Graphics Reference
In-Depth Information
Concurrency of Functional Events
5.6.1
he standard assumption in functional data analysis is independence of the func-
tional observations in the data set. his assumption may not, however, always be
plausible. For instance, if the functional object represents the evolution of the price
inanonlineauction,thenitisquitepossiblethatthepricein one auctionisaffectedby
thepriceofanobjectin another action. hatis,ifthepriceinoneauction jumpstoan
unexpectedly high level, then this may cause some bidders to leave that auction and
move on to another auction of a similar item. his results in a dependence in price
between the two auctions. Or more generally, the result is a dependence between the
two functional objects. Capturing this kind of dependence in a mathematical model
is not a straightforward task. For a start, how can we unveil such a concurrency in
graphical fashion? One promising attempt in this direction is the work of Hyde et al.
(
), which suggests that rug plots canbeusedforthefunctionalobjectsandtheir
derivatives.
Dimensionality of Functional Data
5.6.2
Anotherchallenge whenvisualizing functional data isthedimensionality ofthedata.
As pointed out earlier, it is not uncommon for functional data to have three, four or
even moredimensions. Most standard visualization techniques work wellfor two di-
mensions at most, which is the number of dimensions of the paper that we write on
and the computer screen that we look at. Moving beyond two dimensions is a chal-
lenge in any kind of visualization task, including that of visualizing functional data.
Complex Functional Relationships
5.6.3
In addition to the high dimensionality, functional data is also oten characterized
by complex functional relationships. Take for instance the movement of a object
through time and space. his movement may be well characterized by a three- or
four-dimensional differential equation (Ramsay andSilverman,
).However,how
should we visualize a differential equation? One way is to use phase-plane plots like
that in Fig.
.
. Other approaches have been proposed in Schwalbe (
).
References
Aris,A.,Shneiderman,B.,Plaisant,C.,Shmueli,G.andJank,W.(
).Representing
unevenly-spaced time series data for visualization and interactive exploration. In:
International Conference on Human Computer Interaction (INTERACT
),
-
Sept
, Rome, Italy.
Card, S., Mackinlay, J. and Shneiderman, B. (
). Readings in Information Visual-
ization: Using Vision to hink. Morgan Kaufmann, San Francisco, CA.
Chen, C. (
). Information Visualization: Beyond the Horizon. Springer, Berlin.
Cleveland, W.S., Shyu, M. and Becker, R. (
). he visual design and control of
trellis display. Journal of Computational and Graphical Statistics,
:
-
.
