# cov4: Scatter Matrix based on Fourth Moments In ICS: Tools for Exploring Multivariate Data via ICS/ICA

## Description

Estimates the scatter matrix based on the 4th moments of the data.

## Usage

 `1` ```cov4(X, location = "Mean", na.action = na.fail) ```

## Arguments

 `X` numeric data matrix or dataframe, missing values are not allowed. `location` can be either `Mean`, `Origin` or numeric. If numeric the matrix is computed wrt to the given location. `na.action` a function which indicates what should happen when the data contain 'NA's. Default is to fail.

## Details

If location is `Mean` the scatter matrix of 4th moments is computed wrt to the sample mean. For location = `Origin` it is the scatter matrix of 4th moments wrt to the origin. The scatter matrix is standardized in such a way to be consistent for the regular covariance matrix at the multinormal model. It is given for n x p matrix X by

1/(p+2) ave{[(x_i-x_bar)S^{-1}(x_i-x_bar)'] (x_i-x_bar)'(x_i-x_bar)},

where x_bar is the mean vector and S the regular covariance matrix.

A matrix.

Klaus Nordhausen

## References

Cardoso, J.F. (1989), Source separation using higher order moments, in Proc. IEEE Conf. on Acoustics, Speech and Signal Processing (ICASSP'89), 2109–2112. <doi:10.1109/ICASSP.1989.266878>.

Oja, H., Sirkiä, S. and Eriksson, J. (2006), Scatter matrices and independent component analysis, Austrian Journal of Statistics, 35, 175–189.

## Examples

 ```1 2 3 4 5 6``` ```set.seed(654321) cov.matrix <- matrix(c(3,2,1,2,4,-0.5,1,-0.5,2), ncol=3) X <- rmvnorm(100, c(0,0,0), cov.matrix) cov4(X) cov4(X, location="Origin") rm(.Random.seed) ```

ICS documentation built on March 18, 2018, 1:14 p.m.