Non-negative residual matrix factorization: Problem definition, fast solutions, and applications

Statistical Analysis and Data Mining

Volumn 5, Issue 1, 2012, Pages 3-15

  Tong, Hanghang ^a   Lin, Ching Yung ^a  

^a IBM T J WATSON RESEARCH CENTER   (United States)

Author keywords

Graph mining; Matrix factorization; Non negativity; Scalability

Indexed keywords

MATRIX ALGEBRA; NON-NEGATIVE MATRIX FACTORIZATION;

ENCODINGS; FAST SOLUTIONS; GRAPH MINING; GRAPH PATTERNS; MATRIX FACTORIZATIONS; NON NEGATIVES; NON-NEGATIVITY; PROBLEM DEFINITION; RECENT TRENDS; RESIDUAL MATRIX;

EFFICIENCY;

EID: 84863154938     PISSN: 19321872     EISSN: 19321864     Source Type: Journal    
DOI: 10.1002/sam.10148     Document Type: Article

References (43)

1. D. D. Lee and H. S. Seung, Algorithms for non-negative matrix factorization, In NIPS, 2000, 556-562.
2. P. Drineas, R. Kannan, and M. W. Mahoney, Fast Monte Carlo algorithms for matrices iii: computing a compressed approximate matrix decomposition, SIAM J Comput 36 (2005), 184-206.
3. J. Sun, Y. Xie, H. Zhang, and C. Faloutsos, Less is more: compact matrix decomposition for large sparse graphs, In SDM, 2007.
4. L. Akoglu, M. McGlohon, and C. Faloutsos, Oddball: spotting anomalies in weighted graphs, In PAKDD (2), 2010, 410-421.
5. D. H. Chau, S. Pandit, and C. Faloutsos, Detecting fraudulent personalities in networks of online auctioneers, In PKDD, 2006, 103-114.
6. R. M. Bell, Y. Koren, and C. Volinsky, Modeling relationships at multiple scales to improve accuracy of large recommender systems, In KDD, 2007, 95-104.
7. A. P. Singh and G. J. Gordon, Relational learning via collective matrix factorization, In KDD, 2008, 650-658.
8. P. Tseng, Simple polynomial-time algorithm for convex quadratic programming, In Laboratory for Information and Decision Systems, Massachusetts Institute of Technology, 1988.
9. S.-P. Hong and S. Verma, A note on the strong polynomiality of convex quadratic programming, Math Program 68 (1995), 131-139.
10. J. Sun, H. Qu, D. Chakrabarti, and C. Faloutsos, Neighborhood formation and anomaly detection in bipartite graphs, In ICDM, 2005, 418-425.
11. G. H. Golub and C. F. Van-Loan, Matrix Computations, (2nd ed.), Baltimore, The Johns Hopkins University Press, 1989.
12. D. Achlioptas and F. McSherry, Fast computation of low-rank matrix approximations, J ACM 54(2) (2007), 1-19.
13. K. V. R. Kanth, D. Agrawal, and A. K. Singh, Dimensionality reduction for similarity searching in dynamic databases, In SIGMOD Conference, 1998, 166-176.
14. P. Indyk, Stable distributions, pseudorandom generators, embeddings and data stream computation, In FOCS, 2000, 189-197.
15. H. Tong, S. Papadimitriou, J. Sun, P. S. Yu, and C. Faloutsos, Colibri: fast mining of large static and dynamic graphs, In KDD, 2008, 686-694.
16. D. L. Donoho and V. Stodden, When does non-negative matrix factorization give a correct decomposition into parts? In NIPS, 2003.
17. R. Kompass, A generalized divergence measure for nonnegative matrix factorization, Neural Comput 19(3) (2007), 780-791.
18. J. Kim and H. Park, Toward faster nonnegative matrix factorization: A new algorithm and comparisons, In ICDM, 2008, 353-362.
19. C. H. Q. Ding, T. Li, and M. I. Jordan, Convex and semi-nonnegative matrix factorizations, IEEE Trans Pattern Anal Mach Intell 32(1) (2010), 45-55.
20. P. O. Hoyer, Non-negative matrix factorization with sparseness constraints, J Mach Learning Res 5 (2004), 1457-1469.
21. S. Hyvönen, P. Miettinen, and E. Terzi, Interpretable nonnegative matrix decompositions, In KDD, 2008, 345-353.
22. F. Wang and P. Li, Efficient nonnegative matrix factorization with random projections, In SDM, 2010, 281-292.
23. F. Wang, P. Li, and A. C. König, Efficient document clustering via online nonnegative matrix factorizations, In SDM, 2011, 908-919.
24. C. C. Noble and D. J. Cook, Graph-based anomaly detection, In KDD, 2003, 631-636.
25. D. Chakrabarti, Autopart: Parameter-free graph partitioning and outlier detection, In PKDD, 2004, 112-124.
26. W. Eberle and L. B. Holder, Mining for structural anomalies in graph-based data, In DMIN, 2007, 376-389.
27. V. Chandola, A. Banerjee, and V. Kumar, Anomaly detec- tion: A survey, ACM Comput Surv 41(3) (2009), 15-58.
28. R. Albert, H. Jeong, and A.-L. Barabasi, Diameter of the world wide web, Nature 401 (1999), 130-131.
29. S. Dorogovtsev and J. Mendes Evolution of networks, Adv Phys 51 (2002), 1079-1187.
30. M. Faloutsos, P. Faloutsos, and C. Faloutsos, On power-law relationships of the Internet topology, In SIGCOMM, August-September 1999, 251-262.
31. A. Broder, R. Kumar, F. Maghoul1, P. Raghavan, S. Rajagopalan, R. Stata, A. Tomkins, and J. Wiener, Graph structure in the web: Experiments and models, In WWW Conference, 2000.
32. M. E. J. Newman, The structure and function of complex networks, SIAM Rev 45 (2003), 167-256.
33. D. Xin, J. Han, X. Yan, and H. Cheng, Mining compressed frequent-pattern sets, In VLDB, 2005, 709-720.
34. D. Kempe, J. Kleinberg, and E. Tardos, Maximizing the spread of influence through a social network, In KDD, 2003.
35. F. Chierichetti, R. Kumar, S. Lattanzi, M. Mitzenmacher, A. Panconesi, and P. Raghavan, On compressing social networks, In KDD, 2009, 219-228.
36. G. Flake, S. Lawrence, C. L. Giles, and F. Coetzee, Self-organization and identification of web communities, IEEE Computer 35(3) (2002), 66-71.
37. D. Gibson, J. Kleinberg, and P. Raghavan, Inferring web communities from link topology. In 9th ACM Conference on Hypertext and Hypermedia, New York, 1998, 225-234.
38. M. Girvan and M. E. J. Newman, Community structure is social and biological networks.
39. J. Leskovec, J. M. Kleinberg, and C. Faloutsos, Graphs over time: densification laws, shrinking diameters and possible explanations, In KDD, 2005, 177-187.
40. L. Backstrom, D. P. Huttenlocher, J. M. Kleinberg, and X. Lan, Group formation in large social networks: Membership, growth, and evolution, In KDD, 2006, 44-54.
41. H. Tong, S. Papadimitriou, P. S. Yu, and C. Faloutsos, Proximity tracking on time-evolving bipartite graphs, In SDM, 2008, 704-715.
42. R. Kumar, M. Mahdian, and M. McGlohon, Dynamics of conversations, In KDD, 2010, 553-562.
43. Y. Chi, X. Song, D. Zhou, K. Hino, and B. L. Tseng, Evolutionary spectral clustering by incorporating temporal smoothness, In KDD, 2007, 153-162.