# Predicting Traffic Sign Retro-Reflectivity Degradation Using Deep Neural Networks
## 3 Study Area and Data Collection
Table 1 shows the detailed attributes of sign sheeting surveyed during the field study. A total of 426 signs were used in the current study. Table 2 shows the distribution of sign sheeting samples among various age categories. Table 3 provides the minimum \(R_{A}\) values for new sheeting type classification as recommended by ASTM-D4956. simple feed-forward deep learning model, a series of non-linear transformation (layer) is applied to the input \(X\). Each intermediate layer will take the output of the previous layer as the input. The last layer will output the \(R_{A}\) prediction. A simple feed-forward layer contains a number of neurons and each neuron is nothing but a linear transformation \(Z=WX+b\) and an activation function \(f(Z)\), where \(W\) and \(b\) are the weights and the bias, respectively. The activation function is used to perform non-linear transformation on the data. The goal of training a deep learning model is to find the optimal \(W\) and \(B\) for each neuron that minimizes the error on the validation dataset. To find the optimal network layouts (number of layers, neurons per layers), we utilized a grid search technique with 5-fold cross-validation on the combined set of training and validation data. We first experimented with a different number of layers and the number of neurons in each layer (with ReLU activation in the hidden layers). Afterwards, we found the optimal number of layers and neurons, and experimented with the different activation functions, dropout, and batch normalization [30]. The final architecture of the model is illustrated in Figure 2 including the details on the number of parameters in each layer of the model and the total number of parameters in the model. We trained our model to be able to predict the retro-reflection value for a traffic sign, where the model will be able to cover all the possible sheeting types, brands of sheeting, color, orientation, observation angle, and the sign ages available in the dataset. The dataset utilized in this study contains both categorical variables, namely the brand, sheeting type and color, and continuous variables such as observation angle, orientation angle, and sign age. While formulating the experimental design, we divided the available data into three sets: training, validation, and testing. The splitting was done based on the combination of brand and sheeting type. This was done to ensure that the model could be evaluated on truly unseen traffic sign. The data was approximately divided into 55% training, 22% validation and the remaining 22% for testing. Since it is usually challenging to incorporate categorical data to network models, we utilized two different feature engineering techniques (i.e., one-hot encoding and entity embedding) to improve the predictive performance of the proposed methods. Figure 2: The Architecture for our model. In (**a**) overview of the architecture, we show an overview of the architecture where each layer name is followed by an integer value in brackets showing the number of neurons in the layer followed by an activation functions. In (**b**) in-depth illustration of the architecture, we plot the detailed architecture with the tensor shape and the total parameters at each layer. In one-hot encoding, for each categorical feature we create a vector with length equal to the number of possible categories in that feature. The vector consists of all zeros except for one index, which is set to 1 corresponding to a unique category in that feature. Since we have five categorical features: 3 brands, 3 sheeting types, 4 colors, 5 orientation and 3 observation angles, applying one-hot encoding expanded our feature space from 6 to 19 dimensions. While one-hot encoding can convert categorical features to numbers, it fails to capture the relationship between the different categories since each category will be either 0 or 1.