Graphics Reference
In-Depth Information
of cross-sectional data vs. time series data. While the information in cross-sectional
data can oten be displayed satisfactorily with the help of standard bar charts, box-
plots, histograms or scatter plots, time series data require special graphs that can
also capture the temporal information. he methods used to displaytime-series data
range from rather simple time-series plots, to streaming video clips for discrete time
series (Mills et al.,
), to cluster- and calendar-based visualization for more com-
plex representations (van Wijk and van Selow,
).
Functional data are different to ordinary data in both structure and concept, and
thus require special visualization methods. While the reasons for visualizing func-
tional data are similar to those for ordinary data, functional data entail additional
challenges that require extra attention. One such challenge is the creation of func-
tional observations. Functional data are typically obtained by recovering the con-
tinuous functional object from the discrete observed data via data-smoothing. he
implication of this is that there are two levels to the study of functional data. hefirst
level uses the discrete observed data to recover the continuous functional object. Vi-
sualizing data at this level is important for detecting anomalies that are related to the
data generation process, such as data collection and data entry, as well as for assess-
ing the fit of the smoothed curves to the discrete observed data. his is illustrated
and discussed further in Sect.
.
. he second and higher level of study operates on
the functional objects themselves. Since at this level the functional objects are the
observations of interest, visualization is now used for the same reasons mentioned
previously for ordinary data: to detect patterns and trends, possible relationships,
andalsoanomalies. InSect.
.
wedescribedifferentvisualizations that enhance data
comprehension and support more formal analyses.
he visualization of functional data has not received much attention in the litera-
turetodate.Mostoftheworkinthisarea hasfocusedonthederivation ofmathemat-
ical models for functional data, with visualization playing a minor role and typically
appearing only as asideproductof the analysis. Some noteworthy exceptions include
thedisplayofsummarystatistics, suchasthe mean andthevariability ofasetof func-
tional objects, the use of phase-plane plots to understand the interplay of dynamics,
and the graphing of functional principal components to study sources of variability
withinfunctional data (RamsayandSilverman,
).Anotherexception isthework
of Shmueli and Jank (
) and Hyde et al. (
), which is focused directly on the
visualization of functional data, and which suggests a few novel ideas for the display
of functional data, such as calendar plots and rug plots.
Most of the visualizations currently used for functional data are static in nature.
By “static” we mean a graph that can no longer be modified by the user without re-
running a piece of sotware code ater it has been generated. A static approach is
useful for differentiating subsets of curves by attributes (e.g., by using color), or for
spotting outliers. A static approach, however, does not permit an interactive explo-
rationofthedata.By“interactive”wemeanthattheusercanperformoperationssuch
aszooming inandout,filtering thedata, andobtaining details about thefiltereddata,
all within the environment of the graphical interface. Interactive visualizations that
can be used forthe special structure of functional data are not straightforward to de-
vise, and so solutions have only recently begun to receive consideration (Aris et al.,
