ChronoView: A Method to Overview Many Temporal Patterns
Kazuo Misue, Member, IEEE(a) Original View(b) Distorted View

Fig. 1. ChronoView representation of temporal tweet patterns (see Section 6 for more information).
Abstract—A temporal pattern is a set of timestamps that accompanies events. Temporal patterns contain diverse valuable informationand suggest tendencies of human activities, occurrences of accidents, etc. Therefore, it is important to identify distinguishing featuresof temporal patterns in event data. Many methods exist for representing time-oriented data. However, it is difficult to observe many
temporal patterns at a glance because most naive methods require a certain area to visualize a temporal pattern. This paper presents
a space-efficient technique for visualizing temporal patterns that facilitates simultaneous visualization of many event groups. Moreover,the limitation of this technique is experimentally studied and a modification is proposed to mitigate it.
Index Terms—Information visualization, Time-oriented data, Temporal patterns, Overview, ChronoView.

1

I NTRODUCTION

Numerous events occur daily: web pages are visited, tweets are sent,purchases are made, photos are taken, and hospitals are visited. Many ofthese events are recorded as log data. A set of such events is associatedwith a set of timestamps. This paper focuses on temporal patterns thatare features of timestamps. Fig. 2 shows examples of temporal patterns.
In the figure, each orange circle represents a timestamp. There arethree patterns: A, B, and C. These patterns have the following features:
Pattern A is independent of the time of day, B is concentrated in themorning, and C is extremely concentrated around 8 p.m.
Determining the temporal features of events is very important. Consider the following questions: Given a sales log, can we determine
when the products were sold? Given an incident log, can we determine
when the site was attacked? These are not simply questions abouttime, but also about features of timestamps, i.e., temporal patterns. To
determine temporal features, we need to overview temporal patterns.

• Kazuo Misue is with the University of Tsukuba.
E-mail: misue@cs.tsukuba.ac.jp.
Manuscript received xx xxx. 201x; accepted xx xxx. 201x. Date of Publication
xx xxx. 201x; date of current version xx xxx. 201x. For information on
obtaining reprints of this article, please send e-mail to: reprints@ieee.org.
Digital Object Identifier: xx.xxxx/TVCG.201x.xxxxxxx

Fig. 2. Examples of temporal patterns

Shneiderman [6] proposed an information-seeking mantra in which an
overview is first performed followed by zooming and filtering, and thendetails-on-demand are extracted. In the early stage of visual tasks, weneed a suitable overview of the data.
However, two kinds of problems are associated with providing an
overview of many temporal patterns. One problem is that a temporal
pattern occupies space. To illustrate a temporal pattern, strip charts(Fig. 2), histograms, and line charts may be used. The size of thesevisual representations often makes it difficult to encode many visual
patterns in a limited space. The other problem is the difficulty in finding
features. One method to observe many temporal patterns at a glance

is to lay out all possible histograms on a display. However, this does
not help us discover similar patterns and outliers because it illustrates
features of individual patterns.
In this paper, we present ChronoView, a method to visualize many
temporal patterns simultaneously. The defining feature of ChronoView
is that each event group (i.e., set of events) is represented by a position on a two-dimensional plane. This enables high space efficiency
when many patterns are involved; however, there exists ambiguity inrepresentation. We performed some experiments to characterize theambiguity and considered measures to reduce it.
2 R ELATED W ORK
Aris et al. aimed to treat unevenly spaced time series data and developed
several visualization methods [1], while Buono et al. developed a visualization tool for the interactive analysis of time series data [2]. These
tools enabled us to know event occurrences and find the co-occurrenceof several events by visualizing individual timestamps. Krstajić et al.
developed CloudLines to deal with time-based representations of large
and dynamic event data sets in limited space [7]. Their representation
adapts to the data by employing a decay function to let items fade away
according to their relevance. Nguyen et al. developed visualization
techniques for temporally referenced tags that exploit their text sizeand brightness [8].
Dragicevic et al. developed SpiraClock, which displays events in amanner analogous to that of an analog clock but with a spiral representation [4]. Carlis et al. developed a spiral visualization to represent boththe continuity of time and the periodicity of a week, month, or year [3].
This technique allows us to grasp the frequency and periodicity ofevents. Tominski et al. improved the existing spiral representation
using a two-tone pseudo-coloring method and interaction [9]. These
techniques help in easily analyzing multivariate data containing someperiodicity.
To obtain an overview of many temporal patterns, we need more
space-efficient methods.
3 C HRONOV IEW
We developed “ChronoView” [5], a method that facilitates the visualization of many temporal patterns in a limited area.

