eegica: Independent Component Analysis of EEG Data
In eegkit: Toolkit for Electroencephalography Data

Description Usage Arguments Details Value Note Author(s) References Examples

Computes temporal (default) or spatial ICA decomposition of EEG data. Can use Infomax (default), FastICA, or JADE algorithm. ICA computations are conducted via icaimax, icafast, or icajade from the ica package.

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eegica(X, nc, center = TRUE, maxit = 100, tol = 1e-6,
       Rmat = diag(nc), type = c("time", "space"),
       method = c("imax", "fast", "jade"), ...)

`X`	Data matrix with `n` rows (channels) and `p` columns (time points).
`nc`	Number of components to extract.
`center`	If `TRUE`, columns of `X` are mean-centered before ICA decomposition.
`maxit`	Maximum number of algorithm iterations to allow.
`tol`	Convergence tolerance.
`Rmat`	Initial estimate of the `nc`-by-`nc` orthogonal rotation matrix.
`type`	Type of ICA decomposition: `type="time"` extracts temporally independent components, and `type="space"` extracts spatially independent components.
`method`	Method for ICA decomposition: `method="imax"` uses Infomax, `method="fast"` uses FastICA, and `method="jade"` uses JADE.
`...`	Additional inputs to `icaimax` or `icafast` function.

ICA Model The ICA model can be written as X = tcrossprod(S, M) + E, where columns of S contain the source signals, M is the mixing matrix, and columns of E contain the noise signals. Columns of X are assumed to have zero mean. The goal is to find the unmixing matrix W such that columns of S = tcrossprod(X, W) are independent as possible.

Whitening Without loss of generality, we can write M = P %*% R where P is a tall matrix and R is an orthogonal rotation matrix. Letting Q denote the pseudoinverse of P, we can whiten the data using Y = tcrossprod(X,Q). The goal is to find the orthongal rotation matrix R such that the source signal estimates S = Y %*% R are as independent as possible. Note that W = crossprod(R,Q).

Infomax The Infomax approach finds the orthogonal rotation matrix R that (approximately) maximizes the joint entropy of a nonlinear function of the estimated source signals. See Bell and Sejnowski (1995) and Helwig (in prep) for specifics of algorithms.

FastICA The FastICA algorithm finds the orthogonal rotation matrix R that (approximately) maximizes the negentropy of the estimated source signals. Negentropy is approximated using

J(s) = [E\{G(s)\}-E\{G(z)\} ]^2

where E denotes the expectation, G is the contrast function, and z is a standard normal variable. See Hyvarinen (1999) for specifics of fixed-point algorithm.

JADE The JADE approach finds the orthogonal rotation matrix R that (approximately) diagonalizes the cumulant array of the source signals. See Cardoso and Souloumiac (1993,1996) and Helwig and Hong (2013) for specifics of the JADE algorithm.

`S`	Matrix of source signal estimates (`S=Y%*%R`).
`M`	Estimated mixing matrix.
`W`	Estimated unmixing matrix (`W=crossprod(R,Q)`).
`Y`	Whitened data matrix.
`Q`	Whitening matrix.
`R`	Orthogonal rotation matrix.
`vafs`	Variance-accounted-for by each component.
`iter`	Number of algorithm iterations.
`type`	ICA type (same as input).
`method`	ICA method (same as input).

If type="time", the data matrix is transposed before calling ICA algorithm (i.e., X = t(X)), and the columns of the tranposed data matrix are centered.

Nathaniel E. Helwig <helwig@umn.edu>

Bell, A.J. & Sejnowski, T.J. (1995). An information-maximization approach to blind separation and blind deconvolution. Neural Computation, 7, 1129-1159.

Cardoso, J.F., & Souloumiac, A. (1993). Blind beamforming for non-Gaussian signals. IEE Proceedings-F, 140, 362-370.

Cardoso, J.F., & Souloumiac, A. (1996). Jacobi angles for simultaneous diagonalization. SIAM Journal on Matrix Analysis and Applications, 17, 161-164.

Helwig, N.E. (2018). ica: Independent Component Analysis. http://CRAN.R-project.org/package=ica

Helwig, N.E. & Hong, S. (2013). A critique of Tensor Probabilistic Independent Component Analysis: Implications and recommendations for multi-subject fMRI data analysis. Journal of Neuroscience Methods, 213, 263-273.

Hyvarinen, A. (1999). Fast and robust fixed-point algorithms for independent component analysis. IEEE Transactions on Neural Networks, 10, 626-634.

##########   EXAMPLE   ##########

# get "c" subjects of "eegdata" data
data(eegdata)
idx <- which(eegdata$group=="c")
eegdata <- eegdata[idx,]

# get average data (across subjects)
eegmean <- tapply(eegdata$voltage,list(eegdata$channel,eegdata$time),mean)

# remove ears and nose
acnames <- rownames(eegmean)
idx <- c(which(acnames=="X"),which(acnames=="Y"),which(acnames=="nd"))
eegmean <- eegmean[-idx,]

# get spatial coordinates (for plotting)
data(eegcoord)
cidx <- match(rownames(eegmean),rownames(eegcoord))

# temporal ICA with 4 components
icatime <- eegica(eegmean,4)
icatime$vafs
# quartz()
# par(mfrow=c(4,2))
# tseq <- (0:255)*1000/255
# for(j in 1:4){
#   par(mar=c(5.1,4.6,4.1,2.1))
#   sptitle <- bquote("VAF:  "*.(round(icatime$vafs[j],4)))
#   eegtime(tseq,icatime$S[,j],main=bquote("Component  "*.(j)),cex.main=1.5)
#   eegspace(eegcoord[cidx,4:5],icatime$M[,j],main=sptitle)
# }

# spatial ICA with 4 components
icaspace <- eegica(eegmean,4,type="space")
icaspace$vafs
# quartz()
# par(mfrow=c(4,2))
# tseq <- (0:255)*1000/255
# for(j in 1:4){
#   par(mar=c(5.1,4.6,4.1,2.1))
#   sptitle <- bquote("VAF:  "*.(round(icaspace$vafs[j],4)))
#   eegtime(tseq,icaspace$M[,j],main=bquote("Component  "*.(j)),cex.main=1.5)
#   eegspace(eegcoord[cidx,4:5],icaspace$S[,j],main=sptitle)
# }