Graphics Reference
In-Depth Information
In Fig.
.
(let) the pairwise scatterplots suggest there is some clustering of the data
pointsinthissix-variabledataset.hetourprojection(right)revealsthreewell-separ-
ated clusters. he projection revealing the clusters is:
−
.
.
tars
tars
head
aede
aede
aede
−
.
−
.
.
.
−
A
=
.
.
.
.
−
−
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which is primarily a combination of three of the six variables: tars
, aede
, aede
.
Tours
2.2
Most of us are familiar with
-D rotation, which is something we can do in the real
world. We can take an object and rotate it with our hands or walk around an object
to view it from all sides. Views of p-dimensional data can be computed in analogous
ways,byrotatingtheentire p-dimensionaldata(Wegman,
;Carretal.,
;Tier-
ney,
)orbymovinga d
-dimensionalplanethroughthespaceandprojecting
the data onto it. he latter approach is like looking at the data from different sides.
Movement of aprojection plane isachieved byselecting a starting plane anda tar-
get plane and computing intermediate planes using a geodesic interpolation. A geo-
desic is a circular path, which is generated by constraining the planar interpolation
to produce orthonormal descriptive frames. his is the method used in GGobi. It is
more complicated to compute but it has some desirable properties, primarily that
within-plane spin is eliminated by interpolating from plane to plane, rather than
frame to frame. he frame that describes the starting plane is carried through the
sequence of intermediate planes, preventing the data from rotating within the plane
ofview.hatis,weavoiddoingarotationofthedataasinFig.
.
.histypeofwithin-
plane rotation is distracting to the viewer, akin to viewing a scene while standing on
(<
p
)
Figure
.
.
Two different frames that describe the same plane, and the resulting rotated views of the
data
