=Paper=
{{Paper
|id=Vol-2378/shortAT12
|storemode=property
|title=Temporal Concept Analysis with SIENA
|pdfUrl=https://ceur-ws.org/Vol-2378/shortAT12.pdf
|volume=Vol-2378
|authors=Karl Erich Wolff
|dblpUrl=https://dblp.org/rec/conf/icfca/Wolff19
}}
==Temporal Concept Analysis with SIENA==
https://ceur-ws.org/Vol-2378/shortAT12.pdf
Temporal Concept Analysis with SIENA
Karl Erich Wolff1
1 University of Applied Sciences Darmstadt, Darmstadt, Germany
Abstract.Temporal Concept Analysis (TCA) is an extension of Formal Concept
Analysis (FCA) aiming at a conceptual description of temporal phenomena. We
present the latest version of the TCA tool in the program SIENA, a part of the
ToscanaJ Suite. This TCA tool allows for animations of trajectories of tempo-
ral objects in line diagrams of concept lattices. Such concept lattices re- present
views of the given temporal data, as for example a map of a landscape.For gen-
erating views of suitable granularity the many-valued temporal data have to be
scaled using conceptual scaling tools as for example CERNATO. In the TCA
tool in SIENA the temporal database has to satisfy the condition that the many-
valued attributes for temporal objects and time together form a key. Then the
state (of a temporal object o at a time t in a view Q) is defined as a certain ob-
ject concept of a formal object of the formal context generated by the view Q.
The general case of temporal data bases with an arbitrary key leads to the no-
tion of distributed objects which are at each time at possibly many places, as for
example a high pressure zone on a weather map. A state of a distributed object
is defined as a certain set of object concepts. In this workshop we give a
demonstration of SIENA presenting animations of trajectories of temporal ob-
jects. In ToscanaJ we visualize changing distributed objects.
Keywords: Temporal Concept Analysis, states, trajectories.
1. Temporal Concept Analysis
1.1. Introduction
Temporal Concept Analysis (TCA) [3, 4] is an extension of Formal Concept Analysis
(FCA) [2] aiming at a conceptual description of temporal phenomena. TCA offers a
general way of understanding change of concrete or abstract temporal objects in con-
tinuous, discrete or hybrid space and time. 1
1.2. Scaling temporal databases
We start from a temporal database, i.e. a complete many-valued context containing at
least one many-valued attribute explicitly used for describing time. In conceptual
scaling [2] one selects for each many-valued attribute a suitable formal context, called
Copyright ©2019 for this paper by its author. Copying permitted for private and academic pur-
poses.
2! K.E. Wolff
a conceptual scale. From the scaled many-valued context its derived context K is used
to generate specific sub-contexts by selecting interesting subsets of the attribute set of
the derived context. Any such subset Q is called a view. The concept lattice of the
formal context KQ of a view Q is used for many purposes, namely conceptual de-
scriptions of space, time, and (temporal) objects; for a mathematical definition of
Temporal Relational Semantic Systems and their temporal objects we refer to [4].
1.3. Conceptual description of space, time, and objects
To describe changes of objects in a general conceptual setting one has to represent
conceptually not only space and time, but also objects.
Space. For the conceptual description of a space, e.g. a landscape, we take the con-
cept lattice of the formal context KQ of a suitable view Q, for example a set of attrib-
utes derived from the many-valued attributes of longitude and latitude. The formal
concepts of KQ can be used for describing spatial notions, as for example countries,
towns, places, streets and so on.
Time. For the conceptual description of time often several many-valued attributes are
used, e.g. for days, months, and years. The corresponding scales are usually ordinal or
interordinal scales. For the seven days of a week one may wish to choose a cyclic
scale. For temporal notions as for example early morning and late evening one has to
introduce a suitable scale for describing the meaning of these notions by suitable scale
concepts. In any case, the scales for the set T of many-valued time attributes should
be chosen in such a way that the corresponding derived context KT represents the
desired concepts, as for example time intervals.
