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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)
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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]
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]
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?
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
• 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
• - 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
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)
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)
• 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
Model 3 – SVM - Support Vector Machines
SVC & SVR (Vapnik et al, 1996)
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
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
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
Model 4 - STSVR
• Nonlinear Spatio-Temporal Regression by SVM
• Develop ST kernel function• Overcome over-fitting in STANN• Deal with errors• Model nonlinearity & heterogeneity
Case Study: 194 meteorological stations
Case Study – Observations (1951 – 2002)
Nonlinear space-time trends captured by the ANN model – (a) fitted (b) predicted
Predicted (a) STARIMA model (b) Hybrid model (c) Real
STANN – Space-Time Forecasting Results
(a) STARIMA (b) STANN (c) Real.
Residual maps for three fitted years 1970, 1980, and 1990
(a) STANN (b) STARIMA
(a) STANN model (b) STSVR model (c) Real.
STARMA HYBRID STANN STSVR
Model-driven √
Data-driven √ √
Hybrid √
Linear √ √
Nonlinear √ √
Stationary √ √ √ √
Nonstationary √ √ √
Space/TimeDiscrete √ √ √ √
Space Continuous Tim Discrete √ √ √
Spatio‐Temporal Analysis of Network Data and Road Developments
Dr Tao Cheng CEGE UCL
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
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
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
ISTDM for Network Complexity
1) Dynamics2) Spatial dependence3) Spatio-temporal interactions4) Heterogeneity
Modelling spatiality and spatio-temporal dependence(autocorrelation) of networks is the bottleneck.
London Road NetworksCordons Central, Inner, Outer Screenlines
Thames, Northern, five radialsfour peripherals
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
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
Acknowledgements
National High-tech R&D Program (863 Program)
Website
• www.cege.ucl.ac.uk• http://standard.cege.ucl.ac.uk/