Information Technology Reference
In-Depth Information
RAC
AtMr
-0.02
-0.02
CmRb
CrJk
0.04
0.1
0.15
-0.01
0.02
-0.02
-0.04
-0.02
InAs
G
au
t
0.04
0.1
-0.1
-0.02
-0.0
-0.01
0.05
DrgR
0.02
0.05
CmRb
DrgR
KZN
AtMr
0
-0.04
InAs
PubV
Mrd
0
.
0
2
0.2
0.
0
1
WCpe
2
Cm
A
s
0
0.1
2
CmAs
0.005
0.02
1
-0.05
-0.05
0.04
NWst
NCpe
BNRs
Ars
BRs
-0.04
-0.02
Mpml
FrSt
Lim
p
0.05
0.01
0.02
0.01
ECpe
0.1
0.02
0.02
Rape
0.04
-0.04
0.04
0.02
0.02
AGBH
Figure 7.7
Two-dimensional CA biplot of the 2007/08 crime data set resulting from the
SVD
R
−
1
/
2
(
X
−
E
)
C
−
1
/
2
=
U
V
and plotting
U
and
V
. Predictions for the Western
Cape are illustrated.
argument
lambda = TRUE
a biplot is obtained in which it is much easier to use the
biplot axes for prediction purposes. Note that low-dimensional approximations to
e
ij
can
become negative for poorly approximated elements, where the original element is close
to zero (see Table 7.15).
Recall from Section 7.2.3 that, as a result of using
R
−
1
/
2
U
and
C
−
1
/
2
V
as coordi-
nates, the biplot shown in Figure 7.11 satisfies the centroid property that the row points
are given by the mean of the column points, weighted by the row means
R
−
1
X
.This
results in the clustering of the row points as they must all lie within the weighted cen-
troids of the column points. The origin represents the average weighting, given by the
elements of
C1
/
n
. If a row point coincides with a column point then all the weight for
that row must be associated with that column, the remainder being zero. More generally,
row points are attracted to column points with high weights. Column points collinear
