Graphics Reference
In-Depth Information
. Ifthepointswereoriginallyinap-dimensional space, the first p eigenvalues of
B
p are zero. Discard these from Λ (rename
as Λ
), and discard the corresponding eigenvalues from
are nonzero and the remaining n
−
V
(rename as
V
).
Λ
. Find
X=V
, and then the coordinates of the points are given by the rows
of
X
.
As an example, rather than use distances between cities and towns in the UK, the
cost of rail travel between all pairs of the following mainland terminus rail stations
wereused:Aberdeen,Birmingham,Blackpool,Brighton,Dover(Priory),Edinburgh,
Inverness, Liverpool, London, Newcastle upon Tyne, Norwich, Plymouth, She
eld,
Southampton, Swansea. Figure
.
shows a plot of the stations having obtained the
coordinates using the above algorithm. his solution is not unique since any trans-
lation, rotation or reflection of the configuration of points will give rise to another
solution.
Figure
.
.
A map of rail stations using classical scaling
