In street-based transportation science, vehicle volume estimation receives lots of attention, as it provides important insights to several applications, such as situation-aware trip planning, attraction ranking and traffic control systems. In practice, empirical measurements are sparse due to budget limitations and constrained mounting options. Therefore, estimation of vehicle quantity is required to perform mobility analysis at unobserved locations. Accurate vehicle mobility analysis is difficult to achieve due to non-random path selection of the individual persons (resulting from motivated movement behaviour). This causes the vehicle volumes to distribute non-uniformly among the traffic network. Existing approaches (vehicle simulations and data mining methods) are hard to adjust to sensor measurements or require more expensive input data (e.g. high fidelity street networks plans or total number of vehicles in a city) and are, thus, unfeasible. In order to achieve a mobility model that encodes vehicle volumes accurately, we discuss several data mining methods which overcome the limitations of existing methods. These methods incorporate topological information and episodic sensor readings, as well as prior knowledge on movement preferences and movement patterns.

1. MOBILITY MODELS
Thomas Liebig

2. Mobility?

3. Empirical Mobility Data Analysis
[Hägerstrand 70]
[Lenntorp 76]
[Kuijpers 11]
[Leutzbach 72]
[Helbing 97]
[Schadschneider 04]
Traffic Flow Theory
(Physics & Statistics)
Time Geography
(Geomatic)

4. Geo Reference Systems
 WGS84
 e.g. used by GPS
 Mercator System UTM
 http://www.cs.hs-rm.de/~linn/fachsem0809/GeoCoord/Geodaetische_Koordinatensysteme.pdf
4

5. Spatial Data Representation
 Raster/Vector representation
 Properties
 Batch,
 Streams,
 Distributed,
 …
 Memory:
 Spatial RDBMS (PostGIS, Oracle Spatial, …),
 Moving Object Databases [Güting 05]
5

6. Spatial Data Protocols/Interfaces
 Defined by Open Geographic Consortium (OGC)
 Map Layers
 Web Map Service (WMS)
 Web Feature Service (WFS)
 Sensor Layers
 Sensor Observation Service (SOS)
 Storage & Exchange
 KML, GML
 CSV, Geo JSON, Geo PDF …
 Image- and Videoformats
Thomas Liebig @t_liebig TU Dortmund
6

7. Microscopic Traffic observations
 Speed
 Direction
 Acceleration
 Headaway
Dependent on
time, age, sex, purpose, temperature, street
characteristics, density [Weidmann 93]

8. Macroscopic Traffic observations
Measurement Methods (exemplified)
 Camera  density, occupancy
 ATL  flow
flow q(x,t)= #veh/Δt
density ρ(x,t) = #veh/Δx

9. Hierarchy of Motion [Hoogendorn 02]
 Target Selection, initial
planning
 Short-term decisions,
turning decisions, jam
avoidance
 Decisions on Speed an
Acceleration

10. Observations: Target Selection
 Order of multiple goals is selected such that it
minimizes travel distance (e.g. at shopping) [Helbing
97]
 In case of flocking the target selection may change:
taking the exit with the shortest queue [Heliövaara
11]

11. Observations: Path Planning
 Travel path (even the target) is not fixed, may be
re-planned in case of unexpected attractors
[Helbing 97]
 People tend to prefer the quickest path [Borgers &
Timmermans 1986,Guo & Huang 2011,
Hoogendoorn et al. 2002]
 Movement is planned with intermediate, eye-
catching, targets  landmark based navigation
 in some cases (e.g. rain or slippery ground) people
accept detours [Helbing 97]

12. Observations: Group Movement
 Usually, distance between people depends on
density
 But often pedestrians walk in groups of 2, three or
four people [Peters&Ennis 09]
 Formations of these group is staggered and
changes (even without obstacles)
 complex movement intersections among multiple
groups

13. Observations: Collective Behaviour
 Often narrow pathways are passed in alternating
directions by throngs, the frequency of oscillation
increses by the width of the pathway [Helbing 97]
 creation of dirt tracks
 Preference to walkable areas,
 avoidance of uneven ground
 quickest path selection

14. Observed Properties
 Relationship amongst flow
and occupancy and vice
versa
 Fundamental Diagram
 Conservation law
 For long enough
observation period every
object that enters a region
also leaves it

