# Modelling Approaches

The STANDARD Project makes use of the latest advances in spatio-temporal analysis and modelling.

## STARIMA

The Space-Time Autoregressive Integrated Moving-Average (STARIMA) model family is a useful tool for modelling space-time processes that are stationary (or weak stationary) in space and time. It is proposed firstly by Martin and Oeppen (1975) and has gained widespread popularity in modelling multiple time series data that correspond to different spatial locations, which are known as space-time series. The STARIMA model family includes models of different forms of space-time series analysis: STAR (space-time autoregressive), STMA (space-time moving average), STARMA (space-time autoregressive moving-average), and STARIMA (Pfeifer and Deutsch 1980). Currently, STARIMA models have been applied to model space-time dynamic processes in many domains, such as image analysis (Szummer and Picard 1996; Crespo et al. 2007), transport (Kamarianakis and Prastacos 2005), business and economics (Cliff and Ord 1975; Pfeifer and Bodily 1990; Pace et al. 1998, 2000), and physical and environmental sciences (Martin and Oeppen 1975; Bennett 1975; Perry and Aroian 1979; Pfeifer and Deutsch 1980), etc. However, how to accommodate network space-time association in STARIMA model hasn’t been well recognized and examined in the previous traffic research. It hereby is essential to further research network space-time association.

## Support Vector Machines

Boser et al (1992) described a training algorithm that maximises the margin
between the training examples and the class boundary that has come to be known
as SVM. SVM was the first method to employ the
kernel trick in order to treat non-linear problems in a linear fashion.The classification
produced depends only on the so called support vectors, which are the training
examples that are closest to the decision boundary or *hyperplane*.
SVM has a number of advantages over previous techniques:

· The classification achieves errorless separation of the training data

· Outliers are identified by the algorithm and can be removed easily

· The maximal margin means that it is less sensitive to computational inaccuracies

Recently, SVM and SVR (Support Vector Regression) have been applied to spatial and temporal data; this project aims to make use of custom built kernels in order to process space and time simultaneously in order to predict conditions on the road network.

## Geographically Weighted Regression (GWR)

Geographically Weighted Regression (GWR) GWR is a method developed by Fotheringham, Brunsdon and Charlton (1998) for the analysis of spatially varying relationships in response to the lack of sufficient methodologies to analyse local relationships in multivariate spatial datasets. A standard global regression model can be given as follows:

GWR extends this framework by allowing the calculation of local regression parameters, thus the model can be rewritten as:

Where (u_i,v_i) are the coordinates of the ith point in space and β_k (u_i,v_i) is a realisation of the continuous function β_k (u,v) at point i. This means that there is a continuous surface of parameter values. In GWR the coefficients are assumed not to be random but rather a deterministic function of location in space. The weighting of each point is determined by a kernel function (usually Gaussian) which specifies the weight matrix w_ij as a function of distance d_ij.

## Agent Based Modelling

Agent-based modelling (ABM) is the computational simulation of the actions
and interactions of autonomous agents. Agents are designed with an ability
to make decisions and change their behaviours in consideration of local
conditions. Agents will learn rules, adapt and eventually understand the
actions required to best achieve a certain goal. In modelling the behaviour
of individuals, agent-based modelling is able to better understand the
microscopic interactions between agents (be them individuals or collectives)
within a population that, when viewed at a higher level, generate
macroscopic behaviours. The emergence of macroscopic phenomena from these
small interactions help researchers across many fields understand the low
level conditions that lead to behaviours that might otherwise be
misunderstood.

Specifically, this research seeks to move away from the traditional paradigms of transport modelling that aggregate and generalise behaviour.
Instead, it is considered that the emergence of congestion is the
consequence of certain driver decisions at one scale and local interactions
at another. Agent-based modelling will be used to demonstrate this.

## Spatio-Temporal Clustering

Spatio-temporal clustering (STC) is the grouping of similarly behaving observations of a phenomenon having spatial and temporal dimensions. Spatial and temporal dimensions should be integrated in the clustering approach which will lead to capturing the dynamics of the changing observation values with time. STC aims to produce spatio-temporal clusters which maximises the similarities between the observations within clusters while minimizing the similarities between the observations that belong to different clusters. STC has been used in areas as epidemiology, crime science, zoology and network analysis.