Scalable tensor factorizations for incomplete data

Chemometrics and Intelligent Laboratory Systems

Volumn 106, Issue 1, 2011, Pages 41-56

  Acar, Evrim ^a   Dunlavy, Daniel M ^c   Kolda, Tamara G ^b   Mørup, Morten ^d  

^a SCIENTIFIC AND TECHNOLOGICAL RESEARCH COUNCIL OF TURKEY   (Turkey)

^b SANDIA NATIONAL LABORATORIES   (United States)

^c SANDIA NATIONAL LABORATORIES   (United States)

^d TECHNICAL UNIVERSITY OF DENMARK   (Denmark)

Author keywords

CANDECOMP; Incomplete data; Missing data; Optimization; PARAFAC; Tensor factorization

Indexed keywords

ALGORITHM; ARTICLE; CANDECOMP ANALYSIS; COMPUTER MODEL; COMPUTER NETWORK; CONTROLLED STUDY; DATA ANALYSIS; DATA COLLECTION METHOD; ELECTROENCEPHALOGRAM; LATENT STRUCTURE ANALYSIS; MATHEMATICAL AND STATISTICAL PROCEDURES; MATHEMATICAL COMPUTING; PARAFAC ANALYSIS; PRIORITY JOURNAL; REGRESSION ANALYSIS; SCALABLE TENSOR FACTORIZATION; SIMULATION;

EID: 79952446596     PISSN: 01697439     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.chemolab.2010.08.004     Document Type: Article

References (37)

