Artificial neural networks (ANNs), sometimes referred to as computational neural networks (CNNs), are an attempt to emulate features of biological neural networks in order to address a range of difficult information processing, analysis and modelling problems. Sections 8.3.1.3, 8.3.1.4, and 0 provide examples of the application of ANN to practical problems in spatial analysis, including land-use classification and spatial interaction modelling. Within the field of spatial analysis only certain types of ANNs have been found to be especially useful to date. This is not to say that other forms of ANN, developed within the computational science field, are not applicable to such problems, but rather that these areas have yet to be explored in depth. There is also considerable ongoing debate as to whether such methods simply amount to data fitting, with little or no value beyond that of description, an issue that will become clearer as we discuss the issue of generalisation of such methods to unseen datasets.

Biological neurons, or nerve cells, receive multiple input stimuli, combine and modify the inputs in some way, and then transmit the result to other neurons. Most advanced animals (i.e. most life forms more complex than simple worms) have a very large number of such neurons, which in turn have vast numbers of interconnections with other neurons. This complex network structure is a biological neural network (BNN). A BNN is often divided into sub-structures that perform similar functions and the network as a whole is capable of performing very complex information processing.

The principal class of ANNs that we discuss are so-called feedforward networks. Of these, perhaps the most widely used is the multi-level perceptron  (MLP) model (see Section 8.3.1.1 for more details). Other models we discuss below include radial basis function neural networks (RBFNNs, Section 8.3.2, but also compare this with our earlier discussion of RBFs in Section 6.6.4), and self-organising networks (notably SOMs, see further Section 8.3.3).

A typical feedforward ANN consists of three or more inter-connected layers of nodes ― an input layer, one or more hidden intermediate layers (often just 1), and an output layer (Figure 8‑6). The arrows indicate the direction of information flow, feeding information forward from input to output. Note that there may be any number of nodes at each level of the network, and not all nodes need to be connected to every node in the next layer. For example, in Figure 8‑6 hidden node H2 only receives input from input nodes I1 and I3, and only provides output to node O1. This arrangement can be seen as a directed graph, or as a rather complex-looking function mapping.

Figure 8‑6 Simple 3-5-2 feedforward artificial neural network

The connections between the input layer and hidden layer can be described using a weight matrix, W, where the row/column entries w_ij are positive or negative real-valued weights, or 0 if no connection exists. Likewise, the connections between the hidden layer and the output layer can also be viewed as a weight matrix, Z say, again consisting of a set of weights, z_jk. Positive weights in each case imply a reinforcement process associated with the source node or input, whilst negative weights correspond to inhibition.