigenfunctions of Fokker-Planck Operators," Advances in Neural Information Processing Systems 18, pp. 955-962, 2006.
48. M. Newman, "A Measure of Betweenness Centrality Based on Random Walks," Social Networks, vol. 27, no. 1, pp. 39-54, 2005.
49. B. Noble and J. Daniels, Applied Linear Algebra, third ed. Prentice-Hall, 1988.
50. J. Norris, Markov Chains. Cambridge Univ. Press, 1997.
51. L. Page, S. Brin, R. Motwani, and T. Winograd, "The Pagerank Citation Ranking: Bringing Order to the Web," technical report, Computer System Laboratory, Stanford Univ., 1998.
52. C. Palmer and C. Faloutsos, "Electricity Based External Similarity of Categorical Attributes," Proc. Seventh Pacific-Asia Conf. Knowledge Discovery and Data Mining (PAKDD '03), pp. 486-500, 2003.
53. E. Parzen, Stochastic Processes. Holden-Day, 1962.
54. A. Pothen, H. Simon, and K.-P. Liou, "Partitioning Sparse Matrices with Eigenvectors of Graphs," SIAM J. Matrix Analysis and Applications, vol. 11, no. 3, pp. 430-452, 1990.
55. C. Rao and S. Mitra, Generalized Inverse of Matrices and Its Applications. John Wiley and Sons, 1971.
56. Y. Saad, Iterative Methods for Sparse Linear Systems. Soc. for Industrial and Applied Math., 2000.
57. M. Saerens and F. Fouss, A Novel Way of Computing Similarities between Nodes of a Graph, with Application to Collaborative Filtering and Subspace Projection of the Graph Nodes, working paper, IAG, Université catholique de Louvain, 2006.
58. M. Saerens, F. Fouss, L. Yen, and P. Dupont, "The Principal Components Analysis of a Graph, and Its Relationships to Spectral Clustering," Proc. 15th European Conf. Machine Learning (ECML '04), pp. 371-383, 2004.
59. B. Sarwar, G. Karypis, J. Konstan, and J. Riedl, "Recommender Systems for Large-Scale E-Commerce: Scalable Neighborhood Formation Using Clustering," Proc. Fifth Int'l Conf. Computer and Information Technology, 2002.
60. B. Scholkopf and A. Smola, Learning with Kernels. The MIT Press, 2002.
61. J. Shawe-Taylor and N. Cristianini, Kernel Methods for Pattern Analysis. Cambridge Univ. Press, 2004.
62. J. Shi and J. Malik, "Normalised Cuts and Image Segmentation," IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 22, no. 8, pp. 888-905, Aug. 2000.
63. S. Siegel and J. Castellan, Nonparametric Statistics for the Behavioral Sciences, second ed. McGraw-Hill, 1988.
64. A.J. Smola and R. Kondor, "Kernels and Regularization on Graphs," Proc. Conf. Learning Theory (COLT) and Kernels Workshop, M. Warmuth and B. Schölkopf, eds., 2003.
65. S. Wasserman and K. Faust, Social Network Analysis: Methods and Applications. Cambridge Univ. Press, 1994.
66. S. White and P. Smyth, "Algorithms for Estimating Relative Importance in Networks," Proc. Ninth ACM SIGKDD Int'l Conf. Knowledge Discovery and Data Mining, pp. 266-275, 2003.
67. D. Zhou, J. Huang, and B. Scholkopf, "Learning from Labeled and Unlabeled Data on a Directed Graph," Proc. 22nd Int'l Conf. Machine Learning, pp. 1041-1048, 2005.