## 4 Construction of a Timbre Perception Feature Model
### Construction of a Prediction Model  
In this study, multiple linear regression, support vector regression, a neural network, and a random forest algorithm were used to correlate objective parameters and subjective evaluation experimental data to construct a mathematical model of timbre perception features. Stepwise techniques were used for variable entry and removal in the multiple linear regression algorithm [68], and radial basis functions were selected as kernels for support vector regression [69]. A multi-layer perceptron was adopted in the neural network, which included a hidden layer [70]. Random forest is a common ensemble model consisting of multiple CART-like trees, each of which grows on a bootstrap object acquired by sampling the original data cases with replacements [71].  
Before modeling, feature selection was conducted for the target attribute to be predicted. This process consisted of three steps:  
1. _Screening_: removes unimportant or problematic predictors and cases.
2. _Ranking_: sorts remaining predictors and assigns ranks; this step considers one predictor at a time to determine how well it predicts the target variable.
3. _Selecting_: identifies the important subset of features to use in subsequent models.  
During the modeling phase, 80% of the data were used for training and the remaining 20% were used for validation. The input to the model was a 166-dimensional objective parameter set and the  
Figure 4: A psychological scale of 72 musical instruments, including (**a**) bright/dark, (**b**) raspy/mellow, (**c**) sharp/vigorous, (**d**) coarse/pure, and (**e**) hoarse/consonant. The blue squares represent Western orchestral instruments, the yellow triangles represent Chinese minority instruments, and the red circles represent Chinese orchestral instruments. The dotted blue line represents the mean value of the Western orchestral instruments, the dotted yellow line represents the mean value of the Chinese minority instruments, and the dotted red line represents the mean value of the Chinese orchestral instruments.  
output was the value of the five perception dimensions (bright/dark, raspy/mellow, sharp/vigorous, coarse/pure, and hoarse/consonant). Correlation coefficients were used to evaluate the accuracy of the model and represented the results of the correlation analysis between the model prediction data and subjective evaluation data, with higher coefficients representing a more accurate model.  
The accuracy of prediction results for the four algorithms across the five perception dimensions are shown in Table 7. Figure 5 provides a histogram of the prediction accuracy in different dimensions. These experimental results suggested that the proposed technique provided valid predictions in each of the five dimensions. The algorithm exhibiting the best performance exceeded 0.9 for bright/dark, sharp/vigorous, coarse/pure, and hoarse/consonant sound types. The averaged results indicated that the neural network (0.915) and random forest (0.864) outperformed multiple linear regression (0.665) and support vector regression (0.670). The neural network was particularly accurate in its predictions of the five perception dimensions.