A POLYLINE-BASED VISUALIZATION TECHNIQUE FOR TAGGED TIME-VARYING DATA - Information Visualisation: Techniques, Usability and Evaluation - page 165

This technique initially displays representative polylines. By smoothly
switching clustering results, it can seamlessly change the number of
representative polylines to be displayed. Also, the technique provides a
click interface, so users can specify interesting representatives by clicking.
It also provides a sketch interface, so users can specify interesting
representatives which have partial shapes similar to the sketched curves.

Extension to the tagged time-varying data visualisation

This section proposes an extended visualization technique for tagged time-
varying data. This chapter extends the aforementioned time series data as
follows: we describe the tags of the i-th polyline as w i = (w i1 , w i2 , ..., w im );
w ij denotes the tag at the j-th time of the i-th polyline, as well as p ij
denoting the value at the j-th time of the i-th polyline.

Clustering and representative polyline selection

The extended technique displays an adequate number of representative
polylines to reduce cluttering among the polylines and improve
readability. The technique clips the polylines into several intervals, and
then generates clusters of clipped polylines for each interval, where
clipped polylines in a cluster are similarly shaped and tagged.
The technique first generates a grid covering the drawing area, and
then divides it into

a u subspaces, as shown in Fig. 9.1(a). This chapter
formalizes the grid as follows: h i is the i -th horizontal line of the grid
)

b

( 0 d i d b ( 0 d i d a )

, v i is the i -th vertical line of the grid , t i is the time at

v i , and b i is the value at h i .
The technique first samples P at t 0 to t a , and temporarily quantizes the
sampled values at b 0 to b b . The technique then generates groups of
polylines, if the polylines have the same quantized values both at t i-1 and t i ,
as shown in Fig. 9.1(b). It then clips polylines of a group by t i-1 and t i , as
shown in Fig. 9.1(c), and generates clusters of the clipped polylines.
The procedure for clustering tagged polylines is shown in Fig. 9.2,
where the colours of the polylines denote their dominant tags. Here, the
technique regards the clipped polylines as n -dimensional vectors, while
they contain n time steps between t i-1 and t i . This step first divides the
clipped polylines according to tags, as shown in Fig. 9.2 (b), using a
dendrogram from the polylines constructed according to similarities of

jt w . The technique then applies
a non-hierarchical clustering (e.g. k-means) to the polylines in each

( w , )

jt

their n -dimensional vectors …,

i 1 i