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Computational and Mathematical Methods in Medicine
Volume 2014, Article ID 413801, 10 pages
http://dx.doi.org/10.1155/2014/413801
Research Article

Validation in Principal Components Analysis Applied to EEG Data

Biomedical Engineering Program, COPPE, Federal University of Rio de Janeiro, P.O. Box 68510, 21941-972 Rio de Janeiro, RJ, Brazil

Received 1 May 2014; Revised 13 August 2014; Accepted 14 August 2014; Published 8 September 2014

Academic Editor: Ezequiel López-Rubio

Copyright © 2014 João Carlos G. D. Costa et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Linked References

  1. J. C. Gower, “Some distance properties of latent root and vector methods used in multivariate analysis,” Biometrika, vol. 53, no. 3-4, pp. 325–338, 1966. View at Publisher · View at Google Scholar · View at MathSciNet
  2. I. T. Jolliffe, Principal Component Analysis, Springer Series in Statistics, Springer, New York, NY, USA, 2nd edition, 1986. View at Publisher · View at Google Scholar · View at MathSciNet
  3. W. J. Krzanowski, “Sensitivity in metric scaling and analysis of distance,” Biometrics, vol. 62, no. 1, pp. 239–244, 2006. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  4. L. Lebart, “Which bootstrap for principal axes methods?” in Selected Contributions in Data Analysis and Classification, Studies in Classification, Data Analysis and Knowledge Organization, pp. 581–588, Springer, New York, NY, USA, 2007. View at Google Scholar · View at MathSciNet
  5. B. Efron, “Bootstrap methods: another look at the jackknife,” The Annals of Statistics, vol. 7, no. 1, pp. 1–26, 1979. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  6. M. Linting, J. J. Meulman, P. J. F. Groenen, and A. J. van der Kooij, “Stability of non-linear principal components analysis: an empirical study using the balanced bootstrap,” Psychological Methods, vol. 12, no. 3, pp. 359–379, 2007. View at Publisher · View at Google Scholar · View at Scopus
  7. G. Pfurtscheller, D. Flotzinger, and J. Kalcher, “Brain-computer interface—a new communication device for handicapped persons,” Journal of Microcomputer Applications, vol. 16, no. 3, pp. 293–299, 1993. View at Publisher · View at Google Scholar · View at Scopus
  8. C. M. Krause, L. Sillanmäki, M. Koivisto et al., “The effects of memory load on event-related EEG desynchronization and synchronization,” Clinical Neurophysiology, vol. 111, pp. 2071–2078, 2000. View at Google Scholar
  9. W. Klimesch, “EEG alpha and theta oscillations reflect cognitive and memory performance: a review and analysis,” Brain Research Reviews, vol. 29, no. 2-3, pp. 169–195, 1999. View at Publisher · View at Google Scholar · View at Scopus
  10. L. Lebart, A. Morineau, and K. M. Warwick, Multivariate Descriptive Statistical Analysis: Correspondence Analysis and Related techniques for Large Matrices, John Wiley & Sons, New York, NY, USA, 1984. View at MathSciNet
  11. G. H. Golub and C. F. van Loan, Matrix Computations, John Hopkins University Press, Baltimore, Md, USA, 3rd edition, 1996. View at MathSciNet
  12. R. B. Cattell, “The Scree test for the number of factors,” Multivariate Behavioural Research, vol. 1, no. 1, pp. 245–276, 1966. View at Google Scholar
  13. D. A. Jackson, “Stopping rules in principal components analysis: a comparison of heuristical and statistical approaches,” Ecology, vol. 74, no. 8, pp. 2204–2214, 1993. View at Publisher · View at Google Scholar · View at Scopus
  14. B. Efron and R. Tibshirani, “Bootstrap methods for standard errors, confidence intervals, and other measures of statistical accuracy,” Statistical Science, vol. 1, no. 1, pp. 54–75, 1986. View at Google Scholar · View at MathSciNet
