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3.2.1 SOM network construction and training

The input and output neurones in a SOM are known as the sensory cortex and the mapping cortex, respectively, by analogy with their function in the biological neural system. Since the SOM training algorithm is based on the competitive concept, the output layer is also called the competitive layer.

The number of neurones in the input and output layers defines a SOM network. The number of input neurones is equal to the number of input features. However, there are no clear rules about the specification of the number of output neurones. Generally, the output layer of a SOM is a two-dimensional layer made up of n×m (n, m>1) neurones, with each neurone relating to a fixed position in the two-dimensional output space. Although a one-dimensional output layer is possible, such an arrangement is seldom seen in remote sensing applications. It is assumed that adjacent neurones in the rows and columns of the output layer are spaced apart at a Euclidean distance of unity. The neurones in the input layer and the output layer are linked by synaptic weights w_ji, where i and j are the identifiers of the input and output neurones, respectively. The weights w_ji are initialised randomly and are then continually adjusted during training in order to organise the relationships among the input patterns. Once the training is complete, the final weights w_ji describe what is called a topological feature space, which is the characterisation of input features in terms of the weights. An example of a SOM structure is shown in Figure 3.6.

The SOM training strategy is based on the concept of competitive learning. The neurones in the output layer have to compete with other neurones in that layer in order to ‘win’ the opportunity of interaction with the input pattern. The result is that the weights connecting the input layer to the winning neurone and its neighbours are adjusted simultaneously, while other weights remain unchanged. Eventually, the neurones that are close together will have similar properties (in terms of weight magnitude).

3.2.1.1 Unsupervised training

Training of a SOM begins with the initialisation of the weights w_ji to random values. Then, for each input feature vector , where k is the input data dimension, the squared distances between an input neurone and each output neurone j are calculated using the Euclidean distance measure:

(3.11)

where is the input to neurone i at iteration n, and is the weight from input neurone i to output neurone j at iteration n. The selected output

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