=Paper=
{{Paper
|id=Vol-541/paper-2
|storemode=property
|title=A Chorematic Approach to Characterizing Movement Patterns
|pdfUrl=https://ceur-ws.org/Vol-541/paper02klippel.pdf
|volume=Vol-541
}}
==A Chorematic Approach to Characterizing Movement Patterns==
https://ceur-ws.org/Vol-541/paper02klippel.pdf
A Chorematic Approach to Characterizing
Movement Patterns1
Alexander Klippel
Department of Geography, GeoVISTA Center, The Pennsylvania State University
Abstract. We adopt a perspective of characterizing movement patterns on the
basis of conceptual primitives that we call movement choremes: . This theory is
an extension of our existing work on wayfinding choremes that specifically
addressed movement patterns important for wayfinding and route directions. Just
like in our previous work the goal is to develop a formal language that allows for
characterizing the movement of individual agents and entities from a cognitively
unifying perspective. By this we mean that while our main work concentrates on
the conceptual level of movement patterns, the framework is intended to
incorporate externalizations such as natural language and graphics (sketches) and
also formal theories of qualitative movement and spatial relation characterizations.
We discuss our approach in relation to existing frameworks such as RCC and the
9-intersection formalism to ground the potential of a formal-spatial language
approach.
Keywords. Movement Choremes, Topology, Conceptual Language of Movement
1. Introduction
How can we characterize movement patterns? We can, for example, adopt a formal
approach and characterize movement patterns on the basis of manifold spatial calculi
that capture static and dynamic spatial relations (e.g., van der Weghe, Billen, Kuijpers,
& Bogaert, 2008). We can also investigate how humans make sense of movement
patterns or how they perceive and structure movement events. Although many formal
approaches are inspired by general results from cognitive studies, it is still an open
question if they adequately bridge the gap between cognitive and formal
characterizations. While we will not close this gap completely with this contribution,
we do hope to make it a little less wide. To do so, we extend our approach to
characterizing movement patterns on the basis of conceptual primitives that are termed
here: movement choremes ( ). In the following, we first offer an early taxonomy to
1
We would like to thank the anonymous reviewers for extremely valuable
comments on this paper. Research for this paper is based upon work supported by the
National Science Foundation under Grant No. 0924534 and funded by the National
Geospatial-Intelligence Agency/NGA through the NGA University Research Initiative
Program/NURI program. The views, opinions, and conclusions contained in this
document are those of the author and should not be interpreted as necessarily
representing the official policies or endorsements, either expressed or implied, of the
National Science Foundation, National Geospatial-Intelligence Agency or the U.S.
Government.
characterize movement patterns from the perspective of conceptual primitives. We then
discuss examples how to formally ground conceptual primitives in current frameworks
of topology and how topological formalisms might benefit from adopting a perspective
of conceptual primitives.
2. Theoretical underpinning: Conceptual primitives and the relation between
spatial representation and conceptual structure
What does it mean to be a (cognitive) conceptual primitive? Due to the flexible nature
of the human mind, this question on conceptual primitives may have more than one
answer. In general, though, we follow the approach outlined by Mandler (Mandler,
1992), who states that conceptual primitives are not to be interpreted as primitives in an
atomic sense (i.e., their descriptions may be divided or compartmentalized further).
Rather, they are foundational; foundational to the cognitive system. They are what
allow us to create concepts about the things we encounter in our environments, which
in turn allow us to communicate events as we meaningfully segment the potentially
continuous stream of information into these foundational concepts. An example would
be the understanding of direction changes of moving agents whether in constraining
networks (such as streets) or differently structures spaces (e.g., deserts). Instead of
using 360 degrees (or even decimals) we can expect that a cognitive system uses a
much smaller number of qualitative equivalence classes. The following aspects should
be kept in mind:
• The number of equivalence classes is not cast in stone, that is, there can be
flexibility regarding the level of granularity.
• Equivalent classes do not segmenting space homogenously. It is sensible to
assume that they differ in size and extent. This fact is reflected in behavioral
research, linguistic expressions, and formal characterizations.
• There may even be a modality specific difference, for example, comparing the
linguistic and non-linguistic conceptualization of direction information. To
which extent this can be modeled is an open question.
3. Toward a taxonomy for single agent movement patterns from a chorematic
perspective
We present a first draft of a movement patterns taxonomy for single agents/entities.
This taxonomy is organized according to critical cognitive concepts of movement
patterns. It is a work in progress and meant as a guideline for structuring ideas and
discussions from a cognitive perspective2.
