From K-means to higher-way co-clustering: Multilinear decomposition with sparse latent factors

IEEE Transactions on Signal Processing

Volumn 61, Issue 2, 2013, Pages 493-506

  Papalexakis, Evangelos E ^a,b   Sidiropoulos, Nicholas D ^a,c   Bro, Rasmus ^d  

^a TECHNICAL UNIVERSITY OF CRETE   (Greece)

^b Carnegie Mellon University ^*  (United States)

^c University of Minnesota   (United States)

^d UNIVERSITY OF COPENHAGEN   (Denmark)

Author keywords

Co clustering; compressed sensing; factor analysis; k means; multi way analysis; sparsity; tensor decomposition; triclustering; unsupervised clustering

Indexed keywords

CO-CLUSTERING; COMPRESSIVE SENSING; K-MEANS; MULTI-WAY ANALYSIS; SPARSITY; TENSOR DECOMPOSITION; TRICLUSTERING; UNSUPERVISED CLUSTERING;

DIGITAL STORAGE; FACTOR ANALYSIS; MATRIX ALGEBRA; TENSORS;

CLUSTERING ALGORITHMS;

EID: 84872112858     PISSN: 1053587X     EISSN: None     Source Type: Journal    
DOI: 10.1109/TSP.2012.2225052     Document Type: Article

References (38)

