Graphics Reference
In-Depth Information
d
rs
for Shakespearean data
Figure
.
.
Histogram of d
rs
−
Procrustes Analysis
3.5
he classical scaling analysis and the non-metric scaling of the terminal train station
data produced different, but similar, configurations of points. Since arbitrary trans-
lations, rotations and reflections of these configurations give equally valid solutions.
In order to make a clear visual comparison of the two, we need to match one config-
uration with theother. hisis achieved using Procrustesanalysis. Procrustesanalysis
finds the isotropic dilation, translation, reflection and rotation that best match one
configuration to another. A detailed account of this and allied methods is given by
Gower and Dijksterhuis (
). (According to Greek mythology Procrustes was an
innkeeper living near Athens who would subject his guests to extreme measures to
make them fit his beds. If they were too short, he would stretch them, or if they were
too long, he would cut off their legs.)
Suppose a configuration of n points in a q-dimensional Euclidean space, with co-
ordinates given by the n by q matrix
, is to be matched to another configuration of
points in a p-dimensional Euclidean space
X
(
p
q
)
,withcoordinatesgivenbythen
by p matrix
. Note, it is assumed that the rth point in the X space is in a one-to-
one correspondence with the rth point in the Y space. First p
Y
−
q columns of zeros
areaddedtotheendofmatrix
X
in order to give the matrices the same dimensions.