Objects. For the conceptual description of objects one might take the formal objects
of a many-valued context. That is sometimes appropriate, but in temporal data it is
often useful to take time points, e.g. days, as the formal objects. Since the formal ob-
jects of a many-valued context form a key it is a restriction to assume that the objects
or the time points also have to form a key. Usually, there are many kinds of objects
and also several kinds of times, e.g. local times. Therefore, in TCA we emphasize to
describe temporal objects as formal concepts of scales of many-valued attributes.
Then the formal objects of the used many-valued context just represent row labels of
the statements given in the rows of the data table.
2. The TCA tool in SIENA
The well-known ToscanaJ Suite [1] contains a program SIENA which has a tool for
drawing (nested) line diagrams of concept lattices. Into this drawing tool Peter Becker
has embedded the TCA tool. It allows for drawing and animating trajectories of tem-
poral objects in line diagrams of concept lattices. The menu of the TCA tool can be
shown by clicking in SIENA on View \ Show Temporal Controls. Before using the
TCA tool the many-valued context of a temporal database has to be scaled, and all
Temporal Concept Analysis with SIENA !3
views (in German: Sichten) of interest have to be generated using the program CER-
NATO (developed by NAVICON, now obtainable from the Ernst-Schröder-Zentrum).
Finally, the scaled temporal database together with all generated views has to be ex-
ported as an XML file and then imported into SIENA by clicking on File\ Import
Cernato XML. The names of all views can be seen in the main menu of SIENA under
the tab Diagrams in the top left. Clicking on the name of a view Q a line diagram of
the concept lattice of KQ as generated in CERNATO is shown. Often this diagram can
be improved graphically in SIENA using five different Movements, a scalable Grid
and an effective Rescale possibility.
2.1. The object-time key
The temporal database used in the TCA tool has to fulfill the following condition:
(OTK) There are two many-valued attributes, say object and time, together forming a
key.
In some temporal databases a single many-valued attribute time forms a key. Then
any further attribute together with time forms a key, hence OTK is satisfied.
In Table 1 an example of a temporal database satisfying OTK is shown. The first
statement is interpreted as: Mary has been at time 0 in London.
Table 1. A temporal database with an object-time key
statement object time town
1 Mary 0 London
2 Mary 1 Paris
3 Charly 1 Paris
To distinguish clearly between objects and formal objects we just remark that in
Table 1 the statements 1,2,3 are the formal objects of this many-valued context and
therefore also the formal objects of its derived context; the objects in Table 1 are the
values Mary and Charly of the many-valued attribute object.
In the TCA tool in SIENA the column in the database containing the temporal ob-
jects can be chosen using the tab DATA\Sequence Column. In the same way the col-
umn containing the time values can be chosen using the tab DATA\Timeline Column.
To define the trajectory of an object o in a view Q we first need the notion of a
state of an object o at a time t in a view Q and then the definition of a transition.
4! K.E. Wolff
2.2. The state of an object at a time in a view
Assume that we have chosen a view Q and a temporal object o, and we are interested
where object o has been at time t in the concept lattice of KQ according to the given
temporal database. By OTK, the pair (o,t) occurs in exactly one row g of the given
database where g is a formal object of the derived context KQ. Let γQ denote the ob-
ject concept mapping of KQ. Then the object concept γQ(g) is defined to be the state of
object o at time t in the view Q, denoted by γQ(o,t); for further information see [3,4].
2.3. Transitions and trajectories
For introducing transitions in the TCA tool the values of the selected many-valued
time attribute have to be integers. For each object o its o-time is the set of time values
occurring together with o in the same row, hence o-time := {s | ∃g object(g) = o and
time(g) = s}. The partial mapping next o-time assigns to each not maximal time value
s in o-time the minimum of all o-time values t > s. A pair (s,t) satisfying next o-
time(s) = t is called a base o-transition and the pair (γQ(o,s), γQ(o,t)) of states is called
the o-transition generated by the base o-transition (s,t) in the view Q.
