A Visualization and Level-of-Detail Control Technique for Large Scale
Time Series Data
Yumiko Uchida∗

Takayuki Itoh†

Ochanomizu UniversityOchanomizu University

1 I NTRODUCTION
We have various interesting time series data in our daily life, such as
weather data (e.g., temperature and air pressure) and stock prices.
Polygonal line chart is one of the most common ways to represent
such time series data. We often draw multiple polygonal lines in
one space to compare the time variation of multiple values. However, it is often difficult to read the values if the number of polygonallines gets larger.
This poster presents a technique for visualization and level-ofdetail control of large number of time series data. The techniquegenerates clusters of time series values, and selects representativevalues for each cluster, as a preprocessing. The technique thendraws the representative values as polygonal lines. It also provides
a user interface so that users can interactively select interesting representatives, and explore the time series values which belong to theclusters of the representatives.
2 R ELATED W ORK
Readability of jammed lines is a common problem of information
visualization techniques, including graph drawing and parallel coordinates. Recently several novel techniques for the problem havebeen presented. Holten’s technique bundles edges of hierarchicalgraph data applying spline curves [1]. Ellis et al. presented a technique to sample edges of parallel coordinates to simplify the visualization results [2].
There have been several works on novel polygonal line chart
tools for visualization of time series data. Wattenberg et al., presented a sketch-based query interface to search for specific shapesof polygonal lines [3]. Hochheiser et al., presented a gradient- andrange-based query interface for polygonal lines [4].
3 P ROPOSED T ECHNIQUE
3.1 Technical Overview
This poster supposes the following time series data, consisting ofa set of values V = (v1 , v2 , ..., vn ), where vi = (vi1 , vi2 , ..., vim ), andvi j denotes the i-th value at the j-th time. We draw the set of values
as a polygonal line chart, where the horizontal axis denotes the 1stto the m-th time, and the vertical axis denote the magnitude of thevalues.
The presented technique first generates a grid surrounding thedrawing area, and calculates the positions of polygonal lines of thevalues. It then clusters the polygonal lines using the grid, and selects representative values for each cluster, as a preprocessing. It
then draws the representative values as polygonal lines. This approach drastically eases up the jam of polygonal lines and provides
the simplified view of the time series data, without missing its interesting features.
The presented technique also provides a user interface so thatusers can interactively select interesting representative polygonal∗ e-mail: yumi-ko@itolab.is.ocha.ac.jp† e-mail:itot@is.ocha.ac.jp

lines, by directly clicking, or drawing their shapes. Specifying the representative polygonal lines, the technique draws nonrepresentative polygonal lines belonging to the clusters of the specified representatives. The user interface is useful to interactively
explore the interested parts of the time series data from the simplified view.
3.2 Preprocessing: Clustering and Representative
Polygonal Line Selection
Figure 1 shows the overview of the preprocessing of the presentedtechnique. The technique first samples the time along x-axis, andtemporarily quantizes the values along y-axis. The technique thengenerates groups of polygonal lines, for each of intervals between tth and (t + 1)-th sampled times. Here, the technique assigns the twopolygonal lines to the same group, if both of the quantized values
at t-th and (t + 1)-th times are equal.
It then cancels the quantized values, and applies a clustering algorithm for each of the groups. Our current implementation firstclips the polygonal lines by t-th and (t + 1)-th sampled times, andthen simply calculates the distances of the clipped polygonal lines
for the clustering. If the clipped polygonal lines contain k time steps
between t-th and (t + 1)-th sampled times, the technique regards
them as k-dimensional vectors, and calculates Euclidian distancesamong them.

QuantizeTwo values are in the samegroup in this time period.
Clustering

Figure 1: Overview of the preprocessing. (Upper) Grouping of values
according to the quantized values, for each interval of the sampledtimes. (Lower) Clustering of the grouped values.

