## 3 Music Emotion Regression Experiment
### Optimal Combination Algorithm for Pre-Processing and Feature Selection  
Because the 557-dimension acoustic features were extracted by different toolboxes and each feature had its own physical significance, there were large dynamic range differences or dimensional differences between feature values, which would seriously reduce the performance of regression prediction. Data pre-processing can expand the discrimination of features and improve the accuracy of the prediction. Five mainstream pre-processing methods in Scikit-Learn were adopted with default parameters: StandardScaler, MinMaxScaler, MaxAbsScaler, QuantileTransformer using a uniform distribution (QTU), and QuantileTransformer using Gaussian distribution (QTG).  
Generally, feature selection methods can be divided into three categories: wrapper, filter, and embedded. We chose four feature selection methods in Scikit-Learn: a filter method using correlation measurement (Filter-C), a filter method using information entropy measurement (Filter-I), a wrapper method using recursive feature elimination (RFE) based on extremely randomized trees (Wrapper), and an embedded method based on extremely randomized trees (Embedded). The RFE-based wrapper method uses backward selection, which starts with all features and successively removes features if performance improves. Note that when a wrapper approach is used, the feature selection block in Figure 1 actually contains within it a module for regressor training and performance evaluation.  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Dataset/Classifier** & **LR** & **SVR** & **XGBoost** & **ERT** & **KNN** \\ \hline Valence & \(-1.37\) & \(-0.01\) & \(0.62\) & \(0.66\) & \(-0.15\) \\ Arousal & \(-1.37\) & \(-0.01\) & \(0.39\) & \(0.52\) & \(-0.11\) \\ \hline \hline \end{tabular}
\end{table}
Table 2: R\({}^{2}\) scores of five different regression models.  
Figure 2: The procedure to establish the optimal framework for music emotion regression. Italicized words in the bottom brackets indicate the selected methods of each step, as detailed in the following.  
Using the extremely randomized tree method as the basic regression model, 20 combinations of pre-processing and feature selection were evaluated to obtain the optimal method. The R\({}^{2}\) scores are shown in Table 3, with the best combinations for the different datasets underlined. It was found that MaxAbsScaler performed best for two datasets (Western Music Valence and Chinese Music Arousal) and QTU and MinMaxScaler were the optimal methods for the remaining datasets. When MaxAbsScaler was taken as a pre-processing method for all datasets, regression performance was not significantly reduced compared with the QTU or MinMaxScaler as best method. Therefore, the MaxAbsScaler was selected as the optimal pre-treatment method for all datasets.  
The wrapper method was optimal for three datasets (Western Music Valence, Western Music Arousal, and Chinese Music Arousal). Therefore, the combination of the optimal pre-processing and feature selection methods is MaxAbsScaler and the wrapper method using RFE based on extremely randomized trees.