Patterns of Movement 

 

For an introduction to the purpose and background of this Patterns of Movement taxonomy, please visit the FrontPage first.

 

In order to study the movement behavior of dynamic objects, it is important to take a closer look at movement itself. In other words, it is necessary to know what exactly the variables are that define movement, what constraints and external factors affect movement and most importantly to understand what types of movement patterns can be composed from these primitives of movement.

Generally, movement patterns include any recognizable spatial and temporal regularity or any interesting relationship in a set of movement data, whereas the proper definition (i.e. the instantiation) of “pattern interestingness” depends on the application domain.

 

 

 

 

Generic patterns

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Generic patterns are patterns which can be found in any form of movement behavior and can be extracted applying generic data mining algorithms.  (Dodge et al, 2008)

 

Co-location in space

 

Co-location in space: Occurs when the trajectories of moving objects have some positions in common. There are three types of co-location in space: ordered co-location exists when the common positions are attained in the same order; unordered co-location if the common positions are attained in different orders; and symmetrical co-location when the common positions are attained similarly but in opposite orders.  {(Original source: Andrienko & Andrienko, 2007), (Modified by Dodge et al, 2008)}

 

• Example: For instance, co-location in space occurs during an eye-movement experiment when different test subjects fixate on similar positions on the map; if the visiting order of fixation positions is the same, co-locations are ordered, and unordered otherwise. As another example, tourists visiting the same four places A to C in a city generate co-locations along their trajectories. If the order is from A to C in one case, and reverse in the other, then we have symmetrical co-location.

 

 

Concentration

 

Spatial concentration of moving objects at a certain instance of time. (Dodge et al, 2008)

 

• Example: As an example, congestion denotes a zone of high density in a transportation network. Likewise, fixa-tions are spatially dense positions of eye-movement tracks and represent concentration zones on the underlying image.

   

 

Incidents

 

Laube (2002) introduced incidents as patterns occurring among multiple objects that can be further categorized as the following patterns:

 

Concurrence

 

Is an incident of a set of entities showing the same values of motion attributes at a certain instant or duration. It happens when a set of objects exhibits a synchronous movement or at least similar motion parameter values over a certain duration

 

• Example: a flock of geese flying with similar motion azimuth.

 

 

Co-incidence in space and time

 

Andrienko and Andrienko (2007) introduced a specific kind of incidence considering similar positions of moving objects. There are two variants of co-incidence patterns, full versus lagged. In the case of full co-incidence, the same positions are attained at the same time while in lagged co-incidence, it happens after a time delay.

 

•  Example: For instance, two different flocks of geese reach a particular pond at the same time or separated by a delay of one day.

 

 

 

Opposition

 

A bi- or multi-polar arrangement of motion parameter values, such as the spatial splitting of a group of moving objects shown in a sudden appearance of two opposite motion directions.

 

• Example: For instance, when flying geese are prompted to fly in opposite directions by a source of disturbance.

 

 

Dispersion

 

Is the opposite of concurrence. An evident pattern in a group of MPOs that is performing a non-uniform or random motion.

 

• Example: Movement behavior of all football players for a specific period of time.

 

 

Constancy

 

When the movement variables remain the same or change insignificantly for a particular duration. (Andrienko & Andrienko, 2007)

 

• Example: when a convoy of cars moves along a straight road, at a constant speed, speed and direction and the derived variables remain the same. Similarly, when a flock of geese is heading north on the spring migration or when football players execute a forward move.

 

 

 

Sequence

 

A sequence is an ordered list of visits to a series of locations. It consists of a contiguous series of segments with a known start and end point in space and time. A spatio-temporal sequence refers to an ordered subsequence of locations with their timestamps. {(Cao et al, 2005), (Lee et al, 2004), (Agrawal & Srikant, 1995)}

 

• Example: the tendency of tourists to visit a set of places A to E in a particular sequence A→B→C→D→E within specified duration could be mentioned. Another example is the sequential order of fixations for several runs of an eye-movement experiment.

 

 

Periodicity

 

Temporal periodic patterns indicate cyclical (e.g., yearly, weekly, or daily) phenomena (Lee et al, 2004). Andrienko and Andrienko (2007) introduced spatio-temporal periodicity, or regular repetition as occurrence of the same patterns over pattern sequences at regularly spaced time intervals.

