Graphics Reference
In-Depth Information
Central mass:
)=
n
n
i
=
exp
y
d
′
(−
i
y
i
)−
exp
(−
)
I
CM
(
A
d
−
exp
(−
)
T
is an n
where
XA
=
Y
=[
y
,
y
,
,
y
n
]
d matrix of the projected data.
LDA:
′
A
WA
I
LDA
(
A
)=
−
A
′
(
W
+
B
)
A
g
i
=
n
i
X
i.
X
..
X
i.
X
..
g
i
=
X
i.
X
i.
n
i
j
=
′
arethe“between” and“within” sum-of-squaresmatrices fromlineardiscriminant
analysis, g
′
where
B
=
(
−
)(
−
)
,
W
=
(
X
ij
−
)(
X
ij
−
)
=
is the number of groups, n
i
, i
=
,...,g is the number of cases in
each group.
PCA:
his is only defined for d
=
.
n
i
=
n
Y
n
′
y
i
I
PCA
(
A
)=
Y
=
T
is an n
where
XA
=
Y
=[
y
, y
,
, y
n
]
d matrix of the projected data.
Figure
.
shows the results of using different indices on the same data. he holes
index finds a projection where there is a gap between two clusters of points. he
central mass index finds a projection where a few minor outliers are revealed. he
LDA index finds a projection where three clusters can be seen. he PCA index finds
atrimodaldataprojection.
Manual Controls
Manual controls enable the user to manually rotate a single variable into or out of
a projection. his gives fine-tuning control to the analyst. Cook and Buja (
) has
details on the manual controls algorithm. It is similar to a method called spiders
proposed by Du
n and Barrett (
).
Figure
.
illustrates theuseofmanual controls toexamine theresultsoftheLDA
index (top let plot, also shown at bottom let in Fig.
.
). In this view there are three
very clearly separated clusters of points. he projection is mostly PC
(a large posi-
tive coe
cient), with smaller coe
cients for PC
and PC
. he remaining PCs have
effectively zerocoe
cients. Weexplore the importance of these small coe
cients for
the three-cluster separation. From the optimal projection given by the LDA index
we manually rotate PC
out of the projection and follow by rotating PC
out of the
projection:
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
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.
.
A
=
