A Polyline-Based Visualization Technique for Tagged Time-Varying Data
Department of Computer Science
1Introduction

We have various interesting large scale timevarying data in our daily life (such as ﬁnancial trading, and meteorological data), and they are commonly represented as polyline charts. Consequently,
if hundreds or thousands of polylines are rendered ina single space, it may result in severe cluttering, andthis may cause diﬃculty in reading data values andfollowing data trends.
Several recent works have tried to address thisproblem. Hochheiser et al.[1] presented a gradientand range-based query interface for polyline-based
time-varying data visualization. Uchida et al.[2] presented a time-varying data visualization techniques,featuring sketch query on the clustered view. However, these techniques have dealt with polylines basedon their data values or shapes, and do not use associated information.
Meanwhile, such information may be tightly correlated with the time-varying values. For example,
air temperatures can be associated with weather attributes, blood pressure and electrocardiogram canbe associated with descriptions of activities and soforce. However, it is not always easy to determine thecorrelation between them. We believe it should be
useful if time-varying data visualization techniques
simultaneously display such associated information
to assist the understanding of the correlation.
This thesis presents a new time-varying data visualization technique which supposes the associatedinformation is attached as tags of the values of eachtime step.
2Level-of-detail control for time varying
data visualization

The technique supposes the following taggerd timevarying data, consisting of a set of values P =(p1 , p2 , ..., pn ) represented as n polylines. we describe the tags of the i-th polyline as wi =(wi1 , wi2 , ..., wim ); wij denotes the tag at the j-thtime of the i-th polyline, and the values of a polyline
as pi = (pi1 , pi2 , ..., pim ); pij denotes the value at thej-th time of the i-th polyline. We draw the set ofvalues as a polyline chart, while the horizontal axis
denotes the 1st to the m-th time, and the verticalaxis denote the magnitude of the values.
2.1

Sayaka Yagi

2. Sample P at the time t0 to ta , and temporarily
quantize the sampled values at b0 to bb . Here,bi is the value at the i-th horizontal line of thegrid.
3. Generate groups of polylines, if the polylines
have the same quantized values both at ti−1 andti (as shown in Figure 1(b)).
4. Clip polylines of a group by ti−1 and ti and generate clusters of the clipped polygons (as shownin Figure 1(c)).

Figure 1: Quantization and clipping of polyline.

Figure 2 denotes the procedure, while the colors ofpolylines denote their dominant tags. Here, the technique regards the clipped polylines as n-dimensional
vectors, while they contain n time steps between ti−1
and ti . Procedure for clustering of tagged polylines
is as follows.
1. Divide the clipped polylines according to tags,
using a dendrogram from the polylines constructed according to similarities of their ndimensional vectors (wjti−1 , ..., wjti ) (as shownin Figure 2(b)).
2. Apply a non-hierarchical clustering (e.g. kmeans) to the polylines in each cluster, using
their n-dimensional vectors (pjti−1 , ..., pjti ), andgenerate clusters consisting of similarly tagged
and shaped fragments of polylines (as shown inFigure 2(c)).
3. Select representative polylines for each cluster(as shown in Figure 2(d)).
(a) Clipped polylines(b) Tag-based clustering

Clustering and representative polyline selection

The procedure of quantization and clipping step is
as follows.
1. Generate a grid covering the drawing area, andthen divides into a × b subspaces(as shown inFigure 1(a)).

(c) Shape-based clustering(d) Representative polylines

Figure 2: Clustering of polylines.

2.2Interactive Visualization

The technique represents the time-varying data as
colored polylines. It assigns colors to the tags anddraws the polyline in the assigned colors. If the vertices of a segment of a polyline have diﬀerent tags, itinterpolates the colors along the segments.
Initially our technique draws only the representative polylines. Our current implementation generates
several clustering results, with several conﬁgurationsof the grid and the clustering process. Smoothly replacing the clustering results, our technique seamlessly displays several levels of numbers of representatives.
The technique also provides click and sketch interfaces, so that users can specify interesting representatives by directly clicking or sketching particularshapes. When a user clicks a point on the display,
the technique calculates distances between the point
and all segments of the drawn polylines. If at least
one of the segments of a polyline is enough close to
the clicked point, the technique highlights the current
polyline. When a user draws a curve on the display,
the technique samples several points on the curve,and calculates distances between the sampled points
and all segments of the drawn polylines. If at least
one of the segments of a polyline is enough close toeach of the sampled points, the technique highlights
the current polyline as shown in Figure 3.
Users can specify particular tags to be extracted by
the above query operations. It can highlight only theparts of the polylines corresponding to the speciﬁedtags while the click or sketch operations. Also, it canreactivate only the parts of the non-representative
polylines corresponding to the speciﬁed tags.

green, ”Rainy” in blue, and ”Snowy” in cyan. Exceptionally it draws the segments in gray if we cannot obtain the weather data. While using click or
sketch interfaces, our implementation draws selectedpolylines brightly, and others in gray.
Figure 4 shows a zoom up view of temperature
variation during ﬁve days. Figure 4(a) shows theoriginal view of the tagged temperature data before applying level-of-detail control, and Figure 4(b)shows after applying level-of-detail control with tagbased clustering. Figure 4(a) has many overlaps ofpolylines, especially non-tagged ones colored in gray.
While Figure 4(b) represents the features of the data
more clearly. In Figure 4(b), we can ﬁnd that extremely lower temperature can be often observed
from ”Clear” or ”Sunny” points. It is diﬃcult toobtain such knowledge from the visualization resultswith shape-based clustering without considering tags,
as shown in Figure 4(c).

Figure 4: Zoom up view: (a) without level-of-detail control.
(b) with level-of-detail control (tag-based clustering). (c) withlevel-of-detail control (shape-based clustering).

4Figure 3: Sketch interface.

3Examples

We applied Japanese weather data recorded byAMeDAS (Automated Meteorological Data Acquisition System) to the presented technique. We extracted time-varying temperature data observed at376 points in every 3 hours. We then assigned
weather tags including ”Clear”, ”Sunny”, ”Cloudy”,”Rainy”, and ”Snowy” to temperature value of eachtime of each point.
Our implementation draws the segments of ”Clear”
polylines in red, ”Sunny” in yellow, ”Cloudy” inConclusion

This thesis presented a polyline-based visualization
technique for tagged time-varying data. By using thetechnique, we can easily observe overall features without missing detailed features of tags, while reducing
cluttering among polylines.
The following issues will be our future work:• Discuss more eﬀective representation for:– more kinds of (e.g. more than 10) tags.
– multiple tags at a point.
• Add features to the technique so that we canfocus on time-varying value variations with particular patterns of tag changes.
Reference[1] H. Hochheiser, B. Shneiderman, Dynamic query tools
for time series data sets: Timebox widgets for interactive exploration, Information Visualization, 3(1):1-18,2004.
[2] Y. Uchida, T. Itoh, A visualization and level-of-detailcontrol technique for large scale time series data, 13th
International Conference on Information Visualisation, 80-85, 2009.