Graphics Reference
In-Depth Information
lapped. It is blinded by the assumption that the three classes have equal variance-
covariance. Quadratic discriminant analysis does better in making a rule but cannot
provide a good picture of the solution. he solution of black-box methods such as
forestsand neuralnetworks aregenerally di
cult tounderstand,butbymappingout
a picture of the class structure of these data using a tour we can better understand
how they have worked and the resulting solution.
Tours can help numerical approaches in many ways: to choose which of the tools
at hand works best for a particular problem, to understand how the tools work in
a particular problem, and to overcome the limitations of a particular tool to improve
the solution.
End Notes
2.4
here are numerous recent developments in tours that should be noted. Huh and
Kim (
) describes a grand tour with trailing tails marking the movement of the
points in previous projections. he tour can be constructed in different projection
dimensions and constraints. Yang (
) describes a grand tour with
-D data pro-
jectionsinvirtualenvironments.hecorrelationtourdescribedbyBujaetal.(
b),
and available in GGobi,runs two independent tours of
-Dprojections on horizontal
andvertical axes. hispaperalso describesconstraining thetourtospecial subspaces
such as principal components or canonical coordinates. XGobi (Swayne et al.,
)
contained tools for freezing some axes and touring in the constrained complement
space, and also a section tour, where points outside a fixed distance from the projec-
tionplacewereerased.Wegmanetal.(
)andSymanziketal.(
)discussatour
on the multivariate measurements constrained on spatial locations, which is similar
to the multivariate time series tour discussed in Sutherland et al. (
), where
-D
projections are shown against a time variable.
In summary, tours support exploring real-valued data. hey deliver many projec-
tions of real-valued data in an organized manner, allowing the viewer to see the data
from many sides.
References
Asimov, D. (
). he grand tour: a tool for viewing multidimensional data, SIAM
J Sci Stat Comput
(
):
-
.
Asimov, D. and Buja, A. (
). he grand tour via geodesic interpolation of
-
Frames, Visual Data Exploration and Analysis, Symposium on Electronic Imaging
Science and Technology,IS&T/SPIE.
Buja,A.andAsimov,D.(
a).Grandtourmethods:anoutline,Comput Sci Stat
:
-
.
Buja,A.,Asimov,D.,Hurley,H.andMcDonald,J.A.(
).ElementsofaViewing
Pipeline for Data Analysis, in Cleveland, W.S. and McGill, M.E. (ed), Dynamic
Graphics for Statistics, Wadsworth, Monterey, CA, pp.
-
.