15. Observed Properties
 shock waves [Helbing]
 phantom jams [Schreckenberg]
 Lateral oscilation of people
due to crowd turbulences [Krausz]

16. Observed Properties
 Trajectories contain spatio-
temporal dependencies
[Liebig 08]
 e.g. commuters most likely
stay on a highway than
leaving into the villages
 Individual mobility follows
Lévy Flight [Gonzales 08]
 power law distribution of
distances
S2
S0
S1

17. Some Spatio-Temporal
Data Mining Tasks
 Tesselation
 Usage Pattern
 Profiling, Pattern Recognition
 Trajectory Simplification
 Spatio-Temporal Predictions
 Self Localization and Mapping
 Map Matching
 Routing

18. Mobility, Data Mining and Privacy
short version:
Mobility, Data Mining and
Privacy: The GeoPKDD
Paradigm
http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.190.367
2&rep=rep1&type=pdf
Thomas Liebig @t_liebig TU Dortmund
18

19. Exemplified Spatio-Temporal
Data Mining Tasks
 Tesselation
e.g.
[Voronoi 1908]
“Nouvelles applications des paramètres
continus à la théorie des formes
quadratiques. Deuxième mémoire.
Recherches sur les parallélloèdres primitifs.,”
Journal für die reine und angewandte
Mathematik (Crelle's Journal), no. 134
(December 1908): 198–287, http
://dx.doi.org/10.1515/crll.1908.134.198.
19

20. Exemplified Spatio-Temporal
Data Mining Tasks
 Pattern Mining
e.g.
 Trajectory Pattern Mining
[Giannotti et al. 07]
20

21. Exemplified Spatio-Temporal
Data Mining Tasks
 Profiling, Pattern Matching
e.g.
On Event Detection from
Spatial Time series for Urban
Traffic Applications [Souto 16]
21

22. Exemplified Spatio-Temporal
Data Mining Tasks
 Trajectory Simplification
zB mit
 SimpliFly: A Methodology for Simplification and
Thematic Enhancement of Trajectories
[Vrotsou et al. 2014]
http://www.computer.org/csdl/trans/tg/preprint/06851202.pdf
22

23. Exemplified Spatio-Temporal
Data Mining Tasks
 Self Localization and Mapping
e.g.
 Hector Open Source Modules
for Autonomous Mapping and
Navigation with Rescue Robots
[Kohlbrecher et al. 2014]
23

24. Exemplified Spatio-Temporal
Data Mining Tasks
 Map Matching
e.g.
 Map-Matching for Low-
Sampling-Rate GPS
Trajectories [Lou et al. 09]
http://research.microsoft.com/pubs/105051/Map-
Matching%20for%20Low-Sampling-
Rate%20GPS%20Trajectories-cameraReady.pdf
24

25. Exemplified Spatio-Temporal
Data Mining Tasks
 Spatio-temporal predictions:
Kriging
A Statistical Approach to Some
Mine Valuation and Allied Problems
on the Witwatersrand [Krige 51]
 K-Nearest Neighbour
25

26. Problem: Predict Traffic in a City

27. Some Modelling Goals
 Include sparse macroscopic measurements
 Predict future traffic at observed and unobserved
locations
 Coupling of microscopic and macroscopic values
[Hägerstrand 74]
 Invariance against model homeomorphisms
 Include arbitrary macroscopic measurements
 Applicable to unobserved traffic situations
 incorporate properties of traffic gained from empirical
studies

28. Ex1: Homeomorphism
 Introduce sensor on an edge, how are its predictions?
 Change temporal resolution, do values sum-up?
 Freeway experiment without intersection

29. Ex2: unobserved traffic situation
 Crossing with changing signaling scheme and
unobserved jams

30. Ex3: Spatio-Temporal Dependencies
 All people in WA live in LA and all people in WB live in LB
 Knowledge on origin is important to predict individual
destination.
 People leave at arbitrary times
WB
WA
LA
LB time
space

31. Mobility Modell Properties
 microscopic vs macroscopic
 discrete vs continuous
 deterministic vs stochastic
 high fidelity vs low fidelity
 complete vs. partial
[Schadschneider 04]

32. Recap: Conservation Law
implies gas kinetic models, e.g. Riemann equation
flow q(x,t)= #veh/Δt
density ρ(x,t) = #veh/Δx

