Graphics Reference
In-Depth Information
. henumericalvaluesofeach N-tuple(i.e.,eachdatapoint)shouldberecoverable
fromthescatterplot matrix (abbr.SM)andthe
-coordsdisplay.Bycontrast, this
may not be necessary or desirable for presentation graphics.
. Inthepairwisescatterplotmatrix,theN variables appear N
(
N
−
)
times.
By contrast there are only N axes in
-coords, although there is an additional
preprocessing cost, as pointed out later. For N
, the practical barriers due
to the required display space and visual di
culties limit the use of a SM. hese
barriers are less stringent for
-coords.
. Even when the perspective is used effectively, orthogonal coordinates are inher-
ently limited to N
due to the dimensionality of our existence. With some
“trickery,” the illusion of a few more dimensions can be added. For
=
-coords,
implementation capabilities rather than conceptual barriers determine the max-
imum feasible N.
. In the “Chernoff faces” display, for example, each variable corresponds to a spe-
cific facial feature and is treated accordingly. he correspondence facial feature
variableisarbitrary. Choosingadifferentcorrespondencegives adifferentdis-
play.hefunisthatthereisnogeneralwaytoshowthatthetwodifferentdisplays
portray the same dataset. Of course, this is also true for general “glyph” displays.
. his is true for SM and for
-coords, although it has not been implemented in
general. Incidentally, this is a wonderful M.Sc. thesis topic!
. he real value of visualization, in my opinion, is not the ability to see “zillions of
objects,” but to recognize
relations
among them. We know that projections lose
information, which can possibly be recovered using interactivity. Nevertheless,
important clues that can guide the interaction are lost. So I prefer to start with
a display where all of the information is there even though it may be tricky to
uncover. What visual cues are available and how they guide the exploration are
crucial determining factors.
. he value of rigor is self-evident.
hese and additional issues comprising the discovery process are better appreciated
via the exploration of three real datasets. he basic queries are introduced in the first
example from GIS and are subsequently combined, with boolean operators, for use
on financial data. An example with
variables is briefly discussed before mov-
ing on to automatic classification. Visualization and
-coords play key roles in the
algorithm's conception, internal functions and the visual presentation of the classi-
fication rule. he minimal basis of the variables is found and ordered according to
their predictive value.
he overview at the end provides background on optimizing the use of
-coords
and its applications. his involves:
. learning patterns corresponding to the basic relations and seeking them out for
EDA,
. understanding the design and use of queries,
. the relevance of
-coords to other sophisticated statistical applications like re-
sponse surfaces (Gennings et al.,
), and
. applications to regression, as in the example at the end,
