## 5 The Construction of Timbre Space  
Multidimensional scaling (MDS) was used to construct a 3D timbre perception space to represent the distribution of 37 Chinese instruments more intuitively. Unlike many common analysis methods, MDS is heuristic and does not require assumptions about spatial dimensionality [72]. It also offers the advantages of visualization and helps to identify potential factors affecting the similarity between terms. The construction of a timbre space includes three steps:  
1. _Subjective evaluation experiment based on sample dissimilarity:_ where a dissimilarity matrix between samples was obtained using a subjective evaluation experiment. Existing research has conventionally paired up samples in the material database to score the dissimilarity. The process was simplified in this study, which reduced the workload.  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline  & **Multiple Linear Regression** & **Support Vector Regression** & **Neural Network** & **Random Forest** \\ \hline Bright/Dark & 0.706 & 0.696 & 0.913 & 0.856 \\ Raspy/Mellow & 0.573 & 0.571 & 0.858 & 0.813 \\ Sharp/vigorous & 0.859 & 0.852 & 0.952 & 0.945 \\ Coarse/Pure & 0.481 & 0.518 & 0.928 & 0.827 \\ Hoarse/Consonant & 0.705 & 0.711 & 0.922 & 0.877 \\ Average & 0.665 & 0.670 & 0.915 & 0.864 \\ \hline \hline \end{tabular}
\end{table}
Table 7: A comparison of the accuracies achieved by four algorithms.  
Figure 5: A prediction accuracy histogram for the five perception attributes.  
2. _Dimension reduction of distance matrix based on MDS:_ where the MDS algorithm was used to calculate the dissimilarity matrix such that sample distances in high-dimensional spaces can be represented in low-dimensional spaces (usually two or three dimensions).
3. _Attribute interpretation of each dimension of timbre space:_ where the correlation between each dimension and the timbre perception features was analyzed using a statistical method. Interpretable attributes for each dimension were then acquired from this space.  
The performance of multidimensional scaling algorithms depends on the sample dissimilarity matrix. In previous studies [51; 52], this matrix was acquired using a subjective evaluation experiment that compared and scored the dissimilarity of any two samples. A total of \(n^{2}\)/2 experiments must be conducted for \(n\) samples. This quadratic relationship significantly increases the computational complexity and runtime, which makes quantifying the dissimilarity more difficult. This paper presents an improved methodology in which a set of evaluation indicators were selected (as complete as possible) and all samples were successively scored with each indicator. These results constituted the feature vector for the sample and the distance to each vector was calculated to obtain the dissimilarity of all samples. The 16 timbre evaluation terms shown in Table 3 were used to assess the attributes of each dimension during the analysis phase.  
The method of successive categories was then used to conduct a subjective evaluation experiment on timbre materials for 37 Chinese instruments (experiment C). Grade 9 was performed on 16 perception dimensions in Table 3 and the reliability and validity of the experimental data were analyzed. The Euclidean distance of the feature vectors was calculated, producing a dissimilarity matrix for 37 Chinese instruments. The MDS algorithm was used to process the timbre dissimilarity matrix and construct a 3D timbre perception space.