 

• Example: Migrating geese follow the same path every year.

 

 

Meet

 

A meet pattern consists of a set of MPOs that stay within a stationary disk of specific radius in a certain time interval, that is, they form a stationary cluster. There are two variants of meet, fixed meet and varying meet depending on whether the objects that stay together for a certain duration are the same or change in the meeting region.  {(Gudmundsson & van Kreveld, 2006), (Gudmundsson et al, 2008)}

 

Meet '' (m, k, r): Given a set of n trajectories of entities in the plane, where each trajectory consists of τ line segments, a meeting in a time interval I, where the duration of I is at least k, consists of at least m entities that stay within a stationary disk of radius r during I (note that m ∈ N, k ∈ R and r > 0 are given constants)." (Gudmundsson & van Kreveld, 2006)

 

• Example: As an example for a fixed meet pattern, we mention families of geese that gather in the fall in a specific place to form a flock. An example for a varying meet is the drop-off for rental cars at an airport.

 

 

 

Moving cluster

 

Refers to a set of objects that moves close to each in the same direction other during a specific time interval. Nevertheless, it is not necessary that objects participate the pattern remain the same, but they may enter and leave, while the cluster is moving. {(Kalnis  et al, 2006), (Gudmundsson et al, 2004), (Erwig, 2004)}. Based on this definition, there are two variants of moving clusters, namely fixed-moving cluster and varying-moving cluster whether the participant entities stay together the same or change during the interval. (Gudmundsson & van Kreveld, 2006)

 

"Let g = c1, c2, . . . , ck be a sequence of snapshot clusters such that for each i(1  ≤ i < k), the timestamp of ci is exactly before the timestamp of ci+1. Then g is a ''moving cluster'', with respect to an integrity threshold θ (0 < θ ≤1), if |ci ∩ ci+1|/ |ci ∪ci+1|≥ θ, ∀i : 1 ≤ i < k.'' (Kalnis et al, 2005)

 

Moving cluster ''(m, k, r): Given a set of n trajectories of entities in the plane, where each trajectory consists of τ line segments, a moving cluster in a time interval I, where the duration of I is at least k, consists of at least m entities such that for every point in time within I there is a disk of radius r that contains all the m entities (note that m ∈ N, k ∈ R and r > 0 are given constants)." (Gudmundsson & van Kreveld, 2006)

 

• Example: A flock of migrating geese, a convoy of cars following the same route, and troops that move parallel on a military battlefield are different examples of moving clusters

 

 

Temporal relations

 

These include any temporal relation among various events on the time axis. (Lee et al, 2004)

 

• Example: For instance, a flock of geese usually stops to rest after a long continuous flight.

 

 

Synchronization in time

 

there are two variants of synchronization patterns. Full synchronization happens when similar changes of movement variables (e.g., speed, acceleration, direction, etc.) occur at the same time. In contrast, lagged synchronization happens when the changes of movement variables occur after a time delay.  (Andrienko & Andrienko, 2007)

 

• Example: strikers in a football match start running in similar direction synchronously, when the goalkeeper kicks the ball towards the opponent’s side.

 

 

 

 

Isolated object

 

Refers to an individual moving object (normally belonging to a group of MPOs) pursuing its own path, without any influence on or by the movement of other objects. (Laube & Imfeld, 2002)

 

• Example: when a goose misses the flock and travels alone.

 

 

 

Symmetry

 

Refers to sequences of patterns, where the same patterns are arranged in reverse order. (Andrienko & Andrienko, 2007)

 

• Example: wild geese heading north in the spring, and south in the fall.

 

 

 

Repetition

 

Refers to the occurrence of the same patterns or pattern sequence at different time intervals. (Andrienko & Andrienko, 2007)

 

• Example: For instance, in a football match the strikers may repeatedly sprint along the sidelines or in an eye-tracking experiment the test subjects may repeatedly scan the underlying image up and down.

