Some Developments in Space-Time Modelling with GIS Tao Cheng – University College London (U.K) Intelligent Analysis of Environmental Data (S4 ENVISA Workshop 2009)

1. Integrated Spatio-Temporal Data
Mining for Network Complexity
Tao Cheng
Senior Lecturer
Department of Civil, Environmental & Geomatic Engineering
University College London
Email: tao.cheng@ucl.ac.uk

2. Dr Tao Cheng – Background
• Data quality and uncertainty [1]
of spatial objects
• Multi-scale spatio-temporal
data modelling and analysis
• Intelligent spatio-temporal
data mining [3]
• Some relevant projects:
– 4D GIS for decision support system
[1]
– Managing uncertainty and temporal
updating (EU)
– Experimental modelling of changing
activity patterns using GIS (HK) [2]
– Location-Based Services and the
Beijing Olympics (HK)
– Spatio-temporal data mining (PRC)
[3] [2]
2

3. Outline
• Why integrated spatio-temporal data mining?
• Existing ST analysis methods
– STARIMA, ANN, SVM
• Our approach
– A hybrid model – ANN + STARIMA
– Space-Time Neural Networks – STANN
– Space-Time Support Vector Machines – STSVM
• ISTDM for network complexity?

4. Characteristics of ST Data
• Dynamic, multi-dimensional, multi-scale
• Spatial dependence
“Everything is related to everything else, but near things are more
related than distant things” — Tobler, First Law of Geography
“If the presence of some quantity in a county (sampling unit)
makes its presence in neighbouring counties (sampling units)
more or less likely, we say that the phenomenon exhibits spatial
autocorrelation” — Cliff and Ord
• Temporal dependence
• Heterogeneity & nonlinearity

5. Existing ST analysis methods
• time series analysis + spatial correlation
• spatial statistics + the time dimension
• time series analysis + artificial neural networks
ST dependence ≠ space + time
Integrated modelling of ST is needed –
• seamless & simultaneous
• ST-association/autocorrelation

6. Principle of ST Modelling
Space-time data = global (deterministic) space-time trends +
local (stochastic) space-time variations
Z i (t ) = μi (t ) + ei (t ) Z(t)=u(t)+e(t)
Zi=ui+ei
• zi (t ) - the observation of the data series at spatial location i and at
time t;
• μi (t ) - space-time patterns that explain large-scale deterministic
space-time trends and can be expressed as a nonlinear function in
space and time.
• ei (t ) - the residual term, a zero mean space-time correlated error
that explains small-scale stochastic space-time variations.

7. Model 1 - STARIMA - Spatio-Temporal Auto-
Regressive Integrated Moving Average
p mk q nl
zi ( t ) = ∑∑ φ khW ( h ) z ( t − k ) − ∑ ∑ θ lhW ( h )ε ( t − l ) + ε ( t )
k =1 h = 0 l =1 h = 0
(Pfeifer P E and Deutsch S J, 1980)

8. Model 2 - ANN - Artificial Neural Networks
(Mandic D P and Chambers JA, 2001)
SFNN – spatial interpolation DRNN – time series analysis
( a ) static neuron ( b ) dynamic neuron
n
z i = ∑ iw ij ⋅ z j + b
ˆ z( t ) = iw ⋅ z(t) + lw⋅ z(t − 1) + b
ˆ ˆ
j=1

9. • ANN for space-time trend analysis
n
μ i (t ) = f (∑ β k f (i, t ) + β 0 )
ˆ
k =1
Tao Cheng, Jiaqiu Wang, Xia Li, Accommodating Spatial Associations in
DRNN for Space-Time Analysis, Computers, Environment and Urban System,
under review

10. Model 3 – SVM - Support Vector Machines
SVC & SVR (Vapnik et al, 1996)

11. Our approach – Integrated modelling of ST
Model 1 – STARIMA
p mk q nl
zi ( t ) = ∑∑ φ khW ( h ) z ( t − k ) − ∑ ∑ θ lhW ( h )ε ( t − l ) + ε ( t )
k =1 h = 0 l =1 h = 0
• define weights based upon spatial distance and
spatial adjacency
• consider anisotropy
• able to model spatially continued phenomena

