Location via proxy:   [ UP ]  
[Report a bug]   [Manage cookies]                
Skip to main content

Sequential Extraction of Minor Components

  • Published:
Neural Processing Letters Aims and scope Submit manuscript

Abstract

Principal component analysis (PCA) and Minor component analysis (MCA) are similar but have different dynamical performances. Unexpectedly, a sequential extraction algorithm for MCA proposed by Luo and Unbehauen [11] does not work for MCA, while it works for PCA. We propose a different sequential-addition algorithm which works for MCA. We also show a conversion mechanism by which any PCA algorithms are converted to dynamically equivalent MCA algorithms and vice versa.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Subscribe and save

Springer+ Basic
$34.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Explore related subjects

Discover the latest articles, news and stories from top researchers in related subjects.

References

  1. Amari, S.: Neural theory of association and concept-formation, Biology Cybernetics, 26 (1977), 175-185.

    Google Scholar 

  2. Brockett, R. W.: Least square matching problems, Linear Algebra Appl., 122-124 (1989), 761-777.

    Google Scholar 

  3. Brockett, R.W.: Dynamical systems that sort lists, diagonalize matrices, and solve linear programming problems, Linear Algebra Appl., 146 (1991), 79-91.

    Google Scholar 

  4. Chen, T. P.: Modified Oja's algorithms for principal subspace and minor subspace extraction, Neural Processing Letters, 5 (1997), 105-110.

    Google Scholar 

  5. Chen, T. P., Amari, S. I. and Lin, Q.: A unified algorithm for principal and minor components extraction, Neural Networks, 11 (1998), 385-390.

    Google Scholar 

  6. Chen, T. P., Hua, Y. and Yan, W. Y.: Global convergence of Oja's subspace algorithm for principal component extraction, IEEE Transactions on Neural Networks, 9 (1998), 58-67.

    Google Scholar 

  7. Chen, T. P. and Amari, S. I.: Unified stabilization approach to principal and minor components extraction algorithms, Neural Networks, (Accepted for publication).

  8. Chen, T. P. and Amari, S. I.: Responses, Neural Networks, 12 (1999), 394.

    Google Scholar 

  9. Douglas, S. C., Kung, S. and Amari, S.: A self-stabilized minor subspace rule, IEEE Signal Processing Letter, 5 (1998), 330-332.

    Google Scholar 

  10. Luo, F. L., Unbehauen, R. and Cichocki, A.: A minor component analysis algorithm, Neural Networks, 10 (1997), 291-297.

    Google Scholar 

  11. Luo, F. L. and Unbehauen, R.: A minor subspace analysis algorithm, IEEE Trans. Neural Networks, 8 (1998), 1149-1155.

    Google Scholar 

  12. Luo, F. L. and Unbehauen, R.: Comments on a unified algorithms for principal and minor compoonent extraction, Neural Networks, 12 (1999), 393.

    Google Scholar 

  13. Oja, E.: A simplified neuron model as a principal component analyzer, J. Math. Biology, 15 (1982), 267-273.

    Google Scholar 

  14. Oja, E. and Karhunen, J.: On stochastic approximation of the eigenvectors and eigenvalues of the expectation of a random matrix, J. Mathematical Analysis and Applications, 106 (1985), 69-84.

    Google Scholar 

  15. Oja, E.: Principal components, minor components, and linear neural networks, Neural Networks, 5 (1992), 927-935.

    Google Scholar 

  16. Sanger, T. D.: Optimal unsupervised learning in a single-layerfeed forward network, Neural Networks, 2 (1989), 459-573.

    Google Scholar 

  17. Xu, L., Krzyzak, L. and Oja, E.: Neural nets for dual subspace pattern recognition method, Int. J. Neural Systems, 2 (1991), 169-184.

    Google Scholar 

  18. Xu, L.: Least Mean square error recognition principle for self organizing neural nets, Neural Networks, 6 (1993), 627-648.

    Google Scholar 

  19. Xu L., Oja, E. and Suen, C. Y.: Modified Hebbian learning for curve and surface fitting, Neural Networks, 5 (1992), 441-457.

    Google Scholar 

  20. Wang, L. and Karhunen, J.: A unified neural bigradient algorithm for robust PCA and MCA, Int. J. Neural Systems, 7 (1996), 53-67.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and permissions

About this article

Cite this article

Chen, T., Amari, SI. & Murata, N. Sequential Extraction of Minor Components. Neural Processing Letters 13, 195–201 (2001). https://doi.org/10.1023/A:1011388608203

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1023/A:1011388608203