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

 cov4 R Documentation

## Scatter Matrix based on Fourth Moments

### Description

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

### Usage

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 \times p matrix X by

\frac{1}{p+2} ave_{i}\{[(x_{i}-\bar{x})S^{-1}(x_{i}-\bar{x})'](x_{i}-\bar{x})'(x_{i}-\bar{x})\},

where \bar{x} is the mean vector and S the regular covariance matrix.

### Value

A matrix containing the estimated fourth moments scatter.

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

### Examples

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 Sept. 21, 2023, 9:07 a.m.