In this example we consider a situation in which forecasts of shopping trips in region B are sought, based on data collected in region A (possibly a subset of B), or where regions A and B are the same but studied at different points in time. The data available for region A relates to attributes of source zones or origins (O), destination zones (D), a measure of the distance between each paired origin (i) and destination (j) zone, and the recorded average number of shopping trips (T_ij) per trading day. Here we assume a generalised trip model of the form:

T_ij=f(O_i,D_j,d_ij)

where f() is an unknown function of the attribute data and the separation measure. For example, we may have data for origin zones providing the population numbers (POPUL) and the average household incomes (HOUSINC) which are demand driver or ‘push’ measures; and for destination zones we may have the retail floor space in thousands of square metres (RETAILSP) and the number of parking spaces in thousands (PARKINGSP) which are attraction or ‘pull’ measures. In addition, we can compute a measure of zone separation (DISTANCE), for example as Euclidean distance, network distance, estimated travel time, or some other separation measure. In total these data provide five explanatory variables (input variables) with which we seek to explain one observed variable (output), actual shopping trip levels. As mentioned previously, Fischer (2006) has studied this class of problem over many years, and has shown that ANN models can provide an excellent fit to observed data and provide good quality generalisations from such data.

A simple ANN model for the problem we have described is a 5-m-1 MLP, which we train using the observed data (or more generally a subset of this) and validate and/or test using the remainder of the observed data. Because the data can be seen as a set of rows, with columns corresponding to the 5 input variables and 1 output variable, they are ideally suited to simple text file, spreadsheet or database storage. Indeed, such data are similar to those found in financial and commodity trading, where a range of index, price and volume data by time of day or across days is input and closing prices, for example, are the output. ANNs have found considerable favour in this field and have resulted in the availability of a large number of desktop-based software packages and add-ins (e.g. Excel utilities) targeted specifically at this community of users. For illustrative purposes we have used one such package (from Neural Planner Software) to import a spreadsheet of simulated origin, destination and distance data (inputs) and trip levels (output) that we have generated using the specific variables described above. We have then requested the software to model the data (Figure 8‑16). In this diagram thicker lines identify stronger weights, green lines are positive weights, and red lines negative weights. Bias nodes are not separately illustrated but are including in the modelling. This particular software package uses logistic activation and gradient-based back-propagation (as described in Section 8.3.1.2) to train the network. Data are automatically normalised by the software for processing and then converted back when generating predictions. The software also estimates the preferred number of hidden layer nodes and can automatically increment these from an initial minimum value in order to obtain the best possible result. Between 1 and 3 hidden layers are catered for, but most models of this type can be accommodated with the default one hidden-layer model.

Figure 8‑16 MLP trip distribution model 1

Rows from the input spreadsheet can be assigned explicitly as being for training or validation, or random samples of those provided may be used for validation. Other, non-commercial packages could equally well be used, such as NuMAP from the University of Texas at Arlington. The latter includes a range of ANN facilities and a simple user interface and data file structure. Assuming the training process yields a high quality network (i.e. excellent in terms of its fit to the validation data and any additional test data provided) its use for prediction may then be considered and compared with alternative models (e.g. gravity-based models with calibrated parameters) applied to the same datasets. However, this initial MLP modelling process did not yield good results based on fit to validation data. The process was therefore re-examined, this time log transforming the data (input and output) before commencing, adjusting the learning rate and momentum, and re-running the network modelling. The network on this occasion provided an improved fit to validation data (60% within 10% of known values ― as applied to the log transformed data) using 8 hidden nodes rather than 5, as shown in Figure 8‑17.

Figure 8‑17 MLP trip distribution model 2

The bars in the node ovals indicate the positive and negative component levels, from top to bottom: net input; activation; bias; error

The effective number of model parameters therefore increased, which explains part of the observed improvement. In this example we have also shown the relative importance computed by the model of the input variables. As can be seen, distance is the dominant factor, with the remaining four variables (two push and two pull factors) being of approximately equal significance.

This rather simplistic analysis highlights several issues. First, it is clear that ANN modelling is a powerful and valuable tool for modelling a wide range of data types and problems. Second, each application area presents different challenges, and application-specific modelling (e.g. selection of training, validation and test data sets; transformation and normalisation of input data; network design and control parameter settings) is an important aspect of successful modelling. Finally, ANN modelling may reveal structures in the data that point the way to simpler and more general models.