In the TCA tool the o-transition (γQ(o,s), γQ(o,t)) is graphically represented in a
line diagram of the concept lattice of KQ by an arrow leading from the circle of
γQ(o,s) to the circle of γQ(o,t). The sequence of all o-transitions in the view Q forms
the trajectory of the object o in the view Q.
2.4. Using the TCA tool: Controls, Data, Arrows, Options
To show a line diagram of a view Q one has to click on Q in the list of Diagrams.
To show in the line diagram of Q the trajectories of all temporal objects click in the
menu of the TCA tool on Controls\Show all transitions. To show the trajectories for
only a few temporal objects these objects can be selected using Data\Sequence. The
selected trajectories can be animated using Controls\Animate transitions. The speed
of the animation can be chosen using Options\Speed (ms/step). Using Controls\Repeat
Animations the chosen animation is repeated until stopped.
To study several trajectories simultaneously step by step the user should first click
on Controls\Start stepping and then use Step Controls.
The arrows of a trajectory can be modified: click on Arrows to see 10 arrows in
different colors. Move the mouse to an arrow to see the name of the temporal object
assigned to it. Double click on an arrow opens a new window where the Color, the
Shape and the Lable of the arrow can be modified.
Using drag and drop each arrow and each label in the line diagram can be moved.
These changes are not saved in SIENA. Hence, use File\Export Diagram to store
good diagrams in jpg- or png-format. To generate nested line diagrams click with the
right mouse on a second view and then click on Nest Diagram.
2.5. An example: Three gymnasts
There is a well-known demonstration for three gymnasts, say Tobias (t), Konstan-
tin (k), and Florian (f), moving between the places 1,2,3 in the following way:
Temporal Concept Analysis with SIENA !5
In the beginning they are standing in a line, Tobias at place 1 facing Konstantin at
place 2 and Florian at place 3. At time 0 Konstantin rolls forward to place 1 while
Tobias jumps straddling over him to place 2 and Florian is standing on place 3. At
time 1 Tobias rolls forward to place 3 while Florian jumps straddling over him to
place 2 and Konstantin is turning (T) on place 1. At each time the gymnast in the
middle (at place 2) rolls to the gymnast jumping over him (see Fig.1). At time 6 the
starting position is reached again. That can be easily represented in a temporal data-
base satisfying (OTK) as shown in Table 2.
Table 2 . A temporal database for three gymnasts
statement gymnast time exercise place
1 Tobias 0 jump 1
… … … … …
8 Konstantin 0 roll 2
… … … … …
21 Florian 6 turn 3
Choosing ordinal scales for place and time, the view of the place-time attributes,
the gymnasts as temporal objects, the time as the Timeline Column we generate Fig.1
with arrows, its colors, shapes and labels as shown.
6! K.E. Wolff
!
Fig. 1. A transition diagram for the movement of three gymnasts t,k,f in some space-time view
generated using CERNATO and SIENA from the temporal database in Table 2.
References
1. Becker, P., Correia, J.H.: The ToscanaJ Suite for Implementing Conceptual Information
Systems. In: Ganter, B., Stumme G., Wille, R. (eds) Formal Concept Analysis. LNCS
(LNAI), vol. 3626, pp. 324-348. Springer Heidelberg (2005).
2. Ganter, B., Wille, R.: Formal Concept Analysis: mathematical foundations. Springer Hei-
delberg (1999); German version: Springer Heidelberg (1996).
3. Wolff, K.E..: States, Transitions, and Life Tracks in Temporal Concept Analysis. In: Gan-
ter, B., Stumme, G., Wille, R. (eds) Formal Concept Analysis. LNCS (LNAI), vol. 3626,
pp. 127-148. Springer Heidelberg (2005).
4. Wolff, K.E..: Temporal Relational Semantic Systems. In: Croitoru M., Ferré, S. (eds.)
ICCS 2010, LNCS (LNAI), vol. 6208, pp. 165–180. Springer Heidelberg (2010).