33. Fluid Modell
 v(x,t) is modeled as static
function of ρ(x,t) so called
fundamental diagram
 fundamental diagram can
be observed empirically

34. Limitations of the Fluid Modell
[Helbing 97]
 If vehicles interact, the impulse and the
kinetic energy are usually not pre-
served. Thus, Newton's Third law of
motion (actio=reactio) is not
applicable.
 Temperature of a vehicle fluid cannot
be matched directly, as it is the
variance of the vehicle speed.
 Vehicular gases are not moving due to
external pressure, but caused by the
inner intention to move with a certain
speed.
 Due to the various movement targets,
separate flows in different directions
occur and interact.
 Vehicular behaviour is anisotropic.

35. Micro Simulation
 Control individual speed,
direction and route
 according to
 surrounding vehicles/pedestrians
 start/goal
 capabilities
 Multi Agent System
 MatSim
 Vissim
 SUMO
 …

36. Force Based Simulation
[Chraibi&Seyfried 10]
 Continuos space
 Space dependent on speed
 Repulsive forces
 Other pedestrians
 Obstacles
 Attractive forces

37. Floor Field Agent Based Simulation
[Kretz&Schreckenberg 06]
 Discrete space
 Cellular automaton
 Three floor fields
 Static floor field
 Holds precomputed distances to exit
 Dynamic floor field
 Influence of the other agents
 Vector field of motion of the agents
 Values diffuse and decay over time
 Obstacle floor field
 Repulsive force of obstacles

38. Cellular Automaton
[Nagel Schreckenberg 92]
 discrete spatio-temporal cells
(density, speed)
 Integer values for speed, density
 Transition rules independent of
 Data
 Time
 update rules based on previous
time slice
 microscopic properties can be
included in individual
 choice of direction and
 speed parameters

39. Nagel-Schreckenberg Model
In every round for all cars
 Speed := min(speed+1,max_Speed)
 Speed := min(distance to next car, Speed)
 with probability p:
Speed := max(0,Speed-1)
 Move!

40. Time Geography
 Past of the point
influences its present
and future…
 „All objects are related,
but close objects are
more related than
others“
 Space time prism,
Brownian Bridges, …

41. k-NN
 space-time discrete model of
(flow,density)
 may adapt to previous
model properties
 time (in)dependent
 continuous or discrete
features
 flexible dependency
structures
 commonly used in traffic
flow modeling

42. Mean Field Theory
[Schadschneider, Schreckenberg ‚93]
 space-time discrete
probabilistic model (flow)
 prediction based on
surrounding states in
previous time-slice
 transition probabilities not
time dependent

43. Traffic Prediction with STRF
[Liebig et al. 17]
 Space-time discrete
probabilistic model (flow)
 Flow discretized in classes
 transition probabilities
depend on absolute time
 trained from observations
 prediction dependent on its
Markov Blanket

44. Spatio-Temporal Random Fields
[Piatkowski et al. 12]

45. Spatio-Temporal Random Fields
[Piatkowski et al. 12]

46. TLMC Training Local Models from Label
Counts [Stolpe et al. 15]
 space-time discrete model of
flow
 flow discretized in classes
 Time independent transition
model, previously trained on
data
 dependency on observation
time series at neighboring
cells

47. TLMC: Centralized vs Decentralized
47
 For training, each node provides recorded sequences
 of measurements and
 of labels
Global Model
Centralize data
Local Models
Exchange data with fixed number of
neighbours

48. Global Model
48
Advantages
 Potential use of standard classifiers
 Access to all data eases modeling of the
whole joint distribution P(X,Y) between
observations and labels
Disadvantages
 Limited bandwidth can be a bottleneck
 High communication costs correlate with
energy consumption of wireless devices

49. TLMC: Local models
49
Informal Idea
 Predict label at node Pi with horizon r from current and
previous sensor measurements at neighbouring nodes

50. TLMC: Local Models
50
 Data preprocessing at each node Pi
 Slide window of size p over measurements
sequence Vi , creating windows xt
 Shift labels in Li by horizon r such that they
align correctly with each window
 The local data Di at Pi then looks like
t time
p
r
Vi
Li

51. TLMC: Learning task
51




52. Alternatives for Training Local Models
52

53. Local Models and Transmission of
Labels53
Advantages
 Labels usually can be encoded with less bits than sensor
values
 Constant number of neighbours solves bandwidth problem
Disadvantages
 Sending all labels still in order of sending all observations
 Individual labels provide ground truth on individual sensor
measurements
 Apply label aggregation, learn from Label Proportions

