Graphics Reference
In-Depth Information
Figure . . Concept of the relativity of a statistical graph for a continuous dataset (the Iris data)
he relativity concept does not usually hold for a matrix visualization or paral-
lel coordinates type of display, since one can easily destroy the property with a ran-
dom permutation. Itis common practice toapply various permutation algorithms to
sort the columns and rows of the designated matrix, so that similar (different) sam-
ples/variables are permuted to make them closer (more distant) rows/columns.
Global Criterion: Robinson Matrix
It is usually desirable to permute a matrix to make it resemble a Robinson matrix
(Robinson, ) as closely as possible, because of the smooth and pleasant visual
effect of permuted matrix maps. A symmetric matrix is called a Robinson matrix if
its elements satisfy r ij
k.Iftherowsand
columns of a symmetric matrix can be permuted to those of a Robinson matrix, we
callitpre-Robinson.Foranumericalcomparison, threeanti-Robinson lossfunctions
(Streng, ) are calculated for each permuted matrix, D
r ik if j
k
i and r ij
r ik if i
j
<
<
<
<
=
d ij
,fortheamountof
deviation from a Robinson form with distance-type proximity:
,
p
i =
AR
i
I
d ij
d ik
I
d ij
d ik
(
)=
j < k < i
(
<
)+
i < j < k
(
)
,
)= p
AR
(
s
I
(
d ij
<
d ik
d ij
d ik
+
i < j < k
I
(
d ij
d ik
d ij
d ik
j < k < i
i =
.
)= p
AR
(
w
I
(
d ij
<
d ik
)
j
k
d ij
d ik
+
i < j < k
I
(
d ij
d ik
)
j
k
d ij
d ik
j < k < i
i =
AR
i
counts only the number of anti-Robinson events in the permuted matrix;
(
)
AR
s
sumstheabsolutevaluesoftheanti-Robinsondeviations;AR
w
isaweighted
(
)
(
)
version of AR
(
s
)
penalizedbythedifferenceinthecolumnindicesofthe twoentries.
Elliptical Seriation
Chen ( )introduced a permutation algorithm called rank-two elliptical seriation
that extracts the elliptical structure of the converging sequence of iteratively formed
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