Correlation elimination in multivariate correlated data

A simple transformation method to diminish correlations between correlated variables.

USAGE: [Y CovY] = Correlation_elimination( X )

INPUT:
X denote multivariate original observations (correlated data)

OUTPUT:
Y denote the multivariate uncorrelated data

CovY is the covariance of Y
_________________________________________

Example:
Transform the multivariate Poisson-Weibull (X) data to new uncorrelated data (Y)

%Generating random data (using NORTA method)
corrZ=[1 0.5;0.5 1];
Z=mvnrnd([0 0],corrZ,1000);
X(:,1)=poissinv(normcdf(Z(:,1)),3);
X(:,2)=wblinv(normcdf(Z(:,1)),3,2);
X=X';
[Y CovY] = Correlation_elimination( X )

_________________________________________

This function transforms original correlated variables to uncorrelated variables.

It is useful to transform multivariate normal or non-normal data to new set of variables without correlations.

One of the applications of this function is in quality control area.
_________________________________________

See also skewreduction function by Babak, using following two functions together with transform original correlated data (X) to multivariate uncorrelated normal (close to normal) data:

[Y CovY] = Correlation_elimination( X )
[zt r sk]=skewreduction(y)

_________________________________________

References:

1- Niaki STA, Abbasi B. "A Transformation Technique in Designing Multi-Attributes C Control Charts," Scientia Iranica, International Journal of Science & Technology, 2008, 15(1), 125-130,

2-Niaki STA, Abbasi B. "Fault Diagnosis in Multivariate Control Charts Using Artificial Neural Networks," J. Qual. & Relia. Eng. Int., 2005, 21(8), 825-840,

3- Golnabi S., Houshmand A., "Multivariate Shewhart X-bar Chart" Internet Statistics, 4,—A web based journal (1999).