Non-Gaussian Component Analysis

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Description

The function performs Non-Gaussian Component Analysis as described in Blanchard et.al. (2005).

Usage

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ngca(data, L=c(1000,1000,1000), T=10, m=3, eps=1.5, npca=min(dim(x)[2],
     dim(x)[1]), filter.time="None", filter.space=FALSE, method="temporal",
     dg.trend = 2, h.space=3, h.time=3, keepv=TRUE, delta = NULL)

Arguments

data

Observation matrix (dimension Nxd)

L

Number basis functions in each of four classes.

T

Number of Fast ICA iterations

m

Number of non-Gaussian components.

eps

Threshold (defaults to 1.5)

npca

Reduce space to npca principal components. This can be used to avoid standardizing by numerically singular covariance matrices. In fMRI this allows to reduce the dimensionality assuming that the interesting non-Gaussian directions are also characterized by larger variances.

filter.time

Choice of temporal filtering before analysis: "None", "Low", "Both", "High" (default "None")

filter.space

Choice of spatial filtering before analysis: logical, default FALSE

method

Either "spatial" or "temporal". Specifies the type of NGCA to perform.

dg.trend

not yet documented

h.space

bandwidth for spatial filtering. default 3

h.time

bandwidth for temporal filtering. default 3

keepv

if TRUE intermediate results from fast ICA step are kept.

delta

not yet documented

Details

The function performs Non-Gaussian Component Analysis as described in Blanchard et.al. (2006). The procedure uses four classes of basis functions, i.e. Gauss-Power3, Hyperbolic Tangent and the real and complex part of the Fourier class. See Blanchard et.al. (2005) for details.

Value

The function returns a list with components

ihat

Matrix containing the first m NGCA directions as columns.

sdev

Standard deviations of the principal components of the thresholded ICA directions

xhat

first m components of the rotated data

v

If keepv==TRUE the set of directions v^{(k)}

normv

If keepv==TRUE the norm of each v^{(k)}.

...

Author(s)

J\"org Polzehl polzehl@wias-berlin.de

References

Blanchard, G., Kawanabe, M., Sugiyama, M., Spokoiny, V. and M\"uller K.-R. (2005). In Search of Non-Gaussian Components of a High-Dimensional Distribution. Journal of Machine Learning Research. pp. 1-48.