Skip to main content
SpringerLink
Log in

Feature evaluation in fMRI data using random matrix theory

  • Regular article
  • Published:
Computing and Visualization in Science

Abstract

Quantitative descriptors of intrinsic properties of fMRI data can be obtained from the theory of random matrices. We study data reduction based on the comparison of empirical correlation matrices with a suitably chosen ensemble of random positive matrices. Accordingly, data dimensions can be discarded if the quality of fit of the data spectrum deviates locally from the theoretical result, which is derived here analytically. Further, more complex quantities such as the number variance are discussed and shown to be potentially useful in an analogous manner.

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

Access this article

Log in via an institution

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

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Alon N., Krivelevich M., Vu V.H. (2002) On the concentration of eigenvalues of random symmetric matrices. Israel J. Math. 131, 259–268

    MATH  MathSciNet  Google Scholar 

  2. Beenakker, C.W.J.: Random-matrix theory of quantum transport. Rev. Modern Phys. 69(3) (1997)

  3. Brody, T.A., Flores, J., French, J.B., Mello, P.A., Pandey, A., Wong, S.S.M.: Random-matrix physics: spectrum and strength fluctuations. Rev. Modern Phys. 53(3) (1981)

  4. Dodel, S.: Data driven analysis of brain activity and functional connectivity in fMRI. Göttingen University (2000)

  5. Dodel S., Herrmann J.M., Geisel T. (2000) Localization of brain activity—blind separation for fMRI data. Neurocomputing 32–33, 701–708

    Google Scholar 

  6. Dodel, S., Herrmann, J.M., Geisel, T.: Stimulus-independent data analysis for fMRI. In: Emergent Neural Computational Architectures Based on Neuroscience—Towards Neuroscience-Inspired Computing. Lecture Notes in Computer Science 2036, pp. 39–53. Springer, Berlin Heidelberg New York (2001)

  7. Guhr, T., Ma, J.-Z., Meyer, S., Wilke, T.: Statistical analysis and the equivalent of a thouless energy in lattice qcd dirac spectra. Phys. Rev. D 59 (1999)

  8. Mehta M.L. (1991) Random Matrices. Academic, Boston

    MATH  Google Scholar 

  9. Voultsidou M., Dodel S., Herrmann J.M. (2005) Neural networks approach to clustering of activity in fmri data. IEEE Trans. Med. Imaging 12(8): 987–996

    Article  Google Scholar 

  10. Wigner E.P. (1967) Random matrix theory in physics. SIAM Rev. 9, 1–23

    Article  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Physics, University of Crete, P.O. Box 2208, Heraklion, Crete, Greece

    Marotesa Voultsidou

  2. Center for Complex Systems and Brain Sciences, Florida Atlantic University, 777 Glades Road, Boca Raton, FL, 33431, USA

    Silke Dodel

  3. Institut für Nichtlineare Dynamik, Universität Göttingen, Bunsenstr. 10, 37073, Göttingen, Germany

    J. Michael Herrmann

Authors
  1. Marotesa Voultsidou
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Silke Dodel
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. J. Michael Herrmann
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to J. Michael Herrmann.

Additional information

Communicated by G.Wittum.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Voultsidou, M., Dodel, S. & Herrmann, J.M. Feature evaluation in fMRI data using random matrix theory. Comput. Visual Sci. 10, 99–105 (2007). https://doi.org/10.1007/s00791-006-0037-6

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00791-006-0037-6

Keywords

Search

Navigation