EEG, Nonparametric Multivariate Statistics, and Dementia Classification
We are considering the problem of performing statistical inference with functions as independent or dependent variables. Specifically, we will work with the spectral density curves of electroencephalographic (EEG) measurements. These represent the distribution of the energy in the brain on different frequencies and therefore provide important information on the electric activity of the brain. We have data of 315 patients with various forms of dementia. For each individual patient, we have one measurement on each of 17 EEG channels. We will look at three different methods to reduce the high dimensionality of the observed functions: 1. Modeling the functions as linear combinations of parametric functions, 2. The method of relative power (i.e., integration over prespecified intervals, e.g., the classical frequency bands), and 3. A method using random projections. The quantities that these methods return can then be analyzed using multivariate inference, for example, using the R package npmv (Ellis et al., J Stat Softw 76(1): 1–18, 2017, ). We include a simulation study comparing the first two methods with each other and consider the advantages and shortcomings of each method. We conclude with a short summary of when which method may be used.
KeywordsDimension reduction Functional data Multivariate inference Random projections Rank statistics
The chapter was finished during a research stay of the third author at the University of Warsaw supported by the grant of the Czech Ministry of Education, Youth and Sports.
- 1.Cannings, T.I., Samworth, R.J.: Random projection ensemble classification. arXiv:1504.04595 (2015)
- 2.Cannings, T.I., Samworth, R.J.: RPEnsemble: Random projection ensemble classification (2016). R package version 0.3Google Scholar
- 3.Coleman, T.F., Li, Y.: An interior trust region approach for nonlinear minimization subject to bounds. SIAM J. Optim. 6(2), 418–445 (1996)Google Scholar
- 4.Ellis, A.R., Burchett, W.W., Harrar, S.W., Bathke, A.C.: Nonparametric inference for multivariate data: the R package npmv. J. Stat. Softw. 76(1), 1–18 (2017)Google Scholar
- 5.Fahrmeir, L., Tutz, G.: Multivariate statistical modelling based on generalized linear models. Springer, New York (1994)Google Scholar
- 6.Ihl, R., Dierks, T., Martin, E.M., Frölich, L., Maurer, K.: Importance of the EEG in early and differential diagnosis of dementia of the Alzheimer type. Fortschritte der Neurologie-Psychiatrie 60(12), 451–459 (1992)Google Scholar
- 7.Johnson, W.B., Lindenstrauss, J.: Extensions of Lipschitz mappings into a Hilbert space. Contemp. math. 26(189–206), 1 (1984)Google Scholar
- 8.Klimesch, W., Doppelmayr, M., Russegger, H., Pachinger, T., Schwaiger, J.: Induced alpha band power changes in the human EEG and attention. Neurosci. Lett. 244(2), 73–76 (1998)Google Scholar
- 9.Rossini, P.M., Rossi, S., Babiloni, C., Polich, J.: Clinical neurophysiology of aging brain: from normal aging to neurodegeneration. Prog. Neurobiol. 83(6):375–400 (2007)Google Scholar
- 10.Shaobing, S.S., Donoho, D.L., Saunders, M.A.: Atomic decomposition by basis pursuit. SIAM J. Sci. Comput. 20(1), 33–61 (1998)Google Scholar
- 11.Vecchio, F., Babiloni, C., Lizio, R., Fallani, F.V. Blinowska, K., Verrienti, G., Frisoni, G., Rossini, P.M.: Resting state cortical EEG rhythms in Alzheimer’s disease: toward eeg markers for clinical applications: a review. Suppl. Clin. Neurophysiol. 62, 223–236 (2012)Google Scholar
- 12.Veselý, V., Tonner, J., Hrdličková, Z., Michálek, J., Kolář, M.: Analysis of PM10 air pollution in Brno based on generalized linear model with strongly rank-deficient design matrix. Environmetrics 20(6), 676–698 (2009)Google Scholar