## 5 Impact Sound Generation for Object Materials
### Results of Learning  
Figure 15 shows the results of learning by HSD using the two GAN architectures, constructed based on residual block and our proposed method. The two columns on the left are the sample data, that is, the images extracted from the HSD, and the central two columns are the results of training using the GAN architecture based on Residual Block. The two columns on the right are generated images, as the result of learning using the GAN architecture, by the proposed method. In order to quantitatively evaluate the generated image (by the trained model, using the GAN architecture), we performed the evaluation based on Frechet Inception Distance [37] (FID). The FID can calculate differences in feature representations extracted from pre-trained inception networks, with standard datasets, such as CIFAR-10 and ImageNet. Figure 14: Generated spectrogram images of six material classes. Figure 15: Comparison of sample data of each class and spectrogram image generated by Generator. As a result, it is frequently used as an index for quantitatively judging the quality of the generated image. A low FID means that the actual sample and the generated sample are more similar. Assuming that the distribution of each image is the set \(A_{i}\), each element is \(a\in A_{i}\), and the output of the Inception network is \(h\), the formulae for obtaining the mean vector \(\mu\) and covariance \(\Sigma\) of each image group are as follows. \[\mu=\frac{1}{|A|}\sum_{h\in H}h \tag{5}\]  
\[\Sigma=\frac{1}{|A|-1}\sum_{h\in H}(h-\mu)(h-\mu)^{T} \tag{6}\]  
Assuming that the feature vector, obtained from the trained inception network, follows a multivariate normal distribution, the formula for calculating the Wasserstein-2 distance between the distributions of image sets \(A_{1}\) and \(A_{2}\) is as follows. \[\text{FID}(A_{1},A_{1})=\left|\mu_{1}-\mu_{2}\right|^{2}+\text{Tr}(\Sigma_{1}+ \Sigma_{2}-2(\Sigma_{1}\times\Sigma_{2}))^{\frac{1}{2}} \tag{7}\]  
Table 5 lists the results of the compared learning models using this index. The learning models used for comparison are as follows. WaveGAN, which is a method for generating sound data by GAN, and TacGAN, which generates tactile vibration using spectrogram images, were learned using the datasets. The DCGAN model, which was referred to as the structure of the loss function, was trained in the same way. The learning model based on residual block and the learning model based on residual and SE block (Squeeze-and-Excitation Block) [38] were trained using the same dataset. A total of 2400 spectrogram images, generated using each GAN learning model, were randomly selected, and the FID with the sample images was calculated. The SE block, proposed by [PERSON] et al. [38], is not a specific network but, rather, one component in the network. One advantage of SE block is that it can be expected to improve the accuracy of existing models, while suppressing the increase in the amount of calculation of the entire model. As we can see in Table 5, the proposed method obtained the best evaluation in the FID evaluation index. In addition, the FID value of the proposed method was smaller than that of the proposed method combining residual block and SE block and the generative model of only residual block. These results demonstrate that the SE block architecture is useful, for the purpose of this learning. Next, we discuss the correlation between the evaluation of the FID value and the sound evaluation. In general, in GAN learning for the purpose of image generation, as described above, the smaller the FID value, the closer the distance between the training image group and the generated image group; we can presume that the training data succeeded in generating more similar images. The results, shown in Table 5, confirmed that the proposed method was able to generate data closest to the training data, among the compared learning models.