  15. P. Diaconis and B. Efron, “Computer-intensive methods in statistics,” Scientific American, vol. 248, no. 5, pp. 116–131, 1983. View at Publisher · View at Google Scholar
  16. D. G. Altman and P. Royston, “What do we mean by validating a prognostic model?” Statistics in Medicine, vol. 19, pp. 453–473, 2000. View at Google Scholar
  17. F. E. Harrel Jr., K. L. Lee, and D. B. Mark, “Multivariable prognostic models: issues in developing models, evaluating assumptions and adequacy, and measuring and reducing errors,” Statistics in Medicine, vol. 15, pp. 361–387, 1996. View at Google Scholar
  18. B. Efron, “Estimating the error rate of a prediction rule: improvement on cross-validation,” Journal of the American Statistical Association, vol. 78, no. 382, pp. 316–331, 1983. View at Publisher · View at Google Scholar · View at MathSciNet
  19. L. Milan and J. Whittaker, “Application of the parametric bootstrap to models that incorporate a singular value decomposition,” Applied Statistics, vol. 44, no. 1, pp. 31–49, 1995. View at Publisher · View at Google Scholar
  20. R. Sibson, “Studies in the robustness of multidimensional scaling: procrustes statistics,” Journal of the Royal Statistical Society B: Methodological, vol. 40, no. 2, pp. 234–238, 1978. View at Google Scholar
  21. H. S. M. Coxeter, Regular Polytopes, Dover, New York, NY, USA, 2nd edition, 1973. View at MathSciNet
  22. W. F. Eddy, “A new convex hull algorithm for planar sets,” ACM Transactions on Mathematical Software, vol. 3, no. 4, pp. 398–403, 1977. View at Google Scholar
  23. B. Efron, “Bootstrap confidence intervals: good or bad?” Psychological Bulletin, vol. 104, no. 2, pp. 293–296, 1988. View at Publisher · View at Google Scholar · View at Scopus
  24. R. Dubes and A. K. Jain, “Validity studies in clustering methodologies,” Pattern Recognition, vol. 11, no. 4, pp. 235–254, 1979. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at Scopus
  25. A. D. Gordon, “A review of hierarchical classification,” Journal of the Royal Statistical Society A, vol. 150, no. 2, pp. 119–137, 1987. View at Publisher · View at Google Scholar · View at MathSciNet
  26. G. W. Milligan and P. D. Isaac, “The validation of four ultrametric clustering algorithms,” Pattern Recognition, vol. 12, no. 2, pp. 41–50, 1980. View at Publisher · View at Google Scholar · View at Scopus
  27. S. M. Kay and S. L. Marple Jr., “Spectrum analysis—a modern perspective,” Proceedings of the IEEE, vol. 69, no. 11, pp. 1380–1419, 1981. View at Publisher · View at Google Scholar · View at Scopus
  28. D. M. Simpson, C. J. Tierra-Criollo, R. T. Leite, E. J. B. Zayen, and A. F. C. Infantosi, “Objective response detection in an electroencephalogram during somatosensory stimulation,” Annals of Biomedical Engineering, vol. 28, no. 6, pp. 691–698, 2000. View at Publisher · View at Google Scholar · View at Scopus
  29. K. Paul, V. Krajča, Z. Roth, J. Melichar, and S. Petránek, “Quantitative topographic differentiation of the neonatal EEG,” Clinical Neurophysiology, vol. 117, no. 9, pp. 2050–2058, 2006. View at Publisher · View at Google Scholar · View at Scopus
  30. R Core Team, R: A Language and Environment for Statistical Computing, R Foundation for Statistical Computing, Viena, Austria, 2012.
  31. H. Bengtsson, “R.matlab: Read and write of MAT files together with R-to-Matlab conectivity,” R package version 1.7.0, 2013, http://CRAN.R-project.org/package=R.matlab.
  32. Signal Developers, “Signal: signal processing,” 2011, http://r-forge.r-project.org/projects/signal.
