# Ensemble Learning of Hybrid Acoustic Features for Speech Emotion Recognition
## 3 Materials and Methods
### Classification  
Emotion classification is aimed at obtaining an emotional state for the input feature vector using a machine learning algorithm. In this study, classification experiments were conducted using ensemble learning algorithms to verify the effectiveness of the proposed HAF. Ensemble learning is considered a state-of-the-art approach for solving different machine learning problems by combining the predictions of multiple base learners [75]. It improves the overall predictive performance, decreases the risk of obtaining a local minimum and provides a better fit to the data space by combining the predictions of several weak learners into a strong learning algorithm. In this study, we applied bagging and boosting machine learning because they are widely used effective approaches for constructing ensemble learning algorithms [76; 77; 78; 79]. Bagging is a technique that utilizes bootstrap sampling to reduce the variance of a decision tree and improve the accuracy of a learning algorithm by creating a collection of learning algorithms that are learned in parallel [79; 80; 81]. It performs random sampling with replacement over a simple averaging of all the predictions from different decision trees to give a more robust result than a single decision tree. Boosting creates a collection of learning algorithms that are learned sequentially with early learners to fit decision trees to the data and analyze data for errors. It performs random sampling with replacement over a weighted average and reduces classification bias and variance of a decision tree [79]. One of the bagging ensemble algorithms investigated in this study was random decision forest (RDF), which is an extension over bagging that is popularly called random forest [75; 82]. RDF can be constituted by making use of bagging based on the CART approach to raise trees [83]. The other bagging ensemble learning algorithms investigated in this study were Bagging with SVM as the base learner (BSVM) and bagging with the multilayer perceptron neural network as the base learner (BMLP). The boosting ensemble algorithms investigated in this study were the gradient boosting machine (GBM), which extends boosting by combining the gradient descent optimization algorithm with boosting technique [75; 82; 84], and AdaBoost with CART as the base learner (ABC), which is one of the most widely used boosting algorithm to reduce sensitivity to class label noise [79; 85]. AdaBoost is an iterative learning algorithm for constructing a strong classifier by enhancing weak classification algorithms and it can improve data classification ability by reducing both bias and variance through continuous learning [81]. The standard metrics of accuracy, precision, recall and F1-score have been engaged to measure the performances of the learning algorithms with respect to a particular set of features. The accuracy \begin{table}
\begin{tabular}{c c c} \hline \hline
**Group** & **Type** & **Number** \\ \hline
**Prosodic** & & \\ \hline Energy & Logarithm of Energy & 10 \\ \hline Pitch & Fundamental Frequency & 70 \\ \hline Times & Zero Crossing Rate & 24 \\ \hline
**Spectral** & & \\ \hline Cepstral & MFCC & 133 \\ \hline Shape & Spectral Roll-off Point & 12 \\ \hline Amplitude & Spectral Flux & 12 \\ \hline Moment & Spectral Centroid & 22 \\ \hline Audio & Spectral Compactness & 10 \\ \hline Frequency & Fast Fourier Transform & 9 \\ \hline Signature & Spectral Variability & 21 \\ \hline Envelope & LPCC & 81 \\ \hline
**Total** & & **404** \\ \hline \hline \end{tabular}
\end{table} 
Table 2: List of the selected prosodic and spectral features. of a classification algorithm is often judged as one of the most intuitive performance measures. It is the ratio of the number of instances correctly recognized to the total number of instances. Precision is the ratio of the number of positive instances correctly recognized to the total number of positive instances. Recall is the ratio of the number of positive instances correctly recognized to the number of all the instances of the actual class [86].