Learning a bi-stochastic data similarity matrix

Proceedings - IEEE International Conference on Data Mining, ICDM

Volumn , Issue , 2010, Pages 551-560

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

^a Cornell University ^*  (United States)

^b MICROSOFT RESEARCH   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

ADJACENCY MATRICES; BELONG TO; BREGMAN DIVERGENCES; CLUSTERING RESULTS; DATA POINTS; DATA SIMILARITY; EUCLIDIAN DISTANCE; GENERAL METHOD; K-MEANS CLUSTERING; KL-DIVERGENCE; MATRIX; NORMALIZED CUTS; OPTIMAL SOLUTIONS; OTHER ALGORITHMS; PUBLIC DATA; STOCHASTIC DATA; STOCHASTIC MATRICES;

DATA MINING; MATRIX ALGEBRA; STOCHASTIC SYSTEMS;

CLUSTERING ALGORITHMS;

EID: 79951733157     PISSN: 15504786     EISSN: None     Source Type: Conference Proceeding    
DOI: 10.1109/ICDM.2010.141     Document Type: Conference Paper

References (24)

1. D. P. Bertsekas. Nonlinear Programming: 2nd Edition. Athena Scientific, 1999.
2. S. Boyd and L. Vandenberghe. Convex Optimization. Cambridge University Press, Cambridge, UK., 2004.
3. P. K. Chan, D. F. Schlag, and J. Y. Zien. Spectral k-way ratiocut partitioning and clustering. IEEE Trans. Computer-Aided Design, 13:1088-1096, 1994.
4. J. N. Darroch and D. Ratcliff. Generalized iterative scaling for log-linear models. The Annals of Mathematical Statistics, 43(5):1470-1480, 1972.
5. W. E. Deming and F. F. Stephan. On a least squares adjustment of a sampled frequency table when the expected marginal totals are known. The Annals of Mathematical Statistics, 11(4):427-444, 1940.
6. I. S. Dhillon, Y. Guan, and B. Kulis. 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, 2004.
7. I. S. Dhillon and J. A. Tropp. Matrix nearness problems with bregman divergences. In SIAM Journal on Matrix Analysis and Applications, volume 29, pages 1120-1146, 2008.
8. C. Ding, X. He, H. Zha, M. Gu, and H. D. Simon. A minmax cut algorithm for graph partitioning and data clustering. In Proceedings of the 1st International Conference on Data Mining, pages 107-114, 2001.
9. J. Duchi, S. Shalev-Shwartz, Y. Singer, and T. Chandra. Efficient projections onto the L1-ball for learning in high dimensions. In Proceedings of the 25th international conference on Machine learning, pages 272-279, 2008.
10. R. Escalante and M. Raydan. Dykstra's algorithm for a constrained least-squares matrix problem. Numerical Linear Algebra with Applications, 3(6):459-471, 1998.
11. W. W. Hager. Updating the inverse of a matrix. SIAM Review, 31(2):221-239, 1989.
12. A. Horn. Doubly stochastic matrices and the diagonal of a rotation matrix. The American Journal of Mathematics, 76:620-630, 1954.
13. A. K. Jain and R. C. Dubes. Algorithms for Clustering Data. Prentice Hall, 1988.
14. J. Liu and J. Ye. Efficient Euclidean projections in linear time. In International Conference on Machine Learning, pages 657-664, 2009.
15. A. Y. Ng, M. I. Jordan, and Y. Weiss. On spectral clustering: analysis and an algorithm. In Advances in Neural Information Processing Systems 14, pages 849-856, 2001.
16. J. Nocedal and S. J. Wright. Numerical Optimization (2nd ed.). Springer-Verlag, Berlin, New York, 2006.
17. J. Shi and J. Malik. Normalized cuts and image segmentation. IEEE Trans. on Pattern Analysis and Machine Intelligence, 22(8):888-905, 2000.
18. R. Sinkhorn and P. Knopp. Concerning nonnegative matrices and doubly stochastic matrices. Pacific J. Math., 21:343-348, 1967.
19. G. W. Soules. The rate of convergence of Sinkhorn balancing. Linear Algebra and its Applications, 150:3 - 40, 1991.
20. F. F. Stephan. An iterative method of adjusting sample frequency tables when expected marginal totals are known. The Annals of Mathematical Statistics, 13(2):166-178, 1942.
21. A. Strehl and J. Ghosh. Cluster ensembles - a knowledge reuse framework for combining multiple partitions. Journal of Machine Learning Research, 3:583-617, 2002.
22. F. Wang, X. Wang, and T. Li. Generalized cluster aggregation. In Proceedings of The 21st International Joint Conference on Artificial Intelligence, pages 1279-1284, 2009.
23. R. Zass and A. Shashua. A unifying approach to hard and probabilistic clustering. In Proceedings of International Conference on Computer Vision, pages 294-301, 2005. (Pubitemid 44054972)
24. H. Zha, X. He, C. Ding, M. Gu, and H. Simon. Spectral relaxation for k-means clustering. In Advances in Neural Information Processing Systems 14, 2001.