Neural Computing

Neural computing refers to any of a number of computational methods that involve emulation of neurological function in human or animal brains. The most widely applied method of this kind is the artificial neural network (ANN), often simply referred to as neural net. Other methods include image processing, pattern recognition, and cellular automata. ANNs are modeled loosely on neurons in the brain and share an ability to generalize from specific information and to learn. They are applied principally to classification problems.

An ANN is a simple model of brain function consisting of an interconnected set of neurons. Each neuron has a number of inputs and outputs and converts a given combination of input signal levels to a defined signal output level. Typically, signal output levels are a weighted sum of input signal levels, often with a threshold applied so that the end result is a binary output regardless of the exact weighted sum of the inputs. This simple model of a neuron was first proposed by Warren McCulloch and Walter Pitts during the 1940s. The arrangement of interconnections between neurons usually is layered. An input layer receives signals derived from observational data. Each layer in a series of layers of neurons receives input from the previous layer, with its outputs feeding into neurons in the next[Page 332] layer. Many interconnection patterns are possible, but the details are relatively unimportant from an application perspective.

In classification tasks, a network may operate in either supervised mode or unsupervised mode. Supervised networks are trained on data where the desired classifications are known, often from ground truth empirical observations. In this mode, the weights associated with each input to each neuron are iteratively adjusted to produce the best possible match between the desired outputs and the network outputs. After training, the network can be applied to other data sets where the applicable classifications are not known. Unsupervised networks are similar to classical classification procedures such as clustering analysis.

The most common application of neural nets in geography is to the classification of remote sensed imagery. In this context, data from a number of channels form the input data, and land cover classifications form the desired output data. Training data are composed from regions of the study area for which reliable observational data are available. Although this is the most frequent application, it is possible to apply ANNs to classification problems in human geography or where the goal is estimating or predicting the likelihood of a particular outcome based on a number of factors.

In common with more traditional classification methods, an ANN maps each combination of input variables onto a classification. However, whereas traditional methods are restricted to simple mathematical combinations of input variables, ANN classifications assume nothing about their relative importance, enforce no distributional assumptions on data, and do not assume that linear combinations of variables are inherently more useful than complex nonanalytic functions. Nonreliance on analytic functions is both a strength and a weakness of ANNs. On the one hand, it admits the possibility of complex mappings from inputs to outputs that can reflect subtleties in observational data that are not readily represented by linear mathematical functions. On the other hand, the output from ANNs is not easily summarized. This has frequently led to ANNs being seen as “black box” solutions; that is, although they might work, they might not provide much insight into problems.

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