Improving clustering by learning a bi-stochastic data similarity matrix

Knowledge and Information Systems

Volumn 32, Issue 2, 2012, Pages 351-382

  Wang, Fei ^a   Li, Ping ^a   König, Arnd Christian ^b   Wan, Muting ^a  

^a Cornell University ^*  (United States)

^b MICROSOFT RESEARCH   (United States)

Author keywords

Bi stochastic matrix; Bregman divergence; Clustering

Indexed keywords

BISMUTH COMPOUNDS; GRAPH STRUCTURES; MATRIX ALGEBRA; STOCHASTIC SYSTEMS;

ADJACENCY MATRICES; BI-STOCHASTIC MATRICES; BREGMAN DIVERGENCES; BREGMANIAN BI-STOCHASTICATION; CLUSTERING; CLUSTERING RESULTS; EUCLIDEAN DISTANCE; KULLBACK-LEIBLER DIVERGENCE;

K-MEANS CLUSTERING;

EID: 84864322831     PISSN: 02191377     EISSN: 02193116     Source Type: Journal    
DOI: 10.1007/s10115-011-0433-1     Document Type: Article

References (36)

1. Banerjee A, Dhillon I, Ghosh J, Merugu S (2004) A generalized maximum entropy approach to bregman co-clustering and matrix approximation. In: ACM SIGKDD conference on knowledge discovery and data mining. pp 509-514.
2. Banerjee A, Merugu S, Dhillon IS, Ghosh J (2005) Clustering with bregman divergences. J Mach Learn Res 6: 1705-1749.
3. Bertsekas DP (1999) Nonlinear programming, 2nd edn. Athena Scientific, Belmont.
4. Boyd S, Vandenberghe L (2004) Convex optimization. Cambridge University Press, Cambridge.
5. Chan PK, Schlag DF, Zien JY (1994) Spectral k-way ratio-cut partitioning and clustering. IEEE Trans Comput Aided Des 13: 1088-1096.
6. Cui J, Liu H, He J, Li P, Du X, Wang P (2011) Tagclus: a random walk-based method for tag clustering. Knowl Inf Sys 27(2): 193-225.
7. Darroch JN, Ratcliff D (1972) Generalized iterative scaling for log-linear models. Ann Math Stat 43(5): 1470-1480.
8. Deming WE, Stephan FF (1940) On a least squares adjustment of a sampled frequency table when the expected marginal totals are known. Ann Math Stat 11(4): 427-444.
9. Dhillon IS, Guan Y, Kulis B (2004) A unified view of kernel k-means, spectral clustering and graph cuts. Technical report, Department of Computer Science, University of Texas at Austin. TR-04-25.
10. Dhillon IS, Tropp JA (2008) Matrix nearness problems with bregman divergences. SIAM J Matrix Anal Appl 29: 1120-1146.
11. Ding C, He X, Zha H, Gu M, Simon HD (2001) A min-max cut algorithm for graph partitioning and data clustering. In: Proceedings of the 1st international conference on data mining. pp 107-114.
12. Duchi J, Shalev-Shwartz S, Singer Y, Chandra T (2008) Efficient projections onto the L1-ball for learning in high dimensions. In: Proceedings of the 25th international conference on machine learning. pp 272-279.
13. Escalante R, Raydan M (1998) Dykstra's algorithm for a constrained least-squares matrix problem. Numer Linear Algebra Appl 3(6): 459-471.
14. Hager WW (1989) Updating the inverse of a matrix. SIAM Rev 31(2): 221-239.
15. Horn A (1954) Doubly stochastic matrices and the diagonal of a rotation matrix. Am J Math 76: 620-630.
16. Jain AK, Dubes RC (1988) Algorithms for clustering data. Prentice Hall, Englewood Cliffs.
17. Lanckriet G, Cristianini N, Bartlett P, Ghaoui LE (2004) Learning the kernel matrix with semidefinite programming. J Mach Learn Res 5: 27-72.
18. Li P, Church KW, Hastie TJ (2008) One sketch for all: theory and applications of conditional random sampling. In: NIPS. Vancouver, BC, Canada.
19. Li P, König AC (2011) Theory and applications b-bit minwise hashing. Commun ACM (to appear).
20. Liu J, Ye J (2009) Efficient Euclidean projections in linear time. In: International conference on machine learning. pp 657-664.
21. Ng AY, Jordan MI, Weiss Y (2001) On spectral clustering: analysis and an algorithm. In: Advances in neural information processing systems, vol 14. pp 849-856.
22. Nocedal J, Wright SJ (2006) Numerical optimization, 2nd edn. Springer, Berlin.
23. Pfitzner D, Leibbrandt R, Powers D (2009) Characterization and evaluation of similarity measures for pairs of clusterings. Knowl Inf Syst 19(3): 361-394.
24. Shi J, Malik J (2000) Normalized cuts and image segmentation. IEEE Trans Pattern Anal Mach Intell 22(8): 888-905.
25. Sinkhorn R, Knopp P (1967) Concerning nonnegative matrices and doubly stochastic matrices. Pac J Math 21: 343-348.
26. Sonnenburg S, Rätsch G, Schölkopf B, Rätsch G (2006) Large scale multiple kernel learning. J Mach Learn Res 7(Jul): 1531-1565.
27. Soules GW (1991) The rate of convergence of Sinkhorn balancing. Linear Algebra Appl 150: 3-40.
28. Stephan FF (1942) An iterative method of adjusting sample frequency tables when expected marginal totals are known. Ann Math Stat 13(2): 166-178.
29. Strehl A, Ghosh J (2002) Cluster ensembles-a knowledge reuse framework for combining multiple partitions. J Mach Learn Res 3: 583-617.
30. Tang M, Zhou Y, Li J, Wang W, Cui P, Hou Y, Luo Z, Li J, Lei F, Yan B (2011) Exploring the wild birds migration data for the disease spread study of h5n1: a clustering and association approach. Knowl Inf Syst 27(2): 227-251.
31. Wang F, Li P (2010) Compressed non-negative sparse coding. In: ICDM. Sydney, AU.
32. Wang F, Tan C, König AC, Li P (2011) Efficient document clustering via online nonnegative matrix factorizations. In: SDM.
33. Wang F, Wang X, Li T (2009) Generalized cluster aggregation. In: Proceedings of the 21st international joint conference on artificial intelligence. pp 1279-1284.
34. Yang J, Cheung W, Chen X (2009) Learning element similarity matrix for semi-structured document analysis. Knowl Inf Syst 19(1): 53-78.
35. Zass R, Shashua A (2005) A unifying approach to hard and probabilistic clustering. In: Proceedings of international conference on computer vision. pp 294-301.
36. Zha H, He X, Ding C, Gu M, Simon H (2001) Spectral relaxation for k-means clustering. In: NIPS, Vancover, BC, Canada.