## 3 Results and Discussion  
With the simulated dataset, two sets of analyses were undertaken to identify optimal neural networks, one using the validation set formed via simple random sampling and the other formed using a stratified random sample. The key properties of the selected networks and their ability to classify the datasets are defined in Table 6 with a full set of confusion matrices for each set of analyses shown in Tables 7 and 8. Attention focused especially on the accuracy with which the testing set was classified, as this reflects the accuracy of the final product obtained. It was evident that the accuracy of classification obtained with the use of the simple random sample (98.37%) was slightly higher than that arising from the use of the validation set formed via stratified sampling (96.62%). Although small, this difference was significant (\(p<0.05\)), with the calculated value of \(z\) from Equation (4) given the 26 discordant cases observed being 2.745 (Table 9). It was also evident that the predictions of what might happen as moving from a balanced stratified to random validation sample outlined in the introduction occurred. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Class** & **1** & **2** & \(\cdots\) & **q** & **Total** \\ \hline
1 & \(n_{\mathrm{11}}\) & \(n_{\mathrm{12}}\) & \(\cdots\) & \(n_{\mathrm{1q}}\) & \(n_{\mathrm{1}}\). \\
2 & \(n_{\mathrm{21}}\) & \(n_{\mathrm{22}}\) & \(\cdots\) & \(n_{\mathrm{2q}}\) & \(n_{\mathrm{2}}\). \\ : & : & : & : & : & : \\ q & \(n_{\mathrm{q1}}\) & \(n_{\mathrm{q2}}\) & \(\cdots\) & \(n_{\mathrm{qq}}\) & \(n_{\mathrm{q}}\). \\ \hline Total & \(n_{\mathrm{Note, for example, that relative to the classification obtained with a stratified validation sample, the use of the validation set formed by random sampling resulted in a higher overall accuracy of the testing set. This arose because of a higher accuracy with which the abundant class was classified due to a reduction in omission error (from 27 to 7 cases) and the accuracy of the rarer class it was confused with declined (Tables 7 and 8). Critically, the results suggest that the use of a balanced training set acquired via a stratified random sample may produce a sub-optimal final output. As hypothesized, the use of a stratified sample resulted in a lower accuracy than was achievable because the accuracy with which the abundant class was classified declined, associated with a large omission error due to cases being commissioned into a rarer class. A series of analyses was undertaken to define an optimal neural network using the two validation datasets in the analyses of the remote sensing data. The core focus here is on the classification results from the network determined to be optimal from each series of analyses. Although the precise details of the neural networks are relatively unimportant as the classifications that arise from them are the focus of attention, key details on the networks selected are summarized in Table 10 and the confusion matrices for the testing set are shown in Tables 11 and 12. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Validation** & \multirow{2}{*}{**Architecture**} & \multirow{2}{*}{**Algorithm and**} & \multicolumn{2}{c}{**Classification Accuracy (\%)**} \\
**Dataset** & & & **Iterations** & & **Training Validation Testing** \\ \hline Random & 2:15:2 & Backpropagation 48 & 97.25 & 97.62 & 98.37 \\ Stratified & 2:8:2 & Conjugate gradient 55 & 98.25 & 98.75 & 96.62 \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Key characteristics of the networks selected for the analyses of the simulated data; note: network architecture is expressed as input:hidden:output.