Graphics Reference
In-Depth Information
Figure
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Treemap of Google news headlines
Geometric Graphs
5.4
Geometric graphs form the basis for many data mining and analytic graphics meth-
ods. he reason for this is the descriptive richness of geometric graphs for character-
izing sets of points in a space. We will use some of these graphs in the next section,
for example, to develop visual analytics.
Given a set of points in a metric space, a geometric graph is defined by one or
more axioms. We can get a sense of the expressiveness of this definition by viewing
examples of these graphs on the same set of points in this section; we use data from
the famous Box-Jenkins airline dataset (Boxand Jenkins
),as shown in Fig.
.
.
We restrict the geometric graphs in this section to:
Undirected (edges consist of unordered pairs)
Simple (no edge pairs a vertex with itself)
Planar (there is an embedding in
R
with no crossed edges)
Straight (embedded edges are straight-line segments)
here have been many geometric graphs proposed for representing the “shape” of
asetofpointsX onaplane.Mostofthese areproximitygraphs. A proximity graph (or
neighborhood graph)isageometricgraphwhoseedgesaredeterminedbyanindicator
function based ondistances between agiven setofpoints in ametric space.Todefine
this indicator function, we use an open disk D.WesayDtouchesa point if that point
is on the boundary of D.WesayDcontainsa point if that point is in D.Wecallthe
