## 3 Methodology
### Classification Models  
In the SER system, another crucial factor is the classification model. Many researchers have explored different types of classifiers, such as HMM, the Gaussian mixture model (GMM), k-nearest neighbors (KNN), the artificial neural network (ANN), and the SVM for the speech emotion recognition challenge [36]. Still, there is no common agreement on choosing the most powerful classifier for speech emotion classification. Each classification model has its own advantages and limitations. For this reason, the classification model must be selected depending on the problem.  
In pattern recognition, as well as in classification problems, SVM is known to be one of the most efficient, simple, and widely used machine learning algorithms, especially for binary (two-class classification problems) classification (positive and negative, in our case) [37]. Moreover, it can also be extended to use in multiple classes problems. The basic idea is that it creates a hyperplane (or line) between the classes where the margin reaches the maximum value. The margin is the distance of the nearest training samples from the hyperplane. It can be trained through many training methods. One of them is empirical risk minimization. In this method, a discriminant function \(g(x)\) is estimated from a finite set of examples by minimizing an error function (Equation (13)), where \(R_{emp}\) is the training error, \(z_{k}\) is the correct class, \(g(x_{k})\) is the predicted class, \(w_{1}\) and \(w_{2}\) are two different classes, and \(n\) is the number of points in the dataset. This method is for linearly separable data. For the nonlinear problem, the kernel trick is applied to maximum-margin hyperplanes.  
\[R_{emp}=\frac{1}{n}\sum_{k=1}^{n}(z_{k}-g(x_{k}))^{2};\ z_{k}=\left\{\begin{array} []{ll}+1,&x_{k}\in w_{1}\\ -1,&x_{k}\in w_{2}\end{array}\right. \tag{13}\]  
In many recent studies, recurrent neural networks (RNNs) have been used for the SER task [38; 39; 40; 41; 42]. [PERSON] and [PERSON] [43] investigated the discriminative capabilities of RNNs in SER using low-level acoustic features of speech signals. RNNs are known to be useful in sequential data. Generally, deep neural networks (DNNs) use different parameters at each layer, but RNNs share the same parameters through all steps. However, they inadequately cover long context information because of the gradient vanishing problem. To solve this problem, a long short-term memory (LSTM) RNN was proposed [44], which consisted of recurrently connected memory blocks. In a recent study [45], different neural network architectures were evaluated for the SER task. They used spectrograms to train and evaluate deep learning models. The convolutional neural network (CNN) was used as a feature extractor and an LSTM-RNN was used as a classifier. In addition, in [46], emotions were recognized in both verbal and nonverbal speech sounds using DNN. In [38], statistical and local features were used to recognize emotions from speech. They also evaluated SVM and LSTM-RNN models and reported that the LSTM-RNN model outperformed the SVM with both the local and statistical features of an emotional speech. We also used SVM and LSTM-RNN classification models in our work.