Graphics Reference
In-Depth Information
. understanding that the relational information resides in the crossings,
.
concentrating the relational information in the data into clear patterns that
eliminate the need for polygonal lines altogether
. his last point is illustrated
bythe“proximateplanes”example,whichencouragesresearchintoe
cient(par-
allel) algorithms for accomplishing this on general datasets. We eliminate the
“clutter” by reducing the display into patterns corresponding, at least approxi-
mately, to the multivariate relations in the data.
Before we dive into the specifics of
-coords,we provide a visualization challenge for
the reader to ponder. For a plane
π
c
x
c
x
c
x
c
,
(
.
)
+
+
=
allow the coe
cients to each vary within a small interval. his generates a family of
“close” (let's call them proximate)planes:
−
+
i
Π
=
π
c
x
+
c
x
+
c
x
=
c
, c
i
[
c
i
, c
]
, i
=
,
,
,
(
.
)
hese are the planes generated by small rotations and translations of π with respect
to the three coordinate axes. Together they form a “twisted slab” which, even in
-D
using orthogonal axes, isdi
cult to visualize. Conversely, given lots of points in
-D,
how can we show (using
any
general visual methodyou can think of) that theylie on
a twisted slab, and howcan we visualize sucha formprecisely;for N
andthenfor
any N? In the meantime, you can project, pursue, scale, reduce, scintillate, regress,
corollate or tribulate to your heart's content, but please do not peek at the answer,
which is given at the end of the chapter.
=
Exploratory Data Analysis with
-coords
14.2
Multidimensional Detective
14.2.1
Parallel coordinates transform multivariate relations into
-D patterns suitable for
exploration and analysis. For this reason they are included in lots of sotware tools.
hequeries“ParallelCoordinates+Sotware”onGooglereturnedabout
,
“hits”
and “Scatterplot matrix + Sotware” about
,
at the time of writing. Irrespective
of the apparent relative ratio, the fact that the numbers are comparable astounded
me, having heard the appellations “esoteric,” “unnatural,” “di
cult,” “squiggly,” and
others used in association with
-coords.
he exploration (the venerable name “exploratory data analysis,” EDA, is used in-
terchangeably with the currently more fashionable “visual data mining”) paradigm
is that of a detective, starting from the data, searching for clues leading to conjec-
tures, testing, backtracking until voila ...the “culprit” isdiscovered.hetask ises-
pecially intricate when many variables (i.e., dimensions) are involved, which calls
for the employment of a multidimensional detective (abbrev. MD). As if there were
