Algorithms and literate programs for weighted low-rank approximation with missing data

Springer Proceedings in Physics

Volumn 3, Issue , 2011, Pages 255-273

  Markovsky, Ivan ^a  

^a UNIVERSITY OF SOUTHAMPTON   (United Kingdom)

Author keywords

[No Author keywords available]

Indexed keywords

APPROXIMATION THEORY; MATLAB; ALGORITHMS;

ALTERNATING PROJECTIONS; LITERATE PROGRAMMING; MISSING DATA; MISSING VALUES; SCRIPTING LANGUAGES; SYNTHETIC DATA; VARIABLE PROJECTION; WEIGHTED LOW RANK APPROXIMATIONS; WEIGHTED LOW-RANK APPROXIMATIONS;

APPROXIMATION ALGORITHMS; APPROXIMATION THEORY;

EID: 84904068208     PISSN: 09308989     EISSN: 18674941     Source Type: Conference Proceeding    
DOI: 10.1007/978-3-642-16876-5_12     Document Type: Conference Paper

References (21)

1. J.-F. Cai, E. Candes, and Z. Shen: A singular value thresholding algorithm for matrix completion. http://www-stat.stanford.edu/~candes/papers/ SVT. pdf, 2009.
2. E. Candes and B. Recht: Exact matrix completion via convex optimization. Found. of Comput. Math., 2009.
3. B. De Moor: Structured total least squares and L2 approximation problems. Linear Algebra Appl., 188-189:163-207, 1993.
4. K. Gabriel and S. Zamir: Lower rank approximation of matrices by least squares with any choice of weights. Technometrics 21, 1979, 489-498.
5. G. Golub and V. Pereyra: Separable nonlinear least squares: the variable projection method and its applications. Institute of Physics, Inverse Problems 19, 2003, 1-26.
6. G. Golub and C. Van Loan: An analysis of the total least squares problem. SIAM J. Numer. Anal. 17, 1980, 883-893.
7. GroupLens: Movielens data sets. http://www.grouplens.org/node/73.
8. N. Higham: Computing the nearest correlation matrix -A problem from finance. IMA Journal of Numerical Analysis 22(3), 2002, 329-343.
9. H. Kiers: Setting up alternating least squares and iterative majorization algorithms for solving various matrix optimization problems. Comput. Statist. Data Anal. 41, 2002, 157-170.
10. D. Knuth: Literate Programming. Cambridge University Press, 1992.
11. W. Krijnen: Convergence of the sequence of parameters generated by alternating least squares algorithms. Comput. Statist. Data Anal. 51, 2006, 481-489.
12. J. Manton, R. Mahony, and Y. Hua: The geometry of weighted low-rank approximations. IEEE Trans. Signal Process. 51(2), 2003, 500-514.
13. I. Markovsky: Algorithms and Literate Programs for Weighted Low-Rank Approximation with Missing Data. Technical Report 18296, ECS, Univ. of Southampton, http://eprints.ecs.soton.ac.uk/18296/, 2009.
14. I. Markovsky, M.-L. Rastello, A. Premoli, A. Kukush, and S. Van Huffel: The element-wise weighted total least squares problem. Comput. Statist. Data Anal. 50(1), 2005, 181-209.
15. I. Markovsky and S. Van Huffel: Left vs right representations for solving weighted low rank approximation problems. Linear Algebra Appl. 422, 2007, 540-552.
16. D. Marquardt: An algorithm for least-squares estimation of nonlinear parameters. SIAM J. Appl. Math. 11, 1963, 431-441.
17. N. Ramsey: noweb. http://www.cs.tufts.edu/~nr/noweb/.
18. N. Ramsey: Literate programming simplified. IEEE Software 11, 1994, 97-105.
19. T. Segaran: Programming Collective Intelligence: Building Smart Web 2.0 Applications. O'Reilly Media, 2007.
20. N. Srebro: Learning with Matrix Factorizations. PhD thesis, MIT, 2004.
21. P. Wentzell, D. Andrews, D. Hamilton, K. Faber, and B. Kowalski: Maximum likelihood principal component analysis. J. Chemometrics 11, 1997, 339-366.