Controlling sparseness in non-negative tensor factorization

Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

Volumn 3951 LNCS, Issue , 2006, Pages 56-67

  Heiler, Matthias ^a   Schnörr, Christoph ^a  

^a UNIVERSITY OF MANNHEIM   (Germany)

Author keywords

[No Author keywords available]

Indexed keywords

COMPUTER PROGRAMMING; COMPUTER SCIENCE; IMAGE PROCESSING; PERFORMANCE;

DATA SETS; NON-NEGATIVE TENSOR FACTORIZATION (NTF); SEQUENTIAL CONIC PROGRAMMING; SPARSENESS CONTROL;

TENSORS;

EID: 33745812062     PISSN: 03029743     EISSN: 16113349     Source Type: Book Series    
DOI: 10.1007/11744023_5     Document Type: Conference Paper

References (26)

1. M. Welling and M. Weber, "Positive tensor factorization," Pattern Recog. Letters, vol. 22, no. 12, pp. 1255-1261, 2001.
2. A. Shashua and T. Hazan, "Non-negative tensor factorization with applications to statistics and computer vision," in Proc. of ICML, 2005.
3. T. Hazan, S. Polak, and A. Shashua, "Sparse image coding using a 3D non-negative tensor factorization," in Proc. of ICCV, 2005.
4. J. Shen and G. W. Israël, "A receptor model using a specific non-negative transformation technique for ambient aerosol," Atmospheric Environment, vol. 23, no. 10, pp. 2289-2298, 1989.
5. P. Paatero and U. Tapper, "Positive matrix factorization: A non-negative factor model with optimal utilization of error estimates of data values," Environmetrics, vol. 5, pp. 111-126, 1994.
6. D. D. Lee and H. S. Seung, "Learning the parts of objects by non-negative matrix factorization," Nature, vol. 401, pp. 788-791, Oct. 1999.
7. A. Shashua and A. Levin, "Linear image coding for regression and classification using the tensor-rank principle," in Proc. of CVPR, 2001.
8. D. Donoho and V. Stodden, "When does non-negative matrix factorization give a correct decomposition into parts?," in Adv. in NIPS, vol. 17, 2004.
9. J. B. Kruskal, "Three-way arrays: Rank and uniqueness of trilinear decompositions, with application to arithmetic complexity and statistics," Linear Algebra and its Applications, vol. 18, pp. 95-138, 1977.
10. N. D. Sidiropoulos and R. Bro, "On the uniqueness of multilinear decompositions of N-way arrays," J. of Chemometrics, vol. 14, pp. 229-239, 2000.
11. P. O. Hoyer, "Non-negative matrix factorization with sparseness constraints," J. of Mach. Learning Res., vol. 5, pp. 1457-1469, 2004.
12. D. D. Lee and H. S. Seung, "Algorithms for non-negative matrix factorization," in Adv. in NIPS, 2000.
13. M. Chu, F. Diele, R. Plemmons, and S. Ragni, "Optimality, computations, and interpretation of nonnegative matrix factorizations." submitted to SIAM J. Mat. Anal. Appl., 2004. www4.ncsu.edu:8030/~mtchu/Research/Papers/nnmf.pdf.
14. R. Horst and H. Tuy, Global Optimization. Springer, Berlin, 1996.
15. M. Heiler and C. Schnörr, "Learning non-negative sparse image codes by convex programming," in Proc. of ICCV, 2005.
16. N. Littlestone and M. Warmuth, "Relating data compression, learnability, and the Vapnik-Chervonenkis dimension," tech. rep., Univ. of Calif. Santa Cruz, 1986.
17. R. Herbrich and R. C. Williamson, "Algorithmic luckiness," J. of Mach. Learning Res., vol. 3, pp. 175-212, 2002.
18. B. A. Olshausen and D. J. Field, "Sparse coding with an overcomplete basis set: A strategy employed by V1?," Vision Research, vol. 37, pp. 3311-3325, Dec. 1997.
19. M. S. Lobo, L. Vandenberghe, S. Boyd, and H. Lebret, "Applications of second-order cone programming," Linear Algebra and its Applications, 1998.
20. J. F. Sturm, Using SeDuMi 1.02, a Matlab toolbox for optimization over symmetric cones (updated version 1.05). Department of Econometrics, Tilburg University, Tilburg, The Netherlands, 2001.
21. H. Mittelmann, "An independent benchmarking of SDP and SOCP solvers.," Math. Programming, Series B, vol. 95, no. 2, pp. 407-430, 2003.
22. MOSEK ApS, Denmark, The MOSEK optimization tools version 3.2 (Revision 8) User's manual and reference, 2005.
23. A. M. Buchanan and A. W. Fitzgibbon, "Damped Newton algorithms for matrix factorization with missing data," in CVPR05, vol. 2, pp. 316-322, 2005.
24. H. Tuy, "Convex programs with an additional reverse convex constraint," J. of Optim. Theory and Applic., vol. 52, pp. 463-486, Mar. 1987.
25. R. Rockafellar and R.-B. Wets, Variational Analysis, vol. 317 of Grundlehren der math. Wissenschaften. Springer, 1998.
26. CBCL, "CBCL face database #1." MIT Center For Biological and Computational Learning, http://cbcl.mit.edu/software-datasets, 2000.