Principal components analysis (PCA): For the analysis, we introduce

advertisement
Principal components analysis (PCA): For the analysis, we introduce the following notation.
Let Jt , i; , s  be the current density in voxel i, as estimated by LORETA, in condition  at t
time-frames after stimulus onset for subject s. Let area :Voxel fBA be a function, which
assigns to each voxel i  Voxel the corresponding fBA b  fBA. In a first pre-processing step,
we calculate for each subject s the value of 
the current density averaged over each fBA
(1)
xt , b;  , s  
1
Nb
 J t , i; , s 
ib
where Nb is the number of voxels in the fBA b, in condition  for subject s.
 In the second analysis stage, the mean current density x t,b;,s from each fBA b, for every
subject s and condition, was subjected to spatial PCA analysis of the correlation matrix and

varimax rotation
In the present study the spatial PCA uses the above-defined fBAs as variables sampled
along the time epoch for which EEG has been sampled (0-1000ms; 512 time-frames), and the
inverse solution was estimated. Spatial matrices (each matrix was sized b x t = 36 × 512
elements) for every subject and condition were collected, and subjected to PCA analyses,
including the calculation of the covariance matrix; eigenvalue decomposition and varimax
rotation, in order to maximize factor loadings. In other words, in the spatial PCA analysis we
approximate the mean current density for each subject in each condition as
(2)
xt; , s   x 0  , s    ck (t )x k  , s  ,
k
where here xt;,s  R36 is a vector, which denotes the time-dependent activation of the
fBAs, x 0  ,s is their mean activation, and x k  ,s and c k are the principal components and
 corresponding coefficients (factor loadings) as computed using the principal component
their
 analysis.


References:
(1) Arzouan Y, Goldstein A, Faust M. Brainwaves are stethoscopes: ERP correlates of
novel metaphor comprehension. Brain Res 2007; 1160: 69-81.
(2) Arzouan Y, Goldstein A, Faust M. Dynamics of hemispheric activity during metaphor
comprehension: electrophysiological measures. NeuroImage 2007; 36: 222-231.
(3) Chapman RM, McCrary JW. EP component identification and measurement by
principal components analysis. Brain and cognition 1995; 27: 288-310.
(4) Dien J, Frishkoff GA, Cerbone A, Tucker DM. Parametric analysis of event-related
potentials in semantic comprehension: evidence for parallel brain mechanisms. Brain
research 2003; 15: 137-153.
(5) Dien J, Frishkoff GA. Principal components analysis of event-related potential
datasets. . In: Handy T (ed). Event-Related Potentials: A Methods Handbook.
Cambridge, Mass MIT Press; 2004.
(6) Potts GF, Dien J, Hartry-Speiser AL, McDougal LM, Tucker DM. Dense sensor array
topography of the event-related potential to task-relevant auditory stimuli.
Electroencephalography and clinical neurophysiology 1998; 106: 444-456.
(7) Rosler F, Manzey D. Principal components and varimax-rotated components in eventrelated potential research: some remarks on their interpretation. Biological psychology
1981; 13: 3-26.
(8) Ruchkin DS, McCalley MG, Glaser EM. Event related potentials and time estimation.
Psychophysiology 1977; 14: 451-455.
(9) Spencer KM, Dien J, Donchin E. Spatiotemporal analysis of the late ERP responses to
deviant stimuli. Psychophysiology 2001; 38: 343-358.
(10)
Squires KC, Squires NK, Hillyard SA. Decision-related cortical potentials
during an auditory signal detection task with cued observation intervals. Journal of
experimental psychology 1975; 1: 268-279.
(11)
van Boxtel A, Boelhouwer AJ, Bos AR. Optimal EMG signal bandwidth and
interelectrode distance for the recording of acoustic, electrocutaneous, and photic
blink reflexes. Psychophysiology 1998; 35: 690-697.
Download