## 3 Materials and Methods
### Vehicular CO Prediction Model
#### 3.4.4 Optimization Method  
The capacity of the prediction in MLP model relies on its hyperparameter and structure. In this paper, several network structure hyperparameter combinations were tested to determine a sub-optimal network model for modeling vehicular CO. Table 3 shows the structures and hyperparameters evaluated in the current study and their search space domain. In general, there are two main categories of NN, MLP and radial basis function (RBF). The former uses dot products between inputs and weights and monotonic activation functions such as sigmoid. The MLP uses dot products between inputs and weights and monotonic activation functions such as sigmoid while the RBF uses Euclidean distances between inputs and weights and usually Gaussian activation functions. Both of the networks can be trained with the back-propagation algorithm. In the RBF model, it is not necessary to use multiple hidden layers whereas with MLP, multiple hidden layers are used. In addition, the RBF model is less sensitive to noise than the MLP model. Other parameters of the network are the number of hidden units, training algorithm, error function, activation function, learning rate, and momentum. The number of hidden layers controls the complexity of the designed network. A small number  
Figure 5: The architecture of the proposed neural network for traffic CO prediction (6-3-1).  
of hidden units may result in low prediction capacity due to insufficient learning whereas a large number of hidden layers can reduce the ability of the model to be generalized and can also create overfitting problems. The training algorithm is the optimization method for calculating the weight for each node in the network. There are many training algorithms for NN based on back-propagation; the Broyden-Fletcher-Goldfarb-Shanno (BFGS) and radial basis function training algorithm (RBFT) are the most recommended back-propagation algorithms used for optimization of NN architecture [46]. During training of the network, an objective function or optimization score function was minimized according to the labeled training dataset. The optimizer usually has a learning rate and gradient momentum parameters. In addition, many activation functions such as identity, logistic, and Gaussian could be used in the hidden layers and the output layers of the neural network.  
The total number of instances was 352, which was separated into training 70% (246) and testing 30% (106). This sample size is still small compared to other studies. However, it needs a good approach to handle overfitting problems. One approach is to design a cross-validation evaluation procedure. Other methods are data augmentation or collecting new samples. There are also methods such as transfer learning which requires retrained networks. Overall, training of the neural networks with small datasets requires careful analysis and evaluation before using them in practice. There are also some tricks to improve the performance of neural networks for small datasets. Those include batch normalization, rectified linear unit (relu) activations and regularization methods such as l1 and l2. On the other hand, the hyperparameters of the NN for predicting vehicular CO were chosen based on the implementation of systematic grid-based search that can be applied with the Scikit-Learn algorithm using 100 epochs. Although this method demands high quality of computation, more accurate outputs could result by fine tuning the hyperparameter values. Many models based on various integrations of parameters were generated. Cross validation (10-fold) was applied to validate each model. Therefore, the parameters that resulted in higher accuracy are the best parameters.