some developments in space-time modelling with gis tao cheng – university college london (u.k)
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Some Developments in Space-Time Modelling with GISTao Cheng – University College London (U.K)Intelligent Analysis of Environmental Data (S4 ENVISA Workshop 2009)TRANSCRIPT
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Integrated Spatio-Temporal Data Mining for Network Complexity
Tao Cheng Tao Cheng
Senior LecturerDepartment of Civil, Environmental & Geomatic EngineeringUniversity College LondonEmail: [email protected]
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2
Dr Tao Cheng – Background• Data quality and uncertainty
of spatial objects• Multi-scale spatio-temporal
data modelling and analysis • Intelligent spatio-temporal
data mining
• 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]
[1]
[3]
[2]
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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?
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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
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• time series analysis + spatial correlation
• spatial statistics + the time dimension
• time series analysis + artificial neural networks
Existing ST analysis methods
ST dependence ≠ space + time
Integrated modelling of ST is needed –
• seamless & simultaneous
• ST-association/autocorrelation
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• - the observation of the data series at spatial location i and at time t;
• - space-time patterns that explain large-scale deterministic space-time trends and can be expressed as a nonlinear function in space and time.
• - the residual term, a zero mean space-time correlated error that explains small-scale stochastic space-time variations.
)(z ti
)(tiμ
)(tei
)()()( tettZ iii +μ=
Space-time data = global (deterministic) space-time trends + local (stochastic) space-time variations
Zi=ui+ei
Z(t)=u(t)+e(t)
Principle of ST Modelling
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Model 1 - STARIMA - Spatio-Temporal Auto-Regressive Integrated Moving Average
∑ ∑∑∑= = ==
+−−−=p
k
q
l
n
h
hlh
m
h
hkhi
lk
tltWktzWtz1 1 0
)(
0
)( )()()()( εεθφ
(Pfeifer P E and Deutsch S J, 1980)
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Model 2 - ANN - Artificial Neural Networks
SFNN – spatial interpolation DRNN – time series analysis
( ) a static neuron ( ) neuronb dynamic
∑=
+⋅=n
1jjiji bziwz b1)(tzlwz(t)iw)t(z +−⋅+⋅=
(Mandic D P and Chambers JA, 2001)
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• ANN for space-time trend analysis
)),(()(ˆ 01
β+β=μ ∑=
tifftn
kki
Tao Cheng, Jiaqiu Wang, Xia Li, Accommodating Spatial Associations in DRNN for Space-Time Analysis, Computers, Environment and Urban System, under review
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Model 3 – SVM - Support Vector Machines
SVC & SVR (Vapnik et al, 1996)
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Model 1 – STARIMA
• define weights based upon spatial distance and spatial adjacency• consider anisotropy• able to model spatially continued phenomena
∑ ∑∑∑= = ==
+−−−=p
k
q
l
n
h
hlh
m
h
hkhi
lk
tltWktzWtz1 1 0
)(
0
)( )()()()( εεθφ
Our approach – Integrated modelling of ST
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Model 2 - Hybrid Modelling
STARIMA to model stochastic space-time variations
)()()( tettZ iii +μ=
ANN to model nonlinear space-time trends
• 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
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Model 3 - STANN
∑=
+−⋅+−⋅=n
1ji
)0(j
)1(jii b1)(tzlw1)(tziw(t)zSpace-Time Neuron
• 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
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Model 4 - STSVR
• Nonlinear Spatio-Temporal Regression by SVM
• Develop ST kernel function• Overcome over-fitting in STANN• Deal with errors• Model nonlinearity & heterogeneity
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Case Study: 194 meteorological stations
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Case Study – Observations (1951 – 2002)
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Nonlinear space-time trends captured by the ANN model – (a) fitted (b) predicted
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Predicted (a) STARIMA model (b) Hybrid model (c) Real
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STANN – Space-Time Forecasting Results
(a) STARIMA (b) STANN (c) Real.
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Residual maps for three fitted years 1970, 1980, and 1990
(a) STANN (b) STARIMA
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(a) STANN model (b) STSVR model (c) Real.
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STARMA HYBRID STANN STSVR
Model-driven √
Data-driven √ √
Hybrid √
Linear √ √
Nonlinear √ √
Stationary √ √ √ √
Nonstationary √ √ √
Space/TimeDiscrete √ √ √ √
Space Continuous Tim Discrete √ √ √
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Spatio‐Temporal Analysis of Network Data and Road Developments
Dr Tao Cheng CEGE UCL
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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
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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
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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
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ISTDM for Network Complexity
1) Dynamics2) Spatial dependence3) Spatio-temporal interactions4) Heterogeneity
Modelling spatiality and spatio-temporal dependence(autocorrelation) of networks is the bottleneck.
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London Road NetworksCordons Central, Inner, Outer Screenlines
Thames, Northern, five radialsfour peripherals
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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
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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
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Acknowledgements
National High-tech R&D Program (863 Program)
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Website
• www.cege.ucl.ac.uk• http://standard.cege.ucl.ac.uk/