The relationships among various nonnegative matrix factorization methods for clustering

Proceedings - IEEE International Conference on Data Mining, ICDM

Volumn , Issue , 2006, Pages 362-371

  Li, Tao ^a   Ding, Chris ^b  

^a The Department of Electrical and Computer Engineering   (United States)

^b UNIVERSITY OF CALIFORNIA   (United States)

Author keywords

Matrix factorization; Normalization; Relation; Simultaneous clustering

Indexed keywords

MATRIX FACTORIZATION ALGORITHMS; NONNEGATIVE MATRIX FACTORIZATION (NMF); NORMALIZATION; RESEARCH PROGRESS; SIMULTANEOUS CLUSTERING;

ALGORITHMS; FACTORIZATION; MATRIX ALGEBRA; VARIATIONAL TECHNIQUES;

CLUSTER ANALYSIS;

EID: 49849097634     PISSN: 15504786     EISSN: None     Source Type: Conference Proceeding    
DOI: 10.1109/ICDM.2006.160     Document Type: Conference Paper

References (35)

1. C. C. Aggarwal, J. L. Wolf, P. S. Yu, C. Procopiuc, and J. S. Park. Fast algorithms for projected clustering. In Proceedings of the 1999 ACM SIGMOD international conference on Management of data (SIGMOD'99), pages 61-72. ACM Press, 1999.
2. D. Baier, W. Gaul, and M. Schader. Two-mode overlapping clustering with applications to simultaneous benefit segmentation and market structuring. In R. Klar and O. Opitz, editors, Classifi cation and Knowledge Organization, pages 577-566. Springer, 1997.
3. K. S. Beyer, J. Goldstein, R. Ramakrishnan, and U. Shaft. When is nearest neighbor meaningful? In Proceedings of 7th International Conference on Database Theory(ICDT'99), pages 217-235. Springer, 1999.
4. D. Blei, A. Ng, and M. Jordan. Latent dirichlet allocation. Journal of Machine Learning Research, 3:993-1022, 2003.
5. D. Boley. Principal direction divisive partitioning. Data mining and knowledge discovery, 2:325-344, 1998.
6. W. Castillo and J. Trejos. Two-mode partitioning: Review of methods and application and tabu search. In K. Jajuga, A. Sokolowski, and H.-H. Bock, editors, Classifi cation, Clustering and Data Analysis, pages 43-51. Springer, 2002.
7. H. Cho, I. S. Dhillon, Y. Guan, and S. Sra. Minimum sumsquared residue co-clustering of gene expression data. In Proceedings of the SIAM Data Mining Conference, 2004.
8. M. Cooper and J. Foote. Summarizing video using nonnegative similarity matrix factorization. In Proc. IEEE Workshop on Multimedia Signal Processing, pages 25-28, 2002.
9. I. S. Dhillon. Co-clustering documents and words using bipartite spectral graph partitioning. Proc. ACM Int'l Conf Knowledge Disc. Data Mining (KDD 2001), 2001.
10. I. S. Dhillon, S. Mallela, and S. S. Modha. Informationtheoretic co-clustering. In Proceedings of the 9th ACM SIGKDD International Conference on Knowledge Discovery and Data Mining (SIGKDD 2003), pages 89-98, 2003.
11. C. Ding and X. He. K-means clustering and principal component analysis. Int'l Conf. Machine Learning (ICML), 2004.
12. C. Ding, X. He, and H. Simon. On the equivalence of nonnegative matrix factorization and spectral clustering. Proc. SIAM Data Mining Conf, 2005.
13. C. Ding, T. Li, and M. Jordan. Convex and semi-nonnegative matrix factorizations for clustering and low-dimension representation. Technical Report LBNL-60428, Lawrence Berkeley National Laboratory, 2006.
14. C. Ding, T. Li, and W. Peng. Nonnegative matrix factorization and probabilistic latent semantic indexing: Equivalence, chi-square statistic, and a hybrid method. In Proc. of National Conf. on Artifi cial Intelligence (AAAI-06), 2006.
