Diagonally weighted and shifted criteria for minor and principal component extraction

Proceedings of the International Joint Conference on Neural Networks

Volumn 2, Issue , 2005, Pages 1251-1256

  Hasan, Mohammed A ^a  

^a UNIVERSITY OF MINNESOTA DULUTH   (United States)

Author keywords

Adaptive learning algorithm; Diagonally shifted cost function; Extreme eigenvalues; Generalized MCA; Generalized PCA; Minor component analysis; Neural networks; Power method; Principal component analysis; Symmetric constraints

Indexed keywords

ADAPTIVE LEARNING ALGORITHM; DIAGONALLY SHIFTED COST FUNCTION; GENERALIZED MCA; GENERALIZED PCA; MINOR COMPONENT ANALYSIS; POWER METHOD; SYMMETRIC CONSTRAINTS;

ALGORITHMS; COMPUTATIONAL METHODS; EIGENVALUES AND EIGENFUNCTIONS; LEARNING SYSTEMS; MATRIX ALGEBRA; NEURAL NETWORKS;

PRINCIPAL COMPONENT ANALYSIS;

EID: 33745956994     PISSN: None     EISSN: None     Source Type: Conference Proceeding    
DOI: 10.1109/IJCNN.2005.1556033     Document Type: Conference Paper

References (14)

1. E. Oja, "A simplified neuron model as principal component analyzer," J. Math. Biol., vol. 15, pp. 267-273, 1982.
2. T. D. Sanger, "Optimal unsupervised learning in a single-layer linear feedforward neural network," Neural Networks, vol. 2, no. 6, pp. 459-473, 1989.
3. 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.
4. T. Chen and Shun-ichi Amari, "Unified Stabilization Approach to Principal and Minor Components Algorithms," Neural Networks, Vol. 14, pp. 1377-1387, 2001.
5. J. H. Manton, Uwe Helmke, and Iven M. Y. Mareels, "Dynamical Systems for Principal and Minor Component Analysis," Proceedings of the 42nd IEEE Conference on Decision and Control; Maui, Hawaii, pp. 1863-1868, December 2003.
6. R. W. Brockett, "Dynamical systems that sort lists, diagonalise matrices, and solve linear programming problems," Linear Algebra Appl., 146:79-91, 1991.
7. Absil, P.-A., Mahony, R., Sepulchre, R., Van Dooren, P., "A Grassmann-Rayleigh quotient iteration for computing invariant subspaces," Proceedings of the 39th IEEE Conference on Decision and Control, Volume 5, 12-15, pp. 4241-4246, Dec. 2000.
8. 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.
9. Manton, J.H., "Optimization algorithms exploiting unitary constraints," IEEE Transactions on Signal Processing, Volume 50, Issue 3, Page(s):635-650, March 2002.
10. E. Oja, "Principal components, minor components, and linear neural networks. Neural Networks," 5:927-935, November 1992.
11. L. Xu, "Least mean square error recognition principle for self organizing neural nets," Neural Networks, 6:627-648, 1993.
12. Yongfeng Miao; Yingbo Hua, "Fast subspace tracking by a novel information criterion," Conference Record of the Thirty-First Asilomar Conference on Signals, Systems & Computers, Volume: 2, pp.1312 - 1316, 2-5 Nov. 1997.
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. J. R. Magnus and H. Neudecker, Matrix Differential Calculus with Applications in Statistics and Econometrics, 2nd ed. New York: Wiley, 1991.