Fig. 3. ChronoView layout rulean event group and associates it with a position. This position is thebarycenter of the group’s event timestamp positions.
Function f0 places all timestamps on the circumference, while moving clockwise according to the time elapsed from t0 . If we consider U
to be the set of all timestamps, the position of a timestamp is expressedby the function f0 : U → R2 , given by
f0 (t) = (r cos θt , r sin θt )where r denotes the radius of the clock face circle. When the periodis c,t − t0πθt = − 2π.
(2)2cSuppose E is an event group (a finite set of events), i.e., E ={e1 , e2 , . . . , en } and t(e) denotes the timestamp of event e. We assign
the barycenter of the positions of t(ei ) (i = 1, . . . , n) to the set E. The
position of an event group can be represented by the function
f (E) =

3.1 Basic Idea
The layout rule used by ChronoView is very simple. Each event groupwith a set of timestamps is plotted according to the following procedure:

(1)

3.3

1
∑ f0 (t(e)).
|E| e∈E(3)

Potential Features and Limitations

1. Prepare a plane similar to an analog clock with a suitable period.
In Fig. 3, the period is 24 h (c =24h).

One of the most important features of ChronoView is that a set oftimestamps is represented by a position on a two-dimensional (2D)
plane. This provides several advantages:

2. Represent timestamps as positions on the circumference of theclock face circle.

• Easy to read features of temporal patterns: Position is known to
be excellent for representation of values [10].

3. Place each event group at the barycenter of all timestamps associated with the group.

• High space efficiency for many patterns: Each set is expressed bya point; an area parameter is essentially not used.

For example, assume that there are three event groups: A = {e1:00 },B = {e4:00 , e8:00 }, and C = {e12:00 , e18:00 , e20:00 }, where e1:00 denotes
an event with timestamp 1 a.m. As shown in Fig. 3, Group A is placedat the 1 a.m. position because A is a singleton; Group B is placed at
the barycenter of 4 a.m. and 8 a.m; Group C is placed at the barycenterof 12 p.m., 6 p.m., and 8 p.m.

• Transformation to a density plot. A density plot, for example, aheat map, is available for many patterns.

Unfortunately, ChronoView also has limitations in that a set is represented by a position on a 2D plane — a kind of dimension reduction— causing ambiguity in representation. It is acceptable to place twosimilar temporal patterns at positions close to each other. However, a
3.2 Formalization
problem that needs rectification is that the two patterns that it places
In a sales log, let us assume that a teenage boy buys a beverage at close to each other are not always similar. One way of doing this is totime t. This is considered an event and is accompanied by timestamp t. add additional marks to show detailed patterns. Our tool [12] provides
Events that satisfy certain conditions are considered to be a part of a function to show the details of timestamps.
an event group. For example, all events of buying bottles of orange
juice constitute one event group while all events in which teenagers 4 D ISTRIBUTION ON THE C LOCK FACE C IRCLE
make purchases constitute another group. A temporal pattern is a set of Many temporal patterns seem to occupy positions close to the centertimestamps accompanying an event group.
of the clock face circle. We exhaustively generated many temporal
Let us now formally describe ChronoView. Function f0 determines patterns under some conditions and plotted them on the circle. Fig. 4
the position of a timestamp on the circumference. Function f takes illustrates the results of plotting the following temporal patterns.

T5L6: At each of the five timestamps {00:00, 04:48, 09:36, 14:24,
19:12}, we assume 6 levels of frequencies {0, 1, 2, 3, 4, 5}. The
number of temporal patterns (i.e., dots) is 7, 775(= 65 − 1).
T12L4: At each of the 12 timestamps {00:00, 02:00, 04:00, ..., 22:00},
we assume 4 levels of frequencies {0, 1, 2, 3}. The number of
temporal patterns is 16, 777, 215(= 412 − 1).
T24L2: At each of the 24 timestamps {00:00, 01:00, 02:00, ..., 23:00},
we assume 2 levels of frequencies {0, 1}. The number of temporal
patterns is 16, 777, 215(= 224 − 1).
Fig. 5 shows the distribution of temporal patterns on the clock facecircle. In each histogram, the horizontal axis represents the distancefrom the center, and the height of a bar represents the number of
temporal patterns placed in the area. These histograms show that many
temporal patterns tend to occupy the central region.
5 D ISTORTION OF THE C LOCK FACE C IRCLE
Introduction of distortion methods like fisheye views may resolve visual
clutter near the center. Assignment of more spaces around the center
might decrease visual clutter by increasing the resolution of the central
area. We consider moving the positions of temporal patterns using
some non-linear mapping. Now, assume that the radius of the clock
face circle is 1 for simplicity. When the original positions are expressedby (r, θ ) in the polar coordinate system, we move the points to (d(r), θ )using non-linear mapping d : [0, 1] → [0, 1]. To assign more spacearound the center, we enlarge the region near 0 by choosing concave
function d. We consider the following three kinds of functions:√d1 (r) = r
(4)
π
· r)
2

