# A Review of the Artificial Neural Network Models for Water Quality Prediction
## 5 Result
### Model Structure Determination  
Until recently, a general method for determining the optimal model structure remains unknown [31]. Therefore, different approaches have been adopted to determine the ANN model structure to avoid the initial difficulty in model building step as much as possible. There are three mainstream \begin{table}
\begin{tabular}{c c c} \hline \hline
**Categories** & **Methods** & **Comments** \\ \hline \multirow{3}{*}{supervised} & trial-and-error & Taking the statistical properties of each subset into consideration \\  & temporal partitioning & Dividing the data into diel, diurnal, and nocturnal \\  & M-test & The number of the data points was obtained through the winGamma software \\ \hline \multirow{3}{*}{unsupervised} & ad-hoc & Based on domain knowledge or a casual way \\  & random & Divide the data randomly \\  & cross-validation & e.g., K-fold cross-validation, leave-one-out cross-validation \\ \cline{1-1}  & stratified method & e.g., SOM \\ \hline \hline \end{tabular}
\end{table} 
Table 7: Supervised and unsupervised methods in data dividing. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Categories** & **Methods** & **Comments** \\ \hline \multirow{3}{*}{Normalization} & No details & Built-in functions in platforms \\  & Range scaling & The scale of each feature is in the same range \\  & Standardization & A new variable with zero mean and unit standard deviation \\ \hline \multirow{6}{*}{Missing data imputation} & Only mentioned & Not recommend \\  & Deletion & Not recommend \\  & Linear interpolation & The slope of the assumed line to calculate the data increment \\  & Improved mean value method & Solve the breakpoint phenomenon of mean value method and linear \\  & Missing-refilling scheme & Dividing of ID and SD and using Temporal exponentially moving \\  & Missing-refilling scheme & average to fill the missing data \\  & Gap-filling & Temporal partitioning as gap-filling in order to get continuous \\  & Filling in the predicted values & The missing values of predictors at time T0 are obtained by \\  & of the model & prediction values of the model at time T0 by other predictors \\ \hline \multirow{3}{*}{Data correct Data abnormal} & Smoothing method & The moving average filtering can attenuate high-frequency signals \\  & Mean value method & Need to be corrected as a median of k data before and after \\ \cline{1-1}  & The fixed threshold method & Setting the upper and lower threshold ranges (discard) \\ \hline \hline \end{tabular}
\end{table} 
Table 8: The data preprocessing approaches. methods--namely ad-hoc, stepwise trial-and-error, and global methods--for the determination of an optimal model structure [31] (see Table 9). The neural network structure defines the functional form of the input-output relationship [59]. The model structure determination, an essential step in the model development, refers to the number of layers, the number of nodes in each layer and the way they connect [30], aiming to strike a balance between network complexity and generalization ability [27]. The model structure determination and model training process are often conducted together. For example, when the trial-and-error method is implemented, the weights of the MLPs are optimized at the same time. Categories and comments on the ANN methods in the model structure determination are given in Table 9. M, N, and O are the number of neurons of the hidden layer, input layer, and output layer. A is a constant from 1 to 10. Sqrt is a mathematical function [83] used to calculate the square root of a non-negative real number. Nearly half of the investigated papers did not provide details on the methods used to determine the ANNs structure. When using fixed network structures such as GRNNs, this step is not necessary to carry out, although its proportion is relatively small compared with papers that did not mention this step (see the last two lines in Table 9). In 73 of the 90 times which provide details of the methods, ad-hoc approaches were utilized to determine the structure of model.