FGalgorithm-package {FGalgorithm} | R Documentation |
Execute the Flury and Gautschi diagonalisation algorithm, which tries to simultaneously diagonalize a set of symmetric positive definite matrices.
Description
The minimization of the objective function
is required for a potpourri of statistical problems.
This algorithm (Flury & Gautschi, 1984) is designed to find an orthogonal matrix
of dimension
such that
for all orthogonal matrices B.
The matrices ,...,
are positive-definite and are usually sample covariance matrices
and
s are positive real numbers.
It can be shown (Flury, 1983) that if , then
the following system of equations holds:
where
In other words, Flury and Gautschi algorithms find the solution of the above system of equations.
Also, this algorithm can be used to find the maximum likelihood estimates of common principal components in k
groups (Flury,1984).
Details
Package: | FGalgorithm |
Type: | Package |
Version: | 1.0 |
Date: | 2012-11-14 |
License: | GPL (>= 2) |
Author(s)
Dariush Najarzadeh
Maintainer: Dariush Najarzadeh <D_Najarzadeh@sbu.ac.ir>
References
Flury, B. N. (1983), "A generalization of principal component analysis to k groups", Technical Report No. 83-14, Dept. of Statistics, Purdue University.
Flury, B. N. (1984). Common principal components in k groups. Journal of the American Statistical Association, 79(388), 892-898.
Flury, B. N., & Gautschi, W. (1984). An algorithm for simultaneous orthogonal transformation of several positive definite symmetric matrices to nearly diagonal form. SIAM Journal on Scientific and Statistical Computing, 7(1), 169-184.