(5)

d3 (r) = 1 − (1 − r)2(6)d2 (r) = sin(

By using these functions, the distributions are changed to the ones
shown in Fig. 6 and Fig. 7. Data sets in these figures are all T5L6. The
original distribution is shown in Fig. 4(a) and Fig. 5(a). Function d1
results in a sparse space near the center. Function d2 may fill the centerarea. By observing the characteristics of these functions, we generatefunction d3 . This function can distribute the dots more evenly on thecircle.
Actual distributions depend on the target data, with some target data
possibly requiring more space around the center while other requiring
more resolution peripherally. Function d3 is suitable for such extension.
Function d4 is a generalized form of d3 by replacing the exponent to a.
d4 (r) = 1 − (1 − r)a(7)

When a = 1, the function becomes d4 (r) = r and every dot is placedat the original barycenter (see Fig. 4(a) and Fig. 5(a)). When a = 2, thefunction becomes equivalent to d3 . When a > 2, the function enlarges
the center area to a greater extent. When a < 1, the function enlarges
the peripheral area.
6 E XAMPLES
Fig. 1 shows two examples of ChronoView, both of which represent
tweets on Twitter.
We regard tweets containing the keyword “now” in Japanese, such as“lunch, now” and “Tokyo, now,” as events. “Now” is an English word,
but Japanese tweeters often use it to express their current situation.
Tweets containing “now” convey casual, quotidian behavior. Therefore,
analysis of such data is expected to be useful in the field of market
research.
Our data includes about 30,000 tweets collected in ten days from
June 20, 2011. It contains about 10,000 different words, i.e., 10,000
event groups. To generate the examples, we translated Japanese words
in the tweets into English.

Each event group is represented by a circle, the size of which is
proportional to the number of events. The examples in Fig. 1 only
show event groups including two or more events. Labels are added
only for event groups with 16 or more events to reduce visual clutter.
Fig. 1(a) shows the original view of ChronoView, with all event groups
placed at the barycenter of all included event timestamps. Fig. 1(b)shows a distorted view by using function d4 with a = 2 (i.e., d3 ). We
can observe event groups placed near the center more clearly than in
Fig. 1(a).
7 C ONCLUSION
This paper presented ChronoView, which visualizes many temporal
patterns. The defining feature of ChronoView is that each event groupis represented as a position on a two-dimensional plane. This provides
several advantages, including easy-to-read temporal pattern features,and high space efficiency for many patterns. This representation of setsby positions on a 2D plane causes ambiguity, which tends to occur near
the center of the clock face circle. We exhaustively generated many
temporal patterns under some conditions, plotted them on the clock
face circle, and confirmed the concentration of many dots near thecentral area. We also tried to introduce non-linear mapping to decrease
clutter near the center. Non-linear mapping induces the position ofeach temporal pattern to move away from the barycenter of event
occurrence times. We need to survey observers to understand the effectof these movements on their impressions on a decluttered variant ofChronoView.
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(a) T5L6: 5 timestamps, 6 levels(b) T12L4: 12 timestamps, 4 levels(c) T24L2: 24 timestamps, 2 levels

Fig. 4. Results of plotting many temporal patterns. Dataset induced variation.

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0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0(a) T5L6: 5 timestamps, 6 levels0

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0(b) T12L4: 12 timestamps, 4 levels

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0(c) T24L2: 24 timestamps, 2 levels

Fig. 5. Distribution of temporal patterns on the clock face circle. Dataset induced variation.

(a) d1 (r) =√r(c) d3 (r) = 1 − (1 − r)2(b) d2 (r) = sin(π · r/2)

Fig. 6. Results of plotting many temporal patterns. Variations by mapping functions.
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Fig. 7. Distribution of temporal patterns on the clock face circle. Variations by mapping functions.

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0(c) d3 (r) = 1 − (1 − r)2