Dynamical System for Computing Largest Generalized Eigenvalue

A dynamical system is proposed for generalized eigen- decomposition problem. The stable points of the dynamical system are proved to be the eigenvectors corresponding to the largest generalized eigenvalue.

[1]  Erkki Oja,et al.  Principal components, minor components, and linear neural networks , 1992, Neural Networks.

[2]  Kurt Hornik,et al.  Convergence analysis of local feature extraction algorithms , 1992, Neural Networks.

[3]  Qingfu Zhang,et al.  A class of learning algorithms for principal component analysis and minor component analysis , 2000, IEEE Trans. Neural Networks Learn. Syst..

[4]  Tianping Chen,et al.  Modified Oja's Algorithms For Principal Subspace and Minor Subspace extraction , 1997, Neural Processing Letters.

[5]  J. Príncipe,et al.  An RLS type algorithm for generalized eigendecomposition , 2001, Neural Networks for Signal Processing XI: Proceedings of the 2001 IEEE Signal Processing Society Workshop (IEEE Cat. No.01TH8584).

[6]  Michael D. Zoltowski,et al.  Self-organizing algorithms for generalized eigen-decomposition , 1997, IEEE Trans. Neural Networks.

[7]  Lennart Ljung,et al.  Analysis of recursive stochastic algorithms , 1977 .

[8]  Erkki Oja,et al.  Modified Hebbian learning for curve and surface fitting , 1992, Neural Networks.

[9]  Gene H. Golub,et al.  Matrix computations , 1983 .

[10]  Yan Fu,et al.  Neural networks based approach for computing eigenvectors and eigenvalues of symmetric matrix , 2004 .

[11]  P. Hartman.  Ordinary Differential Equations , 1965 .

[12]  Fa-Long Luo,et al.  A principal component analysis algorithm with invariant norm , 1995, Neurocomputing.

[13]  Michael G. Strintzis,et al.  Optimal linear compression under unreliable representation and robust PCA neural models , 1999, IEEE Trans. Neural Networks.