## 3 Results and Analyses
### Analysis of Clustering Results  
To verify the effectiveness of the proposed method, the accuracy of the optimal sound speed field and the quality of the photoacoustic image are evaluated. It is known that the proposed method applies a clustering algorithm to characterize the regional distribution of  
Figure 8: The optimal results obtained by the proposed method. (**a**) Optimal clustering map. (**b**) Optimal inhomogeneous sound speed field. (**c**) Photoacoustic image obtained by using the optimal inhomogeneous sound speed field. Figure 9: The results obtained by k-means sound speed estimation method. (**a**) Clustering map. (**b**) Inhomogeneous sound speed field. (**c**) Photoacoustic image. The regional distribution of each tissue in the initial and optimal clustering maps is compared with the corresponding real distribution. By observing Figures 10-12, it can be seen that the regional boundary of each tissue in the optimal clustering map is clearer than that in the initial clustering map. Its regional distribution is closer to the real distribution of various tissues in the model. This shows that the proposed method can effectively improve the accuracy of each tissue distribution in the sound speed field through several iterations of cluster analysis. Next, the clustering results of the proposed method and k-means sound speed estimation method are compared by observing Figures 10, 12 and 13. The regional  
Figure 12: The regional distribution of each component in the optimal clustering map. (**a**) Background area. (**b**) Fibrogland tissue. (**c**) Fat tissue. (**d**) Skin tissue. (**e**) Tumor tissue. Figure 13: The regional distribution of each component in the clustering map obtained by the k-means sound speed estimation method. (**a**) Background area. (**b**) Fibrogland tissue. (**c**) Fat tissue. (**d**) Skin tissue. (**e**) Tumor tissue. distribution of each tissue in the optimal clustering map is better than that of the k-means sound speed estimation method, which is closer to the real distribution. This indicates that the clustering performance of the proposed method is superior to that of the k-means sound speed estimation method. To verify the clustering result as a whole, the clustering evaluation index is used to compare the clustering results obtained by the proposed method and the k-means sound speed estimation method. For clustering results, the higher the degree of intra-cluster aggregation and the greater the degree of inter-cluster dispersion, the better the clustering effect. The SSE index is used to evaluate the degree of intra-cluster aggregation of the clustering result. This index is calculated by the formula shown in Equation (8), which is the SSE of the intra-cluster sound pressure data with the intra-cluster mean. The SSE value is smaller, which indicates the intra-cluster aggregation of clustering result is better. The degree of inter-cluster dispersion is evaluated by the separation (SP) index, which represents the average distance between the center points (means) of various clusters as follows:  
\[SP=\frac{2}{K*(K-1)}\sum_{k_{1}=1}^{K}\sum_{k_{2}=k_{1}+1}^{K}\left\|\mu_{k_{ 1}}-\mu_{k_{2}}\right\|_{2}. \tag{27}\]  
where \(K\) represents the number of clusters in the clustering result. \(\mu_{k_{1}}\) represents the mean of the \(k1 st\) cluster. \(\mu_{k_{2}}\) represents the mean of the \(k2 nd\) cluster. The SP value is larger, which indicates the inter-cluster dispersion of clustering result is better. Table 2 presents the SSE and SP values of the clustering results obtained by the two methods. In the clustering results obtained by the proposed method, the SSE value of the optimal clustering result is smaller than that of the initial clustering result, and the SP value is larger. Its clustering effect is better than the initial clustering result. This also shows that the proposed method can correct the regional distribution of each tissue in the sound speed field.