54. TLMC: How to aggregate labels
54
t time
Vi
Li
Vi
Li
Vi
Li
Vi
Li
Vni
At neighbouring node, learn a model that
predicts correctly labels of individual observations,
given own measurement and label proportions,
Pn1
(i)Pi
t time

55. LLP Method
55
 Cluster observations
Vni

56. LLP Method
56
 Assign labels to clusters, such that assignment minimizes number
of misclassified labels in all batches
Vni
Min MSE( , )

57. TLMC: Analysis of Communication Costs
57


 STRF sends more data due to optimization in several iterations

58. Poisson Dependency Networks
[Hadiji, Kersting et al. 16]
 Models count values as
Poisson distributed values
 Dependency Network of
multi-variate Poisson
distributions

59. CNN for Speed Prediction
[Ma et al. 17]
 Represents traffic as images

60. Summary
 Multiple models exist with different
properties/assumptions
 Data driven prediction models
 Physical rule based models
 Data mining methods to
 Extract rules/patterns from data
 Verify and match patterns
 Cluster and Match observations

61. Your questions?
 related topics:
 Sensors
 Communication
 Privacy
 Data storage & Processing
 Semantics, Context & Human Factors
 Routing, Scheduling & Planning
 Event detection
 …

62. Time Geography
 T. Hägerstrand. What about people in Regional Science? Papers in
Regional Science, vol. 24, no. 1, pages 6–21, 1970.
 T. Hägerstrand. Tiidsgeografisk Beskrivning. Syfte och Postulat.
Svensk Geografisk Årsbok, vol. 50, pages 86–94, 1974.
 B. Kuijpers, H. J. Miller and W. Othman. Kinetic space-time prisms. In
Proceedings of the 19th ACM SIGSPATIAL International Symposium
on Advances in Geographic Information Systems, ACM-GIS, GIS,
pages 162–170. ACM, 2011.
 B. Lenntorp. Paths in space-time environments: a time-geographic
study of movement possibilities of individuals. Meddelanden från
Lunds universitets geografiska institution. Royal University of Lund,
Dept. of Geography,1976.

63. Physical Modells
 D. Helbing. Verkehrsdynamik: Neue physikalische Modellierungskonzepte.
Springer, 1997.
 W. Leutzbach. Einführung in die Theorie des Verkehrsflusses. Berlin,
Heidelberg, New York: Springer-Verlag, 1972.
 K. Nagel, M. Schreckenberg. A cellular automaton model for freeway
traffic. Journal de Physique I, EDP Sciences, 1992, 2 (12), pp.2221-2229
 M. Chraibi, A. Seyfried and A. Schadschneider. The generalized centrifugal
force model for pedestrian dynamics. Physical Review E, vol. 82, page
046111, 2010.
 T. Kretz and M. Schreckenberg. The F.A.S.T.-Model. In Samira El Yacoubi,
Bastien Chopard and Stefania Bandini, editors, Cellular Automata, volume
4173 of Lecture Notes in Computer Science, pages 712–715. Springer
Berlin / Heidelberg, 2006.
 A. Schadschneider. "Physik des Straßenverkehrs." Skript zur Vorlesung,
Institute of Theoretical Physics, Cologne University (2004).

64. Traffic Observations
 Weidmann, Ulrich. "Transporttechnik der fussgänger, transporttechnische
eigenschaften des fussgängerverkehrs." Schriftenreihe des IVT 90 (1993).
 Korhonen, Timo, and Simo Heliövaara. "Fds+ evac: herding behavior and exit
selection." Fire Safety Science 10 (2011): 723-734.
 Detection and Simulation of Dangerous Human Crowd Behavior. 2012. Doktorarbeit.
Universitäts-und Landesbibliothek Bonn.
 Peters, Christopher, and Cathy Ennis. "Modeling groups of plausible virtual
pedestrians." IEEE Computer Graphics and Applications 29.4 (2009).
 Gonzalez, Marta C., Cesar A. Hidalgo, and A-L. Barabasi. "Understanding
individual human mobility patterns." arXiv preprint arXiv:0806.1256 (2008).
 S. P. Hoogendoorn, P. H. L. Bovy and W. Daamen. Microscopic Pedestrian
Wayfinding and Dynamics Modelling. In M. Schreckenberg and S. D. Sharma,
editors, Pedestrian and Evacuation Dynamics, pages 123–155, 2002.
 R. Guo and H. Huang. Route choice in pedestrian evacuation: formulated using a
potential field. Journal of Statistical Mechanics: Theory and Experiment, vol. 2011,
no. 04, page P04018, 2011.