  33. E. Dimitriadou, K. Hornik, F. Leisch, D. Meyer, and A. Weingessel, “e1071: misc functions of the department of statistics (e1071),” 2011, http://CRAN.R-project.org/package=e1071.
  34. H. W. Borchers, “Pracma: Practical Numerical Math Functions (pracma),” 2014, http://CRAN.R-project.org/package=pracma.
  35. E. Guadagnoli and W. F. Velicer, “Relation of sample size to the stability of components patterns,” Psychological Bulletin, vol. 103, no. 2, pp. 265–275, 1988. View at Publisher · View at Google Scholar · View at Scopus
  36. E. W. Steyerberg, M. J. C. Eijkemans, F. E. Harrell Jr., and J. D. F. Habbema, “Prognostic modeling with logistic regression analysis: in search of a sensible strategy in small data sets,” Medical Decision Making, vol. 21, no. 1, pp. 45–56, 2001. View at Publisher · View at Google Scholar · View at Scopus
  37. R. M. V. R. Almeida, A. F. C. Infantosi, J. H. R. Suassuna, and J. C. G. D. Costa, “Multiple correspondence analysis in predictive logistic modelling: application to a living-donor kidney transplantation data,” Computer Methods and Programs in Biomedicine, vol. 95, no. 2, pp. 116–128, 2009. View at Publisher · View at Google Scholar · View at Scopus
  38. S. Casarotto, A. M. Bianchi, S. Cerutti, and G. A. Chiarenza, “Principal component analysis for reduction of ocular artefacts in event-related potentials of normal and dyslexic children,” Clinical Neurophysiology, vol. 115, no. 3, pp. 609–619, 2004. View at Publisher · View at Google Scholar · View at Scopus
  39. T. Kobayashi and S. Kuriki, “Principal component elimination method for the improvement of S/N in evoked neuromagnetic field measurements,” IEEE Transactions on Biomedical Engineering, vol. 46, no. 8, pp. 951–958, 1999. View at Publisher · View at Google Scholar · View at Scopus
  40. A. Daffertshofer, C. J. C. Lamoth, O. G. Meijer, and P. J. Beek, “PCA in studying coordination and variability: a tutorial,” Clinical Biomechanics, vol. 19, no. 4, pp. 415–428, 2004. View at Publisher · View at Google Scholar · View at Scopus
  41. I. Milovanović and D. B. Popović, “Principal component analysis of gait kinematics data in acute and chronic stroke patients,” Computational and Mathematical Methods in Medicine, vol. 2012, Article ID 649743, 8 pages, 2012. View at Publisher · View at Google Scholar
  42. P. J. G. da Silva, J. Nadal, and A. F. C. Infantosi, “Investigating the center of pressure velocity Romberg's quotient for assessing the visual role on the body sway,” Revista Brasileira de Engenharia Biomedica, vol. 28, no. 4, pp. 319–326, 2012. View at Publisher · View at Google Scholar · View at Scopus
  43. S. Slobounov, M. Hallett, S. Stanhope, and H. Shibasaki, “Role of cerebral cortex in human postural control: an EEG study,” Clinical Neurophysiology, vol. 116, no. 2, pp. 315–323, 2005. View at Publisher · View at Google Scholar · View at Scopus
  44. A. F. C. Infantosi and A. M. F. L. Miranda de Sá, “A statistical test for evaluating the event-related synchronization/desynchronization and its potential use in brain-computer-interfaces,” in Proceedings of the IFMBE, Latin American Congress on Biomedical Engineering, vol. 18, pp. 1122–1136, Margarita Island, Venezuela, 2007.
  45. P. J. G. Da_Silva, A. M. F. L. Miranda de Sá, and A. F. C. Infantosi, “Dynamic visual stimulation effects on cortical response EEG desynchronization,” in IFMBE Proceedings, World Congress on Medical Physics and Biomedical Engineering, vol. 99, pp. 1573–1576, Beijing, China, 2012.
  46. N. R. Draper and J. A. John, “Influential observations and outliers in regression,” Technometrics, vol. 23, no. 1, pp. 21–26, 1981. View at Publisher · View at Google Scholar · View at MathSciNet