## 1 Introduction
The nature of the training set has a significant impact on the accuracy of predictions by a neural network [2; 15; 32]. For example, the size of the training set, notably in relation to the complexity of the network, can have a marked effect on classification by a neural network [9; 16; 33]. The composition of the training set in terms of relative class abundance is also important [15; 34]. Variations in class abundance can yield imbalanced datasets that, as in other classifiers, can have substantial impacts on the final classification. In a supervised classification with a conventional feedforward neural network it is common for part of the training sample to be used for validation purposes [1; 2; 33; 34; 35; 10]. In this data splitting approach part of the training set is used in the normal way to provide examples of the classes upon which the classifier may learn to form rules to classify cases of unknown membership. The remaining part of the training set forms the validation set and is used to evaluate the performance of the network in terms of the accuracy with which the validation set is classified, as well as help determine when to stop network learning [10; 36; 37; 38; 39]. A variety of approaches exist for the splitting of the training cases to form the training set and the validation set. If reference data are plentiful the training set and validation set could be completely separate and independent samples but if this is not the case other approaches to cross-validation, such as the leave one out approach, may be used [34]; for simplicity, the focus here is on the use of a completely independent validation set. The use of a validation set is important in neural network-based approaches to classification as there is a desire to avoid overfitting to the training data and there are a variety of network parameters that require definition. The latter includes the basic structure of the network (e.g., number of hidden layers and units) and the learning algorithm and parameters (e.g., momentum, learning rate and number of iterations). There is an extensive literature on this topic [2; 10]. The basic idea is that a range of different networks can be defined and one that is optimal for the task at hand, defined with the aid of the validation dataset. Thus, for example, a range of different networks may be generated and the one that classifies the validation set to the highest accuracy is selected for the final classification analysis to produce a thematic map. This analysis might also suggest ways to further enhance the classification by, for example, indicating redundant discriminating variables that could be deleted in order to allow more rapid computation [28; 40]. It is also useful as some approaches used in training may artificially inflate class separability and be unhelpful [23]. Given that the ultimate aim of the analysis in a typical remote sensing application is the production of an accurate thematic map via a classification analysis the nature of the validation set can be important. Commonly, with classifiers that use validation data, the validation set is formed by simply taking cases randomly from the entire set of data acquired for training activity [38; 41] or a separate, often stratified, sample of cases is obtained (e.g., [42]). The size of the validation set is important. As in other aspects of the analysis, the literature contains guidance on the way the reference data should be divided up. For example, [PERSON] et al. [43; 44] suggests that half of the labelled cases be used for training, a quarter for validation and the final quarter for testing. The composition of the sample of cases forming the validation set, notably in terms of the relative abundance of the cases of the classes may vary as a function of the design used to acquire the training dataset. If the validation sample is formed with a simple random sample design it is likely to be imbalanced in composition, with the number of cases of a class reflecting its relative abundance in the region being mapped.