The technique then selects a representative polygonal line foreach cluster. Here, if one of the polygonal lines in a cluster has
been already selected as the representative of another cluster, thetechnique preferentially selects it as the representative of the current cluster, so that we can reduce the total number of representatives. Otherwise, our current implementation simply extracts thepolygonal line, which is the closest to the center of the cluster, as
the representative.
The representative selection result depends on the order of process of clusters. Our current implementation applies the following
orders:• In the order of importance of times.
• In the order of number of polygonal lines in the clusters.

SketchSketch

3.3 Visualization and Level-of-Detail Control
Initially our technique draws only the representative polygonallines. Here, number of representatives depends on the resolution of the grid and the threshold of the clustering process. Ourcurrent implementation prepares several configurations of the gridand the clustering process, and generates several clustering results.
Smoothly replacing the clustering results, our technique seamlessly
displays several levels of numbers of representatives, as if typicalpolygon-based computer graphics techniques switch several levelsof polygon models for the level-of-detail control. Figure 2 shows
an example of level-of-detail control.

Figure 3: Sketch interface. (Left) Time-varying values which havepartial shapes similar to the sketched curve, and pass near the drawn
region, are highlighted. (Right) Time-varying values which have partial shapes similar to the sketched curve are highlighted, even if theyare far away from the drawn region.

ClickSketch

ClickFigure 4: Various highlighting of specified polygonal lines. (Left)
Highlighting of the non-representative polygonal lines, which belong
to the clusters of the clicked representative. (Right) Highlighting bymultiple colors. In this example, values specified by a sketch operation are highlighted in red, and ones specified by a click operation
are in green. Values specified by the both operations are in yellow.

4 C ONCLUSION AND F UTURE W ORKS
This poster presented visualization and level-of-detail technique forpolygonal line charts of large number of time series values. Thefollowing issues will be our future works:

Figure 2: Level-of-detail control. Upper-left figure shows the all timevarying data, and other three figures show the different levels of numbers of representatives.

• Various representation. For example, we would like to represent the number of polygonal lines which belong to the clusters of the representative, by widths or colors of the representatives.
• Applications to various time series data.
• Subjective evaluation by user experiments.

3.4 GUIThe technique provides a user interface to interactively select theinteresting representatives.
The technique provides a click interface, so that users can specify interesting representatives by directly clicking them. It also
provides a sketch interface, so that users can specify interesting
representatives which have partial shapes similar to the sketchedcurves. Figure 3 shows examples of the visualization results using
the sketch interface.
The technique highlights the specified representatives, reacting
to the operations of the above user interface. Also, the technique
can reactivate the non-representative polygonal lines, which belong
to the clusters of the representatives. The technique assigns multiple colors to the specified polygonal lines, so that users can visually
distinguish the interesting values specified by the multiple operations. This interface helps users to explore interesting time series
values. Figure 4 shows examples of the highlighting of polygonallines.

• Integration and linkage with other visualization techniques,
such as time-varying volume visualization techniques.
R EFERENCES[1] D. Holten, Hierarchical Edge Bundles: Visualization of Adjacency
Relations in Hierarchical Data, IEEE Transaction on Visualization andComputer Graphics, Vol. 12, No. 5, pp. 741-748, 2006.
[2] G. Ellis, A. Dix, Enabling Automatic Clutter Reduction in Parallel
Coordinate Plots, IEEE Transaction on Visualization and ComputerGraphics, Vol. 12, No. 5, pp. 717-723, 2006.
[3] M. Wattenberg, D. Jones, Sketching a Graph to Query a Time-Series
Database, Processing of the SIGCHI Conference on Human Factors in
Computing Systems Extended Abstract (CHI2001), pp. 381-382, 2001.
[4] H. Hochheiser, B. Shneiderman, Dynamic Query Tools for Time Series Data Sets: Timebox Widgets for Interactive Exploration, Information Visualization, Vol. 3, No. 1, pp. 1-18, 2004.