 

 

 

Propagation

 

Propagation occurs when one object starts to show a certain movement variable value, and little by little other objects start adopting the same pattern. By the same token, with every time step more objects are involved.  (Laube & Imfeld, 2002)

The difference to the trend-setting pattern discussed below is that propagation always happens gradually and does not necessarily involve the influence of a ‘trend-setter’ object.

 

• Example: in spring geese leave at different times little by little, depending how far north they are going.

 

 

 

Convergence versus divergence

 

Convergence refers to the movement of a set of objects to the same location, while the original movement direction of the involved objects does not change. In other words, the motion azimuth vectors of the objects involved will be intersecting within a specific range and within a specific duration. The objects need not arrive at exactly the same time, however.  Divergence is defined as the opposite pattern of convergence and describes a group of moving objects that disperse from a common location . {(Gudmundsson et al, 2004), (Laube, 2005)}

 

Convergence ''Parameters: m > 1 and r > 0. At least m entities will pass through the same circular region of radius r (assuming they keep their direction)." (Gudmundsson et al, 2004)

 

''Convergence is heading for R. Set of m MPOs at interval i with motion azimuth vectors intersecting within a range R of radius r." (Laube et al, 2004)

 

• Example: For example, several flocks of snow geese may converge toward a lake to rest.

 

 

 

Encounter versus breakup

 

Encounter refers to moving to and meeting at the same location. Encounter is a specific form of convergence pattern where the objects arrive at the same time. In an encounter pattern a set of MPOs have motion azimuth vectors that can be extrapolated from the current movement such that the vectors intersect within a specific range and the MPOs meet at the same time. Conversely, breakup is defined as the opposite of the encounter pattern and describes a divergence, adding a temporal (concurrency) constraint. {(Gudmundsson et al, 2004),(Laube, 2005)}

 

Encounter ''Parameters: m > 1 and r > 0. At least m entities will be simultaneously inside the same circular region of radius r (assuming they keep their speed and direction)." (Gudmundsson et al, 2004)

 

''Encounter is xtrapolated meeting within R. Set of m MPOs at interval i with motion azimuth vectors intersecting within range R of radius r and actually meeting within R extrapolating the current motion." (Laube et al, 2004)

 

• Example: In a football match, an encounter occurs when several players rush towards the ball and reach it at the same time. A breakup occurs when ducks flee from a pond after a gunshot is heard.

 

 

 

Trend versus fluctuation

 

Trend refers to consistent changes in the movement parameters of moving object. (Andrienko & Andrienko, 2007)

 

• Example:  for an airplane circling in a holding pattern the rate of change of the movement direction will remain constant.

 

Conversely, Fluctuation refers to irregular changes in the movement parameters of moving object. (Andrienko & Andrienko, 2007)

 

•  Example: geese fly in V-shape, often an irregular V-formation, sometimes lines.

 

 

 

Trend-setting

 

The trend-setting pattern was introduced by Laube (2002) Trend-setters are defined as objects that anticipate a certain movement pattern that is afterwards followed by a subset of the other moving objects. In another words, trend-setters are objects that influence the movement of others not necessarily in a spatial and temporal proximity  {(Laube & Imfeld, 2002), (Laube, 2005)}. There are two variants of trend-setting namely non-varying trend-setting with a fix subset of followers and varying trend-setting. In case of varying trend-setting, the subset of followers can be change from one time interval to the next duration of the pattern. Similar to a moving cluster, in trend-setting entities move in the same direction or might have other similar movement characteristics such as same speed or acceleration. {(Andersson et al, 2007), (Gudmundsson et al, 2004)}

 

Trend-setting '' Parameters: m > 1, r > 0, and s > 0. At least m entities are within a circular region of radius r, they move in the same direction, and at least one of the entities was already heading in this direction for at least s time steps.'' (Gudmundsson et al, 2004)

 

• Example: For example, in a football game, a striker executing a sudden rush towards the adversary goal acts as a trend-setter, anticipating (or triggering) a similar movement direction by the defenders and his/her own team mates). .