The first level in the taxonomy (see Figure 1) distinguishes whether the trajectory
(also referred to as path or trace) of a moving agent is of interest, or, whether the spatial
2
More comprehensive taxonomies from different perspective such as geography,
granularity, data mining, and visual analysis of movement patterns have been proposed
by several researchers (e.g., Dodge, Weibel, & Lautenschütz, 2008; Yattaw, 1999;
Hornsby & Egenhofer, 2002).
relations bettween the agennt/entity and otther entities in n its environmeent (also includding
the environm ment itself) proovide a contexxt for conceptuualizing movem ment patterns. The
trajectory itsself could be ammended by moovement characcteristics such as speed channges.
We will focu us here, howev ver, on the spattial characterisstics of the trajectory. This fo
ocus
seems to bee legitimate, ass research in m many areas pooints to the im mportance of path
p
characteristiccs (we will reffer to the path aas a trajectory)). Shipley and Maguire (20088, p.
417-418) wrrite: "[...] researrch and theoriees in three areaas-(l) how evennts are represennted
linguisticallyy, (2) how event representatiions develop, and a (3) computtational modells of
event segmeentation-converge on a singgle conclusion:: that event paaths are the most m
important feature
fe for evvent representaation and seg gmentation." T The main spaatial
characteristicc to focus on isi the shape off a trajectory. Recent
R studiess again by Ship
pley
and collaborrators (Shipleyy & Maguire, 2008; Shipley y, Maguire, & Brumberg, 20004;
Shipley & Kellman,
K 20011) have shownn that salient shape characteristics, just like
salient shapee characteristiccs of objects, aare used to meeaningfully seggment a trajectory
(see also Tallmy, 2000).
Figure 1. Movem
ment pattern taxonnomy.
A simillar idea can be b found in manifold reseearch approachhes that form mally
characterize linear structurres; we brieflyy mention threee. A first prom
minent approacch is
discussed in early work byy Freeman (Freeeman, 1975). The T so called F Freeman chainning
is based on coding an objject’s shape ussing an ordereed sequence off directions in the
object’s conntour lines. Classically,
C onnly 8 directiions (equivaleence classes) are
distinguishedd. A second appproach addressses contour linnes of geograpphic entities baased
on shape primitives (Kulikk & Egenhoferr, 2003). Kulik and Egenhofeer use an approoach
called term rewriting
r (Dersshowitz, 1993)) to extract diffferent meaninggful environmeental
features baseed on these shaape primitives. The power off their approachh lies in the ability
of the term rewriting
r system
m to identify mmeaningful com mplex shapes oout of a limitedd set
of primitive shapes. The third and final approach, which used term writing in
combination with a formal grammar, has been adopted in the wayfinding choreme
theory. Wayfinding choremes are conceptual primitives (Brunet, 1987; Klippel, Tappe,
Kulik, & Lee, 2005) used to model route knowledge. Instead of focusing on all aspects
of a complete route (i.e., the complete trajectory of a moving agent), critical points
along the route are used to characterize routes with a limited set of direction primitives,
called wayfinding choremes (Klippel et al., 2005). Wayfinding choremes can be
combined into more complex sequences of movement patterns to reflect cognitive
conceptualizations such as follow the road to the dead end and turn right.
Figure 2. Left: Conceptual neighborhood graph (Freksa, 1992a; Egenhofer & Al-Taha, 1992).
Right: Different paths of hurricanes distinguished by ending relations. All hurricanes start in the
upper right corner of each icon, disconnected from the peninsula (from Klippel & Li, 2009).
This last approach will be used as a basis for developing a cognitively unifying
framework for the characterization of movement patterns. All of these approaches are
well developed and allow for characterizing trajectories. The wayfinding choreme
theory is particularly useful because these characterizations can include important
contextual factors, such as landmarks3.
Another way to conceptualize movement patterns is by characterizing changing
spatial relations between the moving agent/entity and other features or entities in the
environment (see Figure 1). One such related distinction (and the one that we will
explore in greater depth here) is attributed to the importance of topology. We
distinguish movement patterns that involve a change in the topological relationship
between the moving agent/entity and other entities and those where the topological
relations stay constant. The next distinction in the taxonomy important for movement
patterns that involve topological changes is the spatial dimensionality of the moving
object—point versus spatially extended entity. This in itself is an interesting question
from a cognitive conceptual perspective and dependent on the granularity applied to
3
It is not possible to discuss all existing approaches. We would like to point to
some recent development in spatial sciences though to adopt event-based approaches to
the characterization of movement patterns, for example, work by Worboys, Stuart
Hornsby, or Peuquet (Stewart Hornsby & Li, 2009; Worboys, 2005; Mennis, Peuquet,
& Qian, 2000).
characterize and interpret a movement pattern. It is important to note that no physical
entity is a point in a formal sense. However, to characterize a movement pattern as a
trajectory, we do have to assume that the moving entity is indeed a point. We will
discuss the implications of this distinction in the light of recent research on directed
lines, called Dlines (Kurata, 2008; Kurata & Egenhofer, 2008) and the
conceptualization of movement patterns at the geographic scale (Klippel & Li, 2009).
