Sequential Methods for Parametric Discriminant Analysis of the EEG during Sleep

  • L. E. Larsen


In previous pattern recognition studies of the human EEG during sleep (Larsen and Walter 1969 and 1970), a method described as a “two-stage machine” was applied in order to improve classification success rates in a training/testing design (Larsen et al. 1971) with spectral based description of the electroencephalogram (EEG). The same notions were applied to chimpanzee EEG sleep data by Larsen et al. (1972 and 1973) with similar results. The method was based on the idea of a layered decision process aimed first at discriminating two aggregates of groups followed by a later discrimination for the groups within each aggregate taken separately. The aggregates of groups were determined on the basis of cross-group clustering in a discriminant space3 of two dimensions. This paper reports further studies on a possible theoretical basis for the efficacy of the two-stage machine as well as a means to determine aggregate structure and when the technique may be profitably employed.


Direction Cosine Test Space Dispersion Matrix Equal Likelihood Original Coordinate System 
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  1. Anderson, T.W. 1963. Asymptotic theory for principal components analysis. Ann. Math. Stat. 34:122.CrossRefGoogle Scholar
  2. Anderson, T.W., and Bahadur, R.R. 1962. Classification into two multivariate normal distributions with different covariance matrices. Ann. Math. Stat. 33:420.CrossRefGoogle Scholar
  3. Chang, C.L. 1973. Pattern recognition by piecewise linear discriminant functions. IEEE Transactions on Computers, C-22(9), p. 859.CrossRefGoogle Scholar
  4. Dixon, W.J. (ed.) 1968. BMD Biomedical computer programs. Health Sciences Computing Facility, UCLA School of Medicine, Los Angeles, California.Google Scholar
  5. Johnson, L.C, Lubin, A., Naitoh, P., Nute, D., and Austin, M. 1969. Spectral analysis of the EEG in dominant and non-dominant subjects during waking and sleeping. Electroencephalogr. Clin. Neurophysiol. 26:361.PubMedCrossRefGoogle Scholar
  6. Larsen, L.E., Ruspini, E.H., McNew, J.J., Walter, D.O., and Adey, W.R. 1972. A test of sleep staging systems in the unrestrained chimpanzee. Brain Res. 40:319.PubMedCrossRefGoogle Scholar
  7. Larsen, L.E., Ruspini, E.H., McNew, J.J., Walter, D.O., and Adey, W.R., 1973. Classification and discrimination of the EEG during sleep. In P. Kellaway and I. Petersen (eds.), Automation of Clinical Electroencephalography. New York: Raven Press, p. 243.Google Scholar
  8. Larsen, L.E., and Walter, D.O. 1969. On automatic methods of sleep staging by spectra of electroencephalograms. Agressologie 10 (special number):1.Google Scholar
  9. Larsen, L.E., and Walter, D.O. 1970. On automatic methods of sleep staging by EEG spectra. Electroencephalogr. Clin. Neurophysiol. 28:459.PubMedCrossRefGoogle Scholar
  10. Larsen, L.E., Walter, D.O., McNew, J.J., and Adey, W.R. 1971. On the problem of bias in error rate estimation for discriminant analysis. Pattern Recognition 3:217.CrossRefGoogle Scholar
  11. Lawley, D.N., and Maxwell, A.E. 1963. Factor Analysis as a Statistical Method. London: Butterworths.Google Scholar
  12. Rao, C.R. 1963. The use and interpretation of principal components analysis in applied research. Washington, D.C.: U.S. Office of Education Contract Report 2-10-065.Google Scholar
  13. Rao, C.R. 1966. Discriminant function between composite hypotheses and related problems. Biometrika 53:339.Google Scholar

Copyright information

© Plenum Press, New York 1975

Authors and Affiliations

  • L. E. Larsen
    • 1
  1. 1.Walter Reed Army Institute of ResearchUSA

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