Some Developments in Space-Time Modelling with GIS Tao Cheng – University College London (U.K)

Integrated Spatio-Temporal Data Mining for Network Complexity

Tao Cheng Tao Cheng

Senior LecturerDepartment of Civil, Environmental & Geomatic EngineeringUniversity College LondonEmail: tao.cheng@ucl.ac.uk

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/