It is important to note that the role that conceptual neighborhood graphs (Freksa,
1992a; Egenhofer & Al-Taha, 1992) play in movement pattern characterizations differs
according to the dimensionality of the moving entity. As a reminder, conceptual
neighborhood graphs are a form of organizing sets of topological relations (see left side
of Figure 2) in a way that most similar topological relations (there may be differences
in defining similarity that we will ignore here) become conceptual neighbors, that is,
they are directly connected by edges in the conceptual neighborhood graph.
If we conceptualize the moving agent as a spatially extended entity, we can use the
conceptual neighborhood graph that is established on the basis of topological relations
distinguished by the region connection calculus (e.g., Randell, Cui, & Cohn, 1992) or
by different levels of granularity in Egenhofer’s intersection models (Egenhofer &
Franzosa, 1991). To model a movement pattern in this way, the conceptual primitives
(the movement choremes, ) are the topological equivalence classes assuming that
the agent is moving. Extending our previous research on wayfinding choremes to ,
we can, for example, differentiate eight topological relations that constitute the
conceptual neighborhood graph in Figure 2 4 (DC – disconnected, EC – externally
connected, PO – partial overlap , TPP – tangential proper part, NTPP – non-tangential
proper part, and two inverse relations for TPP and NTPP, TPPi and NTPPi,
respectively). It is possible to define a formal language based on these relations. We
will not go into detail here, but we will provide some examples (see also Egenhofer and
Al-Taha, 1992):
• Consider the moving entity is a hurricane and our reference entity is a
peninsula (for the moment we ignore the fact that the hurricane is ‘in’ the
ocean while it is approaching the peninsula, see Stewart Hornsby & Cole,
2007). Critical stages of the hurricane’s movement pattern are associated with
changes in the topological relation between the hurricane and the peninsula.
• A hurricane that never makes landfall has a very short conceptual path. It
exists only of the relation DC ( )
• For a hurricane that does make landfall and, let’s say, dies over land, the
conceptual path gets longer:
• For hurricanes that completely cross the peninsula (assuming the hurricane is
smaller than the peninsula), the path through the conceptual neighborhood
graph looks like this:
4
For a detailed discussion of changing the levels of granularity of conceptual
neighborhood graphs (i.e., five or eight topological relations) see Dube and Egenhofer
(2009).
It is important to keep in mind that the eight primitives (MCs) can be used as a
basic characterization - like letters in the alphabet - and that combinations of these
primitives can be used to characterize more complex movement patterns. An example
would be hurricane Ivan in 2004, which crossed the Southwest of the United States,
went back out into the Atlantic and came back to cross the southern tip of Florida.
Another important aspect is to make a connection to externalizations, such as
linguistics or graphics. To model, for example, the semantics of the verb cross or the
preposition across (as in the hurricane crossed / went across the peninsula), we can
apply the combination of term rewriting rules and a formal grammar (MCG –
movement choreme grammar) to identify (i.e., rewrite) movement characterization. For
example, the complete conceptual path of hurricane Ivan (as briefly characterized in the
preceding paragraph) would look like this:
Within this string of movement concepts, we can identify sub-strings that are
meaningful in their own right (e.g., the sub-string where the hurricane makes landfall
or where its trajectory/path crosses the mainland for the first time). We have not
specified a full grammar on the basis of movement concepts (MCG) yet, but a valid
expression for the concept of across would look like this:
This valid expression in the MCG can be used as a basis for defining term
rewriting rules to process strings of movement concepts into meaningful parts (Klippel
et al., 2005, see also Galton, 1993; Dershowitz, 1993).
One critical question we need to answer is: what constitutes valid expressions in
this formal language. This, of course, is not trivial, as many combinations would be
possible from a formal perspective (as we will see in the next section). The first
constraint comes from the organization of the topological relations as conceptual
neighbors into the conceptual neighborhood graph. Obviously, not all topological
relations can be neighbors with all other topological relations; they are constrained
through the movement patterns of the agent/entity. Consider the example of the
hurricane crossing the peninsula. Assuming that there are no holes in the
conceptualization of the hurricane (i.e., ignoring the eye of the hurricane), its
movement can be conceptualized as translation which results in the path given above
(e.g., . These constraints ensure the validity of the sequence of topological
relations. The hurricane cannot jump from to without going
through . While there may be other scenarios where jumping is
possible (e.g., a tornado), for the moment we will stay, for now, in this more
constrained domain (see Worboys & Duckham, 2006 for a discussion of more flexible
options).
