Large-scale Generalized Procrustes Analysis

Source: R/lgpa.R

We modify generalized Procrustes analysis for large-scale data by first setting a subset of anchor points and applying the attained transformation to the rest data. If sub.id is a vector 1:dim(x)[1], it uses all observations as anchor points, reducing to the conventional generalized Procrustes analysis.

lgpa(x, sub.id = 1:(dim(x)[1]), scale = TRUE, reflect = FALSE)

Arguments

x

a \((k\times m\times n)\) 3d array, where \(k\) is the number of points, \(m\) the number of dimensions, and \(n\) the number of samples.

sub.id

a vector of indices for defining anchor points.

scale

a logical; TRUE if scaling is applied, FALSE otherwise.

reflect

a logical; TRUE if reflection is required, FALSE otherwise.

Value

a \((k\times m\times n)\) 3d array of aligned samples.

References

Goodall C (1991). “Procrustes Methods in the Statistical Analysis of Shape.” Journal of the Royal Statistical Society. Series B (Methodological), 53(2), 285--339. ISSN 00359246.

Author

Kisung You

Examples

if (FALSE) {
## This should be run if you have 'shapes' package installed.
library(shapes)
data(gorf.dat)

## apply anchor-based method and original procGPA
out.proc = shapes::procGPA(gorf.dat, scale=TRUE)$rotated # procGPA from shapes package
out.anc4 = lgpa(gorf.dat, sub.id=c(1,4,9,7), scale=TRUE) # use 4 points 
out.anc7 = lgpa(gorf.dat, sub.id=1:7, scale=TRUE)        # use all but 1 point as anchors

## visualize
opar = par(no.readonly=TRUE)
par(mfrow=c(3,4), pty="s")
plot(out.proc[,,1], main="procGPA No.1", pch=18)
plot(out.proc[,,2], main="procGPA No.2", pch=18)
plot(out.proc[,,3], main="procGPA No.3", pch=18)
plot(out.proc[,,4], main="procGPA No.4", pch=18)
plot(out.anc4[,,1], main="4 Anchors No.1", pch=18, col="blue")
plot(out.anc4[,,2], main="4 Anchors No.2", pch=18, col="blue")
plot(out.anc4[,,3], main="4 Anchors No.3", pch=18, col="blue")
plot(out.anc4[,,4], main="4 Anchors No.4", pch=18, col="blue")
plot(out.anc7[,,1], main="7 Anchors No.1", pch=18, col="red")
plot(out.anc7[,,2], main="7 Anchors No.2", pch=18, col="red")
plot(out.anc7[,,3], main="7 Anchors No.3", pch=18, col="red")
plot(out.anc7[,,4], main="7 Anchors No.4", pch=18, col="red")
par(opar)
}