12. Model 2 - Hybrid Modelling
Z i (t ) = μ i (t ) + ei (t )
ANN to STARIMA to
model model
nonlinear stochastic
space-time space-time
trends variations
• overcome the limits of STARIMA
• Stationarity
• Linearility
Tao Cheng, Jiaqiu Wang, Xia Li, A Hybrid Framework for Space-Time Modeling of
Environmental Data, Geographical Analysis, under review

13. Model 3 - STANN
n
Space-Time Neuron z i (t) = ∑ iw (ji ) ⋅ z j (t − 1) + lw ( 0 ) ⋅ z i (t − 1) + b
ˆ 1
ˆ
j=1
• One step implementation of ANN+ STARIMA
• Accommodate ST associations in ANN
• Deal with nonlinearity & heterogeneity in BP learning
Jiaqiu Wang, Tao Cheng, STANN – Modeling Space-Time Series by Artificial Neural
Networks, International Journal of Geographical Information Science, under review

14. Model 4 - STSVR
• Nonlinear Spatio-Temporal Regression by SVM
• Develop ST kernel function
• Overcome over-fitting in STANN
• Deal with errors
• Model nonlinearity & heterogeneity

15. Case Study: 194 meteorological stations

16. Case Study – Observations (1951 – 2002)

17. Nonlinear space-time trends captured by the ANN model – (a) fitted (b) predicted

18. Predicted (a) STARIMA model (b) Hybrid model (c) Real

19. STANN – Space-Time Forecasting Results
(a) STARIMA (b) STANN (c) Real.

20. Residual maps for three fitted years 1970, 1980, and 1990
(a) STANN (b) STARIMA

21. (a) STANN model (b) STSVR model (c) Real.

23. STARMA HYBRID STANN STSVR
Model-driven √
Data-driven √ √
Hybrid √
Linear √ √
Nonlinear √ √
Stationary √ √ √ √
Nonstationary √ √ √
Space/Time
√ √ √ √
Discrete
Space Continuous
Tim Discrete √ √ √

24. Spatio‐Temporal Analysis of Network Data
and Road Developments
Dr Tao Cheng
CEGE UCL

25. Team (April 2009 – March 2012)
• UCL
– Dr Tao Cheng (PI), Senior Lecturer in GIS
– Prof. Benjamin Heydecker (Co-I), Professor of Transport Studies
– Dr Jingxin Dong, Transport Modelling (F1)
– Dr Jiaqiu Wang, GIS (F2)
– RS, MSc in GIS – SVM/GWR
– EngD, MSc in Transport – Simulation
– 3 visiting scholars, each 2 months
Other PhDs
– Mr Berk Anbaroglu (RS), BSc in Computer Science – outlier
detection
– Ms Garavig Tanaksaranond (RS), MSc in GIS – dynamic
visualization
• TfL RNP&R
– Mr Andy Emmonds, Principal Transport Analyst
– Mr Mike Tarrier, Head of RNP&R
– Mr Jonathan Turner, Performance Analyst

26. Aim
• To quantitatively measure road network
performance
• To understand causes of traffic congestion
– association between traffic and interventions
• traffic flow, speed/journey time
• incidents, road works, signal changes and bus lane changes
• Case study – London

27. What’s new?
• data-driven, mining
• integrated space and time
– ST associations
• combine regression analysis with machine
learning
– improve the sensitivity and explanatory power
• study the heterogeneity and scale of road
performance
– optimal scale for monitoring

28. ISTDM for Network Complexity
1) Dynamics
2) Spatial dependence
3) Spatio-temporal interactions
4) Heterogeneity
Modelling spatiality and spatio-
temporal dependence
(autocorrelation) of
networks is the bottleneck.

29. London Road Networks
Cordons
Central, Inner, Outer
Screenlines
Thames,
Northern,
five radials
four peripherals

30. Challenge (2) - Data issues
• massive – 20GB monthly
• multi-sourced related to 5 different networks
• different scales (density & frequency)
• variable data quality
• contain conflicts, errors, mistakes and gaps

31. Methodology: some preliminary thoughts
• accommodate network structure (topology &
geometry)
• model spatio-temporal correlation
• investigate network heterogeneity
– STGWR
• model impacts of interventions
– STARIMA & DRNN; hybrid; STANN
• Traffic pattern clustering and long-term
prediction
– STANN; STSVM
• sensitivity analysis and accuracy assessment
• simulate congestion in the short term

32. Acknowledgements
National High-tech R&D Program
(863 Program)

33. Website
• www.cege.ucl.ac.uk
• http://standard.cege.ucl.ac.uk/