An additional observation is important to make: Humans have a tendency to pay
particular attention to the ending relation of a movement patterns (or events). This
phenomenon is referred to as the endpoint hypothesis (Regier & Zheng, 2007). To be
able to identify potential segments, that is, sequences of MC (both in the conceptual
path as well as in the actual trajectory) on cognitive grounds, the question we have to
answer is which topological relations are good candidates for defining cognitively
salient ending relations and which ones are not. In other words, while the movement
choremes and the order of movement choremes are constrained by the conceptual
neighborhood graph, the endings (or beginnings, see below) could be arbitrary and
potentially all MC could be equally salient from a formal perspective. While equal
salience of topological relations has been used in recent approaches on similarity
measures (e.g., Schwering & Kuhn, to appear), our own research (Klippel & Li, 2009),
results by Shariff et al. (1998), behavioral assessments of Allen’s temporal calculus (Lu
& Harter, 2006), and various formal approaches (e.g., Camara & Jungert, 2007)
propose that topological (or corresponding temporal) relations do not have the same
cognitive saliency5. For example, while it would be possible to allow for the following
combination of MCs: , it is questionable whether this should
constitute a salient term in the MCG (the grammar of movement concepts).
Figure 3. A dendrogram that shows the result of a cluster analysis (Ward’s method). Participants saw
animated icons similar to the ones in Figure 2. Their task was to create groups out of these icons that they
considered as being similar to each other. The movement patterns that the icons depicted were distinguished
on the basis of topologically defined ending relations. The difference between DC1 and DC2, for example, is
that DC1 are hurricanes that never made landfall while DC2 characterizes hurricanes that completely cross
the peninsula (see Figure 2). The results show clearly that not all topologically defined ending relations are
equally salient from a cognitive conceptual perspective (from Klippel & Li, 2009).
Figure 3 shows the result of an experiment on the salience of topologically defined
ending relations. We used animated hurricane icons as shown in Figure 2. It is clear,
5
These findings reveal a difference between the static and the dynamic domain. In
the static domain research by Knauff and collaborators Knauff, Rauh, & Renz, 1997
indicate equal salience of all topological relations identified by RCC-8 and the 9-
intersection model.
that certain topological relations form conceptual groups and are more similar to each
other than to members of other groups. One striking result is that concepts that exhibit
some kind of overlap (PO, TPP, NTPP) are separated from those that do not overlap
(DC, EC). This conceptual differentiation is also reflected in a linguistic analysis of
labels that participants provided for these groups (see Klippel & Li, 2009 for details)
and strikingly similar to an analysis by Lu and Harter (2006) on the cognitive saliency
of Allen’s intervals (Allen, 1993).
This is an important question if we want to break down a characterization of a
movement pattern into meaningful subparts. While research has been conducted on
these questions, we still need more behavioral validation to guide the way we assign
saliency to the primitives of the MCG and what role they might play in defining
meaningful sub-events. However, the combination of the MCG and term rewriting
offers manifold possibilities to account for differently salient combinations.
Comparable to the case of wayfinding choremes and their processing, the order in
which term rewriting rules are applied allows for specifying more salient (rules that are
applied first) and less salient (rules that are applied last) combinations.
So far we have talked only about the case in which both the moving agent/entity
and the reference entity are spatially extended. Now we are turning to the case in which
the moving entity can be conceptualized as a point while the reference entity (ground)
is considered to be spatially extended. In this case we can build on the well explored
framework of the 9-intersection model (Egenhofer & Mark, 1995) that allows for
specifying the relationship between a line, which in this case would be the trajectory,
and a spatially extended entity. A more elaborate framework is proposed by Kurata and
Egenhofer (Kurata & Egenhofer, 2007) in which a non-directed line is replaced by a
directed line (Dline), a model referred to as 9+ intersection. In this case, the number of
possible relations between the line and the region increases from 19 to 26. The 9+
intersection approach is intended to model human concepts of motion and is the most
elaborate topological approach to characterize single agent movement patterns. We
briefly explore here how this approach could be realized within our framework of MC
and the MCG (see also Kurata & Egenhofer, in press). We start by characterizing only
three basic relations between the moving agent/entity and the spatially extended entity.