15. C. Ding, T. Li, W. Peng, and H. Park. Orthogonal nonnegative matrix tri-factorizations for clustering. In Proceedings of the Twelfth ACM SIGKDD International Conference on Knowledge Discovery and Data Mining, 2006.
16. C. Eckart and G. Young. The approximation of one matrix by another of lower rank. Psychometrika, 1:183-187, 1936.
17. G. Golub and C. Van Loan. Matrix Computations, 3rd edition. Johns Hopkins, Baltimore, 1996.
18. G. Govaert. Simultaneous clustering of rows and columns. Control and Cybernetics, 24(4):437-458, 1995.
19. E. Han, D. Boley, M. Gini, R. Gross, K. Hastings, G. Karypis, V. Kumar, B. Mobasher, and J. Moore. WebACE: A web agent for document categorization and exploration. In Proceedings of the 2nd International Conference on Autonomous Agents (Agents'98). ACM Press, 1998.
20. T. Hastie, R. Tibshirani, and J. Friedman. The Elements of Statistical Learning: Data Mining, Inference, Prediction. Springer, 2001.
21. T. Hofmann. Probabilistic latent semantic analysis. In Proceedings of the 15th Annual Conference on Uncertainty in Artifi cial Intelligence (UAI-99), pages 289-296, 1999.
22. P. O. Hoyer. Non-negative matrix factorization with sparseness constraints. J. Machine Learning Research, 5:1457-1469, 2004.
23. F. D. la Torre and T. Kanadì. Discriminative cluster analysis. In Proceedings of the 23rd International Conference on Machine Learning (ICML 2006), 2006.
24. D. Lee and H. S. Seung. Learning the parts of objects by nonnegative matrix factorization. Nature, 401:788-791, 1999.
25. D. Lee and H. S. Seung. Algorithms for non-negatvie matrix factorization. In T. G. Dietterich and V. Tresp, editors, Advances in Neural Information Processing Systems, volume 13. The MIT Press, 2001.
26. S. Li, X. Hou, H. Zhang, and Q. Cheng. Learning spatially localized, parts-based representation. In Proce IEEE Computer Vision and Pattern Recognition, pages 207-212, 2001.
27. B. Long, Z. Zhang, and P. Yu. Co-clustering by block value decomposition. In KDD '05, pages 635-640, 2005.
28. V. Maurizio. Double k-means clustering for simultaneous classification of objects and variables. In S. Borra, R. Rocei, M. Vichi, and M. Schader, editors, Advances in Classifi cation and Data Analysis, pages 43-52. Springer, 2001.
29. P. Paatero and U. Tapper. Positive matrix factorization: A non-negative factor model with optimal utilization of error estimates of data values. Environmetrics, 5:111-126, 1994.
30. V. P. Pauca, F. Shahnaz, M. W. Berry, R. J. Plemmons. Text mining using non-negative matrix factorization. In Proceedings of the 2004 SIAM International conference on Data Mining (SDM 2004), pages 452-456, Lake Buena Vista, Florida, 2004.
31. F. Sha, L. Saul, and D. Lee. Multiplicative updates for nonnegative quadratic programming in support vector machines. In Advances in Neural Information Processing Systems 15, pages 1041-1048. 2003.
32. W. Xu, X. Liu, and Y. Gong. Document clustering based on non-negative matrix factorization. In SIGIR'03), pages 267-273, 2003.
33. D. Zeimpekis and E. Gallopoulos. Clsi: A flexible approximation scheme from clustered term-document matrices. Proc. SIAM Data Mining Conf, pages 631-635, 2005.
34. H. Zha, C. Ding, M. Gu, X. He, and H. Simon. Spectral relaxation for K-means clustering. Advances in Neural Information Processing Systems 14 (NIPS'01), pages 1057-1064, 2002.
35. H. Zha, X. He, C. Ding, M. Gu, and H. Simon. Bipartite graph partitioning and data clustering. Proc. Int'l Conf. Information and Knowledge Management (CIKM 2001), 2001.