GeneralizedProcrustes function

Generalized Procrustes Analysis

GeneralizedProcrustes(x, tolerance = 1e-05, maxiter = 100, Plot = FALSE)

Arguments

• x: Three dimensional array with the configurations. The first dimension contains the rows of the configurations, the second contains the columns and the third the number of configurations. So x[,,i] is the i-th

  configuration

• tolerance: Tolerance for the Procrustes algorithm.

• maxiter: Maximum number of iterations

• Plot: Should the results be plotted?

Details

Generalized Procrustes Analysis for several configurations contained in a three-dimensional array.

Returns

An object of class GenProcustes.This has components: - History: History of Iterations

• X: Initial configurations in a three dimensional array

• RotatedX: Transformed configurations in a three dimensional array

• Scale: Scale factors for each configuration

• Rotations: Rotation Matrices in a three dimensional array

• rss: Residual Sum of Squares

• Fit: Goodness of fit as percent of expained variance

References

Gower, J.C., (1975). Generalised Procrustes analysis. Psychometrika 40, 33-51.

Ingwer Borg, I. & Groenen, P. J.F. (2005). Modern Multidimensional Scaling. Theory and Applications. Second Edition. Springer

Author(s)

Jose Luis Vicente-Villardon

See Also

PrincipalCoordinates

Examples

data(spiders)
n=dim(spiders)[1]
p=dim(spiders)[2]
prox=array(0,c(n,2,4))

p1=BinaryProximities(spiders,coefficient=5)
prox[,,1]=PrincipalCoordinates(p1)$RowCoordinates
p2=BinaryProximities(spiders,coefficient=2)
prox[,,2]=PrincipalCoordinates(p2)$RowCoordinates
p3=BinaryProximities(spiders,coefficient=3)
prox[,,3]=PrincipalCoordinates(p3)$RowCoordinates
p4=BinaryProximities(spiders,coefficient=4)
prox[,,4]=PrincipalCoordinates(p4)$RowCoordinates
GeneralizedProcrustes(prox)