65. Probabilistic Modeling Approaches
 T. Liebig, C. Körner, and M. May, “Scalable sparse bayesian network learning for
spatial applications,” in Data Mining Workshops, 2008. ICDMW’08. IEEE
International Conference on, 2008, pp. 420-425.
 T. Liebig, C. Körner, and M. May, “Fast visual trajectory analysis using spatial
bayesian networks,” in Data Mining Workshops, 2009. ICDMW’09. IEEE
International Conference on, 2009, pp. 668-673.
 Piatkowski, Nico, Sangkyun Lee, and Katharina Morik. "Spatio-temporal random
fields: compressible representation and distributed estimation." Machine
learning 93.1 (2013): 115-139.
 T. Liebig, N. Piatkowski, C. Bockermann, and K. Morik, “Dynamic Route Planning with
Real-Time Traffic Predictions,” Information Systems, vol. 64, pp. 258-265, 2017.
 Murphy, Kevin P. Machine learning: a probabilistic perspective. MIT press, 2012.
 Schadschneider, Andreas, and Michael Schreckenberg. "Cellular automation models
and traffic flow." Journal of Physics A: Mathematical and General 26.15 (1993):
L679.

66. Spatial Data Mining & Models
 Güting, Ralf Hartmut, and Markus Schneider. Moving objects databases. Elsevier, 2005.
 F. Giannotti and D. Pedreschi. Mobility, Data Mining and Privacy - Geographic Knowledge Discovery. Springer, 2008.
 F. Giannotti, M. Nanni, F. Pinelli and D. Pedreschi. Trajectory pattern mining. In KDD, pages 330–339. ACM, 2007.
 G. Voronoï. Nouvelles applications des paramètres continus à la théorie des formes quadratiques. Deuxième mémoire.
Recherches sur les parallélloèdres primitifs. Journal für die reine und angewandte Mathematik (Crelle’s Journal), no. 134,
pages 198–287, December 1908.
 Vrotsou, Katerina, et al. "SimpliFly: A methodology for simplification and thematic enhancement of trajectories." IEEE
transactions on visualization and computer graphics 21.1 (2015): 107-121.
 G. Souto and T. Liebig, “On Event Detection from Spatial Time series for Urban Traffic Applications,” in Solving Large Scale
Learning Tasks: Challenges and Algorithms, S. Michaelis, N. Piatkowski, and M. Stolpe, Eds., Springer International Publishing,
2016, vol. 9580, pp. 221-233.
 Ma, Xiaolei, et al. "Learning traffic as images: a deep convolutional neural network for large-scale transportation network
speed prediction." Sensors17.4 (2017): 818.
 M. Stolpe, T. Liebig, and K. Morik, “Communication-efficient learning of traffic flow in a network of wireless presence sensors,”
in Proceedings of the Workshop on Parallel and Distributed Computing for Knowledge Discovery in Data Bases (PDCKDD 2015),
CEUR-WS, 2015
 X. Wang and K. M. Kockelmann. Forecasting Network Data: Spatial Interpolation of Traffic Counts from Texas Data. Journal
of the Transportation Research Board, vol. 2105, no. 13, pages 100–108, 2009.
 Habel, L., Molina, A., Zaksek, T., Kersting, K., & Schreckenberg, M. (2016). Traffic Simulations with Empirical Data: How to
Replace Missing Traffic Flows?. In Traffic and Granular Flow'15 (pp. 491-498). Springer International Publishing.
 Lou, Yin, et al. "Map-matching for low-sampling-rate GPS trajectories." Proceedings of the 17th ACM SIGSPATIAL international
conference on advances in geographic information systems. ACM, 2009.
 Kohlbrecher, Stefan, et al. "Hector open source modules for autonomous mapping and navigation with rescue robots." Robot
Soccer World Cup. Springer, Berlin, Heidelberg, 2013.