1. A. Anagnostopoulos, A. Dasgupta, and R. Kumar, "Approximation algorithms for co-clustering," presented at the PODS, Vancouver, BC, Canada, Jun. 9-12, 2008.
2. C. A. Andersson and R. Bro, "The-way toolbox for MATLAB," Chemometrics Intell. Lab. Syst., 2000 [Online]. Available: http://www. models.kvl.dk/nwaytoolbox
3. B.W. Bader, R. A. Harshman, and T. G. Kolda, "Temporal analysis of social networks using three-way DEDICOM," Sandia National Labs., TR SAND2006-2161, 2006.
4. D. Ballabio, T. Skov, R. Leardi, and R. Bro, "Classification of GC-MS measurements of wines by combining data dimension reduction and variable selection techniques," J. Chemometrics, vol. 22, no. 8, pp. 457-463, 2008.
5. A. Banerjee, I. Dhillon, J. Ghosh, S. Merugu, and D. S. Modha, "A generalized maximum entropy approach to Bregman co-clustering and matrix approximation," J. Mach. Learn. Res., vol. 8, pp. 1919-1986, Aug. 2007. (Pubitemid 47416225)
6. R. Bro, E. E. Papalexakis, E. Acar, and N. D. Sidiropoulos, "Co-clustering-A useful tool for Chemometrics," J. Chemometrics, vol. 26, no. 6, pp. 256-263, Jun. 2012.
7. Y. Cheng andG.M. Church, "Biclustering of expression data," in Proc. 8th Int. Conf. Intell. Syst. Molecular Biol., 2000, pp. 93-103.
8. H. Cho, I. S. Dhillon, Y. Guan, and S. Sra, "Minimum sum-squared residue co-clustering of gene expression data," in Proc. 4th SIAM Int. Conf. Data Min., 2004, pp. 114-125.
9. I. S. Dhillon, S. Mallela, and D. S. Modha, "Information-theoretic co-clustering," in Proc. 9th ACM SIGKDD, 2003, pp. 89-98.
10. I. S. Dhillon, "Co-clustering documents and words using bipartite spectral graph partitioning," in Proc. 7th ACM SIGKDD Int. Conf. Knowl. Discovery Data Min., 2001, pp. 269-274.
11. J. Diesner, T. L. Frantz, and K. M. Carley, "Communication networks from the Enron email corpus: It's always about the people. Enron is no different," Comput. Math. Organizat. Theory, vol. 3, no. 3, pp. 201-228, 2005. (Pubitemid 43118967)
12. W. J. Fu, "Penalized regressions: The bridge versus the Lasso," J. Computat. Graph. Statist., vol. 7, no. 3, pp. 397-416, 1998.
13. R. A. Harshman, "Foundations of the PARAFAC procedure: Models and conditions for an "explanatory" multimodal factor analysis," UCLA Working Papers in Phonet., vol. 16, pp. 1-84, 1970.
14. J. A. Hartigan, "Direct clustering of a data matrix," J. Amer. Statist. Assoc., vol. 67, pp. 123-129, 1972.
15. W. J. Heiser, "Convergent computation by iterative majorization: Theory and applications in multidimensional data analysis," in Recent Advances in Descriptive Multivariate Analysis. New York: Oxford Univ. Press, 1994, pp. 157-189 [Online]. Available: http://www.oup.com/us/catalog/general/ subject/Mathematics/ComputationalMathematics/? view=usa&ci=9780198522850
16. P. O. Hoyer, "Non-negative Matrix factorization with sparseness constraints," J. Mach. Learn. Res., vol. 5, pp. 1457-1469, 2004.
17. H. Huang, C. Ding, D. Luo, and T. Li, "Simultaneous tensor subspace selection and clustering: The equivalence of high order SVD and k-means clustering," in Proc. 14th ACMSIGKDD, 2008, pp. 327-335.
18. Y. Kluger, R. Basri, J. T. Chang, and M. Gerstein, "Spectral biclustering ofmicroarray data: Coclustering genes and conditions," Genome Res., vol. 13, pp. 703-716, 2003. (Pubitemid 36511928)
19. J. B. Kruskal, "Three-way arrays: Rank and uniqueness of trilinear decompositions, with application to arithmetic complexity and statistics," Linear Algebra Appl., vol. 18, no. 2, pp. 95-138, 1977.
20. M. Lee, H. Shen, J. Z. Huang, and J. S. Marron, "Biclustering via sparse singular value decomposition," Biometrics, vol. 66, no. 4, pp. 1087-1095, Dec. 2010.
21. D. Lee and H. Seung, "Learning the parts of objects by non-negative matrix factorization," Nature, vol. 401, no. 6755, pp. 788-791, 1999.
22. J. Leskovec, L. A. Adamic, and B. A. Huberman, "The dynamics of viral marketing," ACM Trans. Web (TWEB), vol. 1, no. 1, 2007, Article 5.
23. S. C. Madeira and A. L. Oliveira, "Biclustering algorithms for biological data analysis: A survey," IEEE/ACM Trans. Computat. Biol. Bioinf., vol. 1, no. 1, pp. 24-45, Jan.-Mar. 2004.
24. M. R. Osborne, B. Presnell, and B. A. Turlach, "On the Lasso and its dual," J. Computat. Graphic. Statist., vol. 9, no. 2, pp. 319-337, 2000.
25. E. E. Papalexakis, N. D. Sidiropoulos, and M. N. Garofalakis, "Reviewer profiling using sparse matrix regression," in Proc. IEEE Int. Conf. Data Min. Workshops, 2010, pp. 1214-1219.
26. E. E. Papalexakis and N. D. Sidiropoulos, "Co-clustering asmultilinear decomposition with sparse latent factors," in Proc. IEEE Int. Conf. Acoust., Speech, Signal Process. (ICASSP), Prague, Czech Republic, May 22-27, 2011, pp. 2064-2067.
27. T. Park andG. Casella, "The Bayesian Lasso," J. Amer. Statist. Assoc., vol. 103, no. 482, pp. 681-686, 2008.
28. W. Peng and T. Li, "Temporal relation co-clustering on directional social network and author-topic evolution," Knowl. Inf. Syst., pp. 1-20, Mar. 2010.
29. M. Rajih, P. Comon, and R. A. Harshman, "Enhanced line search: A novel method to accelerate PARAFAC," SIAM J. Matrix Anal. Appl., vol. 30, no. 3, pp. 1148-1171, 2008.
30. I. Schizas, G. B. Giannakis, and N. D. Sidiropoulos, "Exploiting covariance-domain sparsity for dimensionality reduction," in Proc. IEEE CAMSAP, Aruba, Dutch Antilles, Dec. 13-16, 2009.
31. T. Jiang and N. D. Sidiropoulos, "Kruskal's permutation lemma and the identification of CANDECOMP/PARAFAC and bilinear models with constant modulus constraints," IEEE Trans. Signal Process., vol. 52, no. 9, pp. 2625-2636, Sep. 2004.
32. R. Tibshirani, "Regression shrinkage and selection via the Lasso," J. Roy. Statist. Soc. Ser. B (Methodol.), vol. 58, no. 1, pp. 267-288, 1996.
33. G. Tomasi and R. Bro, "A comparison of algorithms for fitting the PARAFAC model," Comput. Statist. Data Anal., vol. 50, no. 7, pp. 1700-1734, 2006. (Pubitemid 43052351)
34. G. Tomasi and R. Bro, "PARAFAC and missing values," Chemometrics Intell. Lab. Syst., vol. 75, no. 2, pp. 163-180, 2005. (Pubitemid 40164340)
35. D. M.Witten, R. Tibshirani, and T. Hastie, "A penalizedmatrix decomposition, with applications to sparse principal components and canonical correlation analysis," Biostatist., vol. 10, no. 3, pp. 515-534, 2009.
36. L. Zhao and M. J. Zaki, "Tricluster: An effective algorithm for mining coherent clusters in 3D microarray data," in Proc. ACM SIGMOD 2005, p. 705.
37. Q. Zhou, G. Xu, and Y. Zong, "Web co-clustering of usage network using tensor decomposition," in Proc. IEEE/WIC/ACM Int. Joint Conf. Web Intell. Intell. Agent Technol., 2009, vol. 3, pp. 311-314.
38. H. Zou, T. Hastie, and R. Tibshirani, "On the degrees of freedom of the Lasso," Ann. Statist., vol. 35, no. 5, pp. 2173-2192, 2007.