 

 

Behavioral patterns

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The generic patterns are usually insufficient to explain specific behavior of particular moving object but they form the building blocks of higher level of movement patterns, which we called behavioral patterns. Behavioral patterns can solely be found in certain types of moving object for example a certain animal species. (Dodge et al, 2008)

 

 

Pursuit/evasion

 

Evasion and pursuit belong together. Evasion refers to one animal (i.e. the prey) trying to move away and escape from a threatening, pursuing animal (i.e. the predator). They describe very high-speed movements combined with large amounts of turning and looping extending over a potentially large area of the environment (Blythe et al, 1996). Pursuit and evasion can be seen as a combination of leadership and trend-setting movements where the evader leads and affects the pursuer’s movement variables.

 

 

Fighting

 

Fighting is a combination of pursuit and evasion, attack and defense. Very high-speed movements are combined with large amounts of tightly intertwined turning, looping and frequent contact (where trajectories meet) in small distance between objects (Blythe et al, 1996). Fighting behavior consists of  a complex combination of different generic patterns such as incidents, concurrence, repetition, co-location in space and time. If fighting occurs among a group of animals, other types of generic patterns such as convergence, divergence, encounter, breakup, and leadership might be involved.

 

 

Play

 

In animals, particularly juveniles, play is a form of practicing behaviors such as pursuit, evasion, fighting, or courtship. Hence, playing behavior consists of a combination of these movement behaviors, exhibiting looping, rapid dashes, and long still pauses. In play, animals repeatedly switch roles between pursuer and evader, or attacker and defender. (Blythe et al, 1996)

 

 

Flock

 

The flock pattern describes a group of animals (representing the generic pattern of a moving cluster) moving in the same direction while staying close together (Gudmundsson et al, 2004), for instance, a flock of sheep.

 

 

Leadership

 

The leadership pattern occurs when there is an individual that acts as the leader of a group for a specific duration. An individual can be said to be a leader if it does not follow anyone and is followed by sufficiently many other individuals at a proximate distance {(Laube & Imfeld, 2002), (Laube, 2005)}. Leadership is a specific kind of the generic pattern trend-setting and is mostly associated with animal or human behavior. The difference to trend-setting, however, is that leadership requires spatial and temporal proximity, while in trend-setting this requirement is less stringent.

 

 

Congestion

 

Refers to movement with slower than usual speeds, longer trip times, and increased queuing. Extreme congestion in road traffic will lead to a traffic jam, with vehicles fully blocked for possible extended periods of time. This pattern can be seen as a combination of meet and concurrence, along with constancy. A convoy of cars is a moving cluster which may move at slow or near-zero speed and hence lead to congestion. Similarly, traffic jams form spots of concentrations (stationary clusters).

 

 

Saccade/ fixation

 

In eye movement tracking studies, researchers typically analyze eye movements in terms of fixations (i.e. pauses over informative regions of interest) and saccades (rapid movements between fixations) (Salvucci, D.D., & Goldberg, 2000). In a spatio-temporal sense, eye movement recordings represent a combination of constancy and repetition of fast high-speed movements between fixations. In a spatial sense, they can be seen as a sequence of concentrations, as fixations represent spots of high spatial density.

 

 

 

 

References

 

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• Andrienko, N. & Andrienko, G. Designing Visual Analytics Methods for Massive Collection of Movement Data. Cartographica 2007, 42(2): 117-138.
• Andersson, M., Gudmundsson, J., Laube, P., & Wolle, T. Reporting leadership patterns among trajectories; SAC '07: Proceedings of the 2007 ACM symposium on Applied computing, ACM 2007, 3-7
• Agrawal, R. & Srikant, R. Mining Sequential Patterns Eleventh International Conference on Data Engineering 1995, IEEE Computer Society, 3.
• Benkert, M., Gudmundsson, J., Hübner, F. & Wolle, T. Reporting Flock Patterns. Lecture Notes in Computer Science, Springer-Verlag; 2006. 4168: 660-671.
• Blythe, P.W., Miller, G.F. & Todd, P.M. Human Simulation of Adaptive Behavior: Interactive Studies of Pursuit, Evasion, Courtship, Fighting, and Play. Proceedings of the Fourth International Conference on Simulation of Adaptive Behavior, 1996. Cambridge, MA: MIT Press/Bradford Books. 13-22

• Cao, H.; Mamoulis, N. & Cheung, D. Mining frequent spatio-temporal sequential patterns. In: Fifth IEEE Intl. Conference on Data Mining, 2005, 8.

