Constrained quadratic optimization problems with applications

Proceedings of the American Control Conference

Volumn 1, Issue , 2005, Pages 243-248

  Hasan, Mohammed A ^a  

^a UNIVERSITY OF MINNESOTA DULUTH   (United States)

Author keywords

Bi iteration; Eigenvalue problem; Information criteria; Learning algorithms; Minor component analysis (MCA); Power method; Principal component analysis (PCA); Principal singular component analysis (PSCA); Self normalizing neural networks; Subspace methods

Indexed keywords

COMPONENT ANALYSIS; DIAGONAL MATRICES; OPTIMIZATION PROBLEMS; QUADRATIC CONSTRAINTS;

CONSTRAINT THEORY; FUNCTIONS; MATRIX ALGEBRA; OPTIMIZATION; PROBLEM SOLVING; QUADRATIC PROGRAMMING; SIGNAL PROCESSING;

CONTROL THEORY;

EID: 23944486227     PISSN: 07431619     EISSN: None     Source Type: Conference Proceeding    
DOI: None     Document Type: Conference Paper

References (17)

1. G. Cirrincione, M. Cirrincione, J. Herault, and S. Van Huffel, "The MCA EXIN Neuron for the Minor Component Analysis," IEEE Trans. on Neural Networks, Vol. 13, No. 1, pp. 160-187, January 2002.
2. T. D. Sanger, "Optimal unsupervised learning in a single-layer linear feedforward network," Neural Networks, 2:459-473, 1989.
3. E. Oja, "Principal components, minor components, and linear neural networks. Neural Networks," 5:927-935, November 1992.
4. L. Xu, "Least mean square error recognition principle for self organizing neural nets," Neural Networks, 6:627-648, 1993.
5. T. Chen and Shun-ichi Amari, "Unified Stabilization Approach to Principal and Minor Components Algorithms," Neural Networks, Vol. 14, pp. 1377-1387, 2001.
6. Yongfeng Miao; Yingbo Hua, "Fast subspace tracking by a novel information criterion," Conference Record of the Thirty-First Asilomar Conference on Signals, Systems & Computers, 1997, Volume: 2, pp.1312-1316, 2-5 Nov. 1997.
7. Hori, G., "A general framework for SVD flows and joint SVD flows," Proceedings of IEEE International Conference on Acoustics, Speech, and Signal Processing, 2003 (ICASSP '03), Volume: 2, 6-10, April 2003, pp: II-693-696.
8. J. B. Moore, R. E. Mahony, and U. Helmke, "Numerical gradient algorithms for eigenvalues and singular value calculations," SIAM J. Matrix Anal. Appl., vol. 15, pp. 881902, 1994.
9. A. Cichocki, Neural network for singular value decomposition, Electron. Lett., vol. 28, pp. 784786, 1992.
10. Da-Zheng Feng; Xian-Da Zhang; Zheng Bao, "A neural network learning for adaptively extracting cross-correlation features between two high-dimensional data streams," IEEE Transactions on Neural Networks, Volume: 15, Issue: 6, pp. 1541-1554, Nov. 2004.
11. A. Edelman, T. A. Arias and S. T. Smith, "The geometry of algorithms with orthogonality constraints" SIAM J. Matrix Anal. Appl., 20(2):303-353, 1998.
12. J.H. Manton, "Optimisation algorithms exploiting unitary constraints," IEEE Trans. Signal Processing, vol. 50, pp. 635-650, 2002.
13. Shan Ouyang; Zheng Bao; Gui-Sheng Liao; Ching, P.C., "Adaptive minor component extraction with modular structure," IEEE Transactions on Signal Processing, Volume: 49, Issue: 9, pp:2127-2137, Sept. 2001.
14. P. Strobach, "Bi-iteration SVD subspace tracking algorithms," IEEE Trans. Signal Processing, vol.45, no.5, pp. 1222-1240, 1997.
15. Shan Ouyang; Yingbo Hua, "Bi-iterative least square versus bi-iterative singular value decomposition for subspace tracking," Proceedings, Acoustics, Speech, and Signal Processing, 2004 (ICASSP '04), Volume: 2, 17-21 May 2004, pp- 353-356.
16. J. R. Magnus and H. Neudecker, Matrix Differential Calculus with Applications in Statistics and Econometrics, 2nd ed. New York: Wiley, 1991.
17. Hasan, M.A., "Natural Gradient for Minor Component Extraction," to be presented at the 2005 International Symposium on Circuits and Systems, May 2005.