# A Novel RBFNN-CNN Model for Speaker Identification in Stressful Talking Environments
## 4 Model Architecture
### RBFNN-CNN Model  
RBFNN is a feedforward neural network model that is relatively fast in comparison with other machine learning models such as multilayer perceptron [38]. Figure 2 shows how the RBFNN layers are comprised [39], where the input vector is represented by the first layer. The second layer, which is also called the hidden layer, is where the RBFs of all input data are stored. For example, the node RBF1 is the vector with the length of n where the RBF of X ([x\({}_{1}\), x\({}_{2}\),..., x\({}_{n}\)]) and C1 (first centroid vector) is described. The RBF1 vector is a measure of how the distance between the first centroid and data X is related to other vectors. Eventually, through utilizing the theory described above, the resulting prediction of the unknown point's class can be made by calculating the RBF of an unidentified data point x in terms of all centroids. Additionally, we calculate the dot product of RBF and W (the weight) and choose the index with the highest value. RBFNN models use a Gaussian function as an activation function in the hidden layer. In this article, the implementation of SUSAS and Arabic Emirati-accent dataset classifications are described. The RBFNN is followed by CNN, in which the final model is the result of cascading RBFNN with CNN (RBFNN-CNN). In the CNN model design, five hidden layers have been used due to the significant outcome in accuracy. The number of input neurons is 957, which represent the features, while the number of output neurons is 50, which represent the classes after categorizing the testing labels, knowing that the output layer is known since the dataset is labeled. Figure 3 illustrates the block diagram of the CNN model that is cascaded with RBFNN, where the output of RBFNN is the input for the CNN model. The block diagram of the RBFNN-CNN model is shown in Figure 4. The activation function that has been applied in this work is \"Softmax\". The standard (unit) Softmax function \(\sigma:R^{K}\to R^{K}\) {\(\backslash\)displaystyle \(\backslash\)sigma:\(\backslash\)mathbb \(\{R\}\) \(\{\backslash\)t\(\}\)\(\{\backslash\)mathbb \(\{R\}\) \(\{\backslash\)[K]\(\}\) is characterized by the following equation [40]. \[\sigma(z)_{i}=\frac{e^{z_{i}}}{\sum_{j=1}^{K}e^{z_{j}}}\;for\;i=1,\ldots,K\; and\;z=(z_{1},\;\ldots,\;z_{k})\in R^{K} \tag{1}\]  
The exponential function is applied to all input vector features and then normalizes the values. At first, audio signals are inserted into the model with zero manipulations. The inserted audios are the input for the next step, named \"preprocessing step\", that is applied to each audio. In addition, this step involves the labeling process for each audio file. The labeling process is where the naming of each sound file is accomplished, e.g., the first sound corresponds to speaker X, etc. Figure 2: RBF model. The output of the preprocessing step includes all of the files along with their labels. This output is the input to the feature extraction process, where each audio file contains special characteristics recognized by the presented MFCC feature extraction method. The output of the feature extraction method entails the essential features as a matrix having feature vectors for each audio. The output encounters all of the matrices that should be used in the classification. Before applying the classification method, we first split the data into training and testing datasets. The next step was to start classifying our data using the proposed model, RBFNN-CNN. RBFNN addresses the theoretical gap in the original RBF and solves the ambiguity regarding the class of the data. Inside the RBFNN, in the hidden layers, each node represents a vector that is stored with its centroid vector. Each node vector represents the distance between first centroid and data X, which are associated with one another. The output of RBFNN is an array of features that contain weights that best estimate the linear relationship among RBFs and the output.