• Dodge, S., Weibel, R. & Lautenschütz, A.-K. (2008). Towards a Taxonomy of Movement Patterns. Information Visualization. Information Visualization (2008) 7, 240–252. doi:10.1057/palgrave.ivs.9500182. (Download pdf)

• Erwig, M. Toward Spatiotemporal Patterns. In: Caluwe, Rita de, Tré, Guy de & Bordogna, Gloria (eds.): Spatio-Temporal Databases – Flexible Querying and Reasoning. Springer, 2004, 29-54.
• Fayyad, U., Piatetsky-Shapiro, G. & Smyth, P. From Data Mining to Knowledge Discovery in Databases. AI Magazine, 1996, 17(3): 37-54.
• Giannotti, F. & Pedreschi, D. Mobility, Data Mining and Privacy – Geographic Knowledge Discovery. Springer-Verlag. eds., 2007
• Gudmundsson, J., van Kreveld, M.J. & Speckmann, B. Efficient Detection of Motion Patterns in Spatio-temporal Data Sets. GIS 2004, 250-257.
• Gudmundsson, J. & van Kreveld, M. Computing Longest Duration Flocks in Trajectory Data. In: Proceedings of the 14th annual ACM international symposium on Advances in geographic information systems 2006 (GIS '06), 35 – 42.
• Gudmundsson, J., Laube, P. & Wolle, T. Movement Patterns in Spatio-Temporal Data. In: Shekhar, S. & Xiong, H. (eds.). Encyclopedia of GIS, Springer-Verlag, 2008.
• Imfeld, S. Time, Points and Space – Towards a Better Analysis of Wildlife Data. PhD Thesis, Department of Geography, University of Zurich, 2000.
• Kalnis P., Mamoulis N. and Bakiras S. On discover-ing moving clusters in spatio-temporal data. In: Proc. 9th International Symposium on Spatial and Temporal Databases 2005 (SSTD '05), 364—381.
• Laube, P. Analysing Point Motion – Spatio-Temporal Data Mining of Geospatial Lifelines. PhD Thesis, Dept. of Geography, University of Zurich, 2005.
• Laube, P., Imfeld, S. Analyzing relative motion within groups of trackable moving point ob jects. In GIScience 2002, Lecture Notes in Computer Sci-ence, Springer, Berlin, 2478, 142–144.
• Laube P., van Kreveld M., and Imfeld S. "Finding REMO-Detecting relative motion patterns in geo-spatial lifelines," in Developments in Spatial Data Handling: Proc. of the 11th International Sympo-sium on Spatial Data Handling 2004, Springer, Berlin Heidelberg New York, 201-214.
• Laube, P. & Purves, R. An Approach to Evaluating Motion Pattern Detection Techniques in Spatio-temporal Data. Computers, Environment and Urban Systems, 2006, 30: 347-374.
• Laube, P., Imfeld, S. & Weibel R. Discovering Relative Motion Patterns in Groups of Moving Point Objects. International Journal of Geographical Information Science 2005, 19(6): 639-668.
• Lee, J.W., Paek, O.H. & Ryu, K.H. Temporal Mov-ing Pattern Mining for Location-based Services. Journal of Systems and Software, 2004, 73: 481-490
• Salvucci, D.D., & Goldberg, J. H. Identifying fixa-tions and saccades in eye-tracking protocols. Proc. of the Eye Tracking Research and Applications Symposium 2000, New York: ACM Press, 71-78.
• Smyth, C.S. Mining mobile trajectories. In: Miller, H.J. & Han, J. (eds.): Geographic Data Mining and Knowledge Discovery, London: Taylor and Francis, 2001, 337-361.
• Turchin, P. Quantitative Analysis of Movement: Measuring and Modelling Population Redistribution in Animals and Plants. Sunderland, Massachusetts: Sinauer Publishers, 1998.
• Yuan, M. & K. Stewart Hornsby, Computation and visualization for the understanding dynamics of geographic domains: A Research Agenda, CRC Press, New York, NY, 2007.