Graphics Reference
In-Depth Information
What are the exceptions?
A useful representation must provide clear answers to these questions.
Inaddition, Csinger (
)referstothe Steven andWeberlawsonhuman percep-
tive capabilities and highlights two basic behaviors of human perception: (i)differ-
encesareperceivedintermsofrelativevariations;(ii)humanperceptionofvariations
is biased and the bias isagainst valuing distances and gradually becomes morefavor-
able toward areas, volumes, and colors.
Traditional(sometimesoverused)factorialmapsanddendrograms,thankstotheir
full correspondence to Bertin's principles, are very popular. Moreover, giving the
maximum prominence to distances, these representations are very helpful in min-
imizing biased perceptions.
In addition, to enrich information that can be transmitted through
-D repre-
sentations, Bertin introduces seven visual variables: position, form, orientation, color,
texture, value,andsize.
he display in Fig.
.
was realized from a real dataset and was chosen because
it is a good example to understand how to read this kind of enriched visualization.
At this point it is not relevant to know which data are represented: in Sect.
.
the
actual informative potentiality of enriched representations will beshown in practice.
Looking at Fig.
.
, the reader can appreciate how the inertia (of the first two PCs) is
distributed among the statistical units and according to the factorial axes. In partic-
ular, units are visualized by means of pies: sizes are calculated according to the total
contribution of each statistical unit; the slice color denotes the share of contribution
toeachfactor(accordingly colored).Influential units arecharacterizedbythebiggest
pies and can be easily and quickly identified even if there are thousands of points on
the plot.
It is possible to obtain a similar representation using either the absolute contri-
butions or the square cosinus associated with the points. hey consist of coe
cients
computable for each axis allowing one to interpret the axes in terms of the units and
the adequacy of the unit representations, respectively (Lebart et al.,
). In partic-
ular:
. Absolutecontributions,whichindicatetheproportionofexplainedvariance
by each variable with respect to each principal axis.
. Squared correlations, which indicate the part of the variance of a variable
explained by a principal axis.
It is also possible to represent both the above measures using an index for drawing
the pies and the other to attribute different brightnesses to the points (a darker point
could denote a high value of the index associated to it).
In the case of cluster representation, it is possible to query a given cluster on the
factorial plane in order to visualize its internal composition (in terms of both units
and variables) through the use of “drill-down” functionalities.
Obviously, clustering methods can be either nonhierarchical or hierarchical. It is
clear that in the case of a hierarchical method that exploits linking functionalities, it
is also possible to link two different views of the same data (the dendrogram and the
factorial plane) in order to obtain more information (Sect.
.
).