1. Acar E., Dunlavy D.M., Kolda T.G., Mørup M. Scalable Tensor Factorizations with Missing Data. Proceedings of the Tenth SIAM International Conference on Data Mining 2010, 701-712. SIAM, URL http://www.siam.org/proceedings/datamining/2010/dm10_061_acare.pdf.
2. Zhang Y., Roughan M., Willinger W., Qiu L. Spatio-temporal compressive sensing and internet traffic matrices. SIGCOMM '09: Proceedings of the ACM SIGCOMM 2009 conference on Data communication 2009, 267-278. ACM, New York, NY, USA. 10.1145/1592568.1592600.
3. Buchanan A.M., Fitzgibbon A.W. Damped Newton algorithms for matrix factorization with missing data. CVPR'05: 2005 IEEE Computer Society Conference on Computer Vision and Pattern Recognition 2005, vol. 2:316-322. IEEE Computer Society. 10.1109/CVPR.2005.118.
4. Acar E., Yener B. Unsupervised multiway data analysis: a literature survey. IEEE Transactions on Knowledge and Data Engineering 2009, 21(1):6-20. 10.1109/TKDE.2008.112.
5. Kolda T.G., Bader B.W. Tensor decompositions and applications. SIAM Review 2009, 51(3):455-500. 10.1137/07070111X.
6. Miwakeichi F., Martínez-Montes E., Valdés-Sosa P.A., Nishiyama N., Mizuhara H., Yamaguchi Y. Decomposing EEG data into space-time-frequency components using parallel factor analysis. NeuroImage 2004, 22(3):1035-1045. 10.1016/j.neuroimage.2004.03.039.
7. Tomasi G., Bro R. PARAFAC and missing values. Chemometrics and Intelligent Laboratory Systems 2005, 75(2):163-180. 10.1016/j.chemolab.2004.07.003.
8. Orekhov V.Y., Ibraghimov I., Billeter M. Optimizing resolution in multidimensional NMR by three-way decomposition. Journal of Biomolecular NMR 2003, 27:165-173. 10.1023/A:1024944720653.
9. Geng X., Smith-Miles K., Zhou Z.-H., Wang L. Face Image Modeling by Multilinear Subspace Analysis with Missing Values. MM '09: Proceedings of the seventeen ACM international conference on Multimedia 2009, 629-632. ACM. 10.1145/1631272.1631373.
10. Ruhe A. Numerical Computation of Principal Components when Several Observations are Missing. Tech. Rep. UMINF-48-74 1974, Department of Information Processing, Institute of Mathematics and Statistics, University of Umea, Umea, Sweden.
11. Gabriel K.R., Zamir S. Lower rank approximation of matrices by least squares approximation with any choice of weights. Technometrics 1979, 21(4):489-498. URL http://www.jstor.org/stable/1268288.
12. E. J. Candès, T. Tao, The power of convex relaxation: Near-optimal matrix completion, arXiv:0903.1476v1 (Mar. 2009).URL http://arxiv.org/abs/0903.1476.
13. E. J. Candès, Y. Plan, Matrix completion with noise, arXiv:0903.3131v1 (Mar. 2009).URL http://arxiv.org/abs/0903.3131.
14. Carroll J.D., Chang J.J. Analysis of individual differences in multidimensional scaling via an N-way generalization of "Eckart-Young" decomposition. Psychometrika 1970, 35:283-319. 10.1007/BF02310791.
15. Harshman R.A. Foundations of the PARAFAC procedure: Models and conditions for an "explanatory" multi-modal factor analysis. UCLA working papers in phonetics 1970, 16:1-84. available at http://www.psychology.uwo.ca/faculty/harshman/wpppfac0.pdf.
16. Kolda T.G., Bader B.W., Kenny J.P. Higher-Order Web Link Analysis Using Multilinear Algebra. ICDM 2005: Proceedings of the 5th IEEE International Conference on Data Mining 2005, 242-249. IEEE Computer Society. 10.1109/ICDM.2005.77.
17. Bro R. Review on multiway analysis in chemistry-2000-2005. Critical Reviews in Analytical Chemistry 2006, 36(3-4):279-293. 10.1080/10408340600969965.
18. Acar E., Bingol C.A., Bingol H., Bro R., Yener B. Multiway analysis of epilepsy tensors. Bioinformatics 2007, 23(13):i10-i18. 10.1093/bioinformatics/btm210.
19. Mørup M., Hansen L.K., Arnfred S.M. ERPWAVELAB a toolbox for multi-channel analysis of time-frequency transformed event related potentials. Journal of Neuroscience Methods 2007, 161(2):361-368. 10.1016/j.jneumeth.2006.11.008.
20. Acar E., Dunlavy D.M., Kolda T.G. A scalable optimization approach for fitting canonical tensor decompositions. Journal of Chemometrics 2011, 25:67-86. 10.1002/cem.1335.
21. Dempster A.P., Laird N.M., Rubin D.B. Maximum likelihood from incomplete data via the em algorithm. Journal of the Royal Statistical Society, Series B 1977, 39(1):1-38.
22. Srebro N., Jaakkola T. Weighted Low-Rank Approximations. IMCL-2003: Proceedings of the Twentieth International Conference on Machine Learning 2003, 720-727.
23. Kiers H.A.L. Weighted least squares fitting using ordinary least squares algorithms. Psychometrika 1997, 62(2):215-266. 10.1007/BF02295279.
24. R. Bro, Multi-way analysis in the food industry: Models, algorithms, and applications, Ph.D. thesis, University of Amsterdam, available at http://www.models.kvl.dk/research/theses/ (1998).
25. Walczak B., Massart D.L. Dealing with missing data: Part I. Chemometrics and Intelligent Laboratory Systems 2001, 58(1):15-27. 10.1016/S0169-7439(01)00131-9.
26. Paatero P. A weighted non-negative least squares algorithm for three-way "PARAFAC" factor analysis. Chemometrics and Intelligent Laboratory Systems 1997, 38(2):223-242. 10.1016/S0169-7439(97)00031-2.
27. Nocedal J., Wright S.J. Numerical Optimization 1999, Springer.
28. Bader B.W., Kolda T.G. Efficient MATLAB computations with sparse and factored tensors. SIAM Journal on Scientific Computing 2007, 30(1):205-231. 10.1137/060676489.
29. B. W. Bader, T. G. Kolda, MATLAB tensor toolbox version 2.4, http://csmr.ca.sandia.gov/ tgkolda/TensorToolbox/ (last accessed March, 2010).
30. Moré J.J., Thuente D.J. Line search algorithms with guaranteed sufficient decrease. ACM Transactions on Mathematical Software 1994, 20(3):286-307. 10.1145/192115.192132.
31. Dunlavy D.M., Kolda T.G., Acar E. Poblano v1.0: A MATLAB Toolbox for Gradient-Based Optimization. Tech. Rep. SAND2010-1422 Mar. 2010, Sandia National Laboratories, Albuquerque, NM and Livermore, CA.
32. Andersson C.A., Bro R. The N-way toolbox for MATLAB. Chemometrics and Intelligent Laboratory Systems 2000, 52(1):1-4. see also http://www.models.kvl.dk/source/nwaytoolbox/. doi:10.1016/S0169-7439(00)00071-X.
33. G. Tomasi, Incomplete data PARAFAC (INDAFAC), http://www.models.kvl.dk/source/indafac/index.asp (last accessed May, 2009).
34. Kruskal J.B. Three-way arrays: rank and uniqueness of trilinear decompositions, with application to arithmetic complexity and statistics. Linear Algebra and its Applications 1977, 18(2):95-138. 10.1016/0024-3795(77)90069-6.
35. Delorme A., Makeig S. EEGLAB: an open source toolbox for analysis of single-trial EEG dynamics. Journal of Neuroscience Methods 2004, 134:9-21. 10.1016/j.jneumeth.2003.10.009.
36. Uhlig S., Quoitin B., Lepropre J., Balon S. Providing public intradomain traffic matrices to the research community. ACM SIGCOMM Computer Communication Review 2006, 36(1):83-86. 10.1145/1111322.1111341.
37. Tucker L.R. Some mathematical notes on three-mode factor analysis. Psychometrika 1966, 31:279-311. 10.1007/BF02289464.