The agent/entity can be either in the exterior (EX), on the boundary (BO), or in the
interior (IN). Additionally, we need to distinguish whether the movement ‘on’ the
boundary occurs only in one point, such as the start and end point, or whether it is an
extended movement along the boundary. In the case where the movement on the
boundary is taking place only in a single point we write (bo) instead of (BO). Please
note that this distinction is also useful in characterizing different forms of crossing
from the interior to the exterior. While this information is beyond a purely topological
characterization, it has received some attention in modeling relationships between two
lines (Xu, 2007). We will not discuss this aspect here in detail. We applied our
characterization of movement patterns based on movement choremes to the examples
of the 26 Dline relations we found in Kurata and Egenhofer’s work (Kurata
& Egenhofer, in press, see Figure 4). A movement pattern corresponding to an agent
crossing the spatially extended entity would correspond to the following sequence:
To further demonstrate the feasibility of our approach based on only 4 conceptual
movement primitives (in case of conceptualizing the moving agent/entity as a point),
we show in Figure 4 how all 26 Dline relations could be characterized on the basis of
MC. Once the grammatical foundations are laid, further processing could be applied.
The combination could be defined as a valid expression in the MCG
and could be simplified to a concept that could be referred to as ‘enter’
(see also Mark & Egenhofer; Kurata & Egenhofer, in
press).
These are just examples of how a characterization of movement patterns on the
basis of movement choremes (that is, conceptual movement primitives) could be
established. We will provide an outlook of ongoing work in the next Section.
Figure 4. Shown are icons depicting the 26 Dline relations. Below each icon the MC notation is provided (EX
for a movement pattern outside an extended spatial entity, IN for a movement patterns inside a spatially
extended entity). Please note that we modeled the relations given in the original icons by Kurata and
Egenhofer (Kurata & Egenhofer, in press). To this end we distinguished between movement patterns on the
boundary that occur only in one point (start, end, and crossing) and movement patterns that are extendedly
taking place on the boundary (bo and BO, respectively). Please also note that we left out the MC and simply
used the subscript to safe space. The power of this approach lies in its potential to identify meaningful
substrings. For example, in case of IN-bo-EX we can summarize the movement patterns to INEX and
associate a semantic (linguistic) concept with it.
4. Summary, conclusions and outlook
This paper presented a short overview of a developing theory for the characterization of
movement patterns. The core notion of this theory are movement choremes, MC. A
movement choreme is a conceptual primitive in the sense that it is foundational for the
cognitive understanding of movement patterns. We are currently restricting ourselves
to the characterization of movement patterns of individual entities. While MCs are
primitives they unfold their full potential through grammatical rules that combine MCs
into chunks (words to use a linguistic metaphor). These chunks are the basis for term
rewriting rules that can be used to meaningfully segment long strings of MCs that
characterize continuous movement patterns.
While we have not combined all aspects discussed such as the characterization of
trajectories and the characterization of topologically changing relations between a
moving agent/entity and entities in its environment, we did show that both aspect can
be characterized using conceptual movement primitives. In a future step we are
planning to fully specify this framework establishing a formal, conceptual language for
movement patterns. One possibility of combining different aspects of movement
patterns into a single notation has been discussed by Steward Hornsby and Cole (2007).
We will follow their approach and we will combine a specification of shape
characteristics of a trajectory with changing spatial relations. For example, using either
Freeman chaining or wayfinding choremes, we could model direction changes of a
hurricane even if, for example, topological relations do not change. We would need to
specify a direction model for example cardinal directions for the geographic scale.
Additionally we need a spatial unit that would allow us to specify individual steps. A
hurricane going West for a while and then turning North toward the main land could be
specified as:
Just like before, we could specify valid expression in the MCG that would allow us
to chunk a sequence of . This valid expression (and others) could be used to
process long strings of MCs.
The other aspect we left out of the specification here is the whole area of changing
spatial relations between a moving agent/entity and entities in the environment that do
not involve changing topological relations. These changes could be specified by using
ordering information (Schlieder, 1995) or other qualitative specification of spatial
relations such as the double cross calculus (Freksa, 1992b). The number of existing
calculi is large and it may be necessary to use different calculi for different spatial
environments and purposes.
One main aspect though in further specifying the MCG is the behavioral validation
and the grounding of formal characterization on a cognitive assessment. For this
purpose we have set up an experimental framework that will extensively assess, first,
the role of topology across different domains and across different topological
transformations. We consider this approach an essential step in tailoring existing
formal specifications toward cognitive adequacy. Second, we will be addressing the
question of different granularities and the scale dependency of conceptualizing moving
entities either as points or as extended spatial entities.
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