## 3 Proposed Method
### Method of Extracting Speech Characteristics
#### 3.2.2 Data Augmentation  
Data augmentation involves expanding an original dataset through techniques such as rotation, reversal, and adjustments to saturation or brightness. Insufficient datasets can lead to overfitting issues and hinder model generalization and enhancement of its performance. These problems stem from the dependence of analysis models on internal datasets when facing a lack of datasets and limited images. To address these challenges, this study adopted a data augmentation approach to ensure dataset diversity and expansion.  
\[\big{(}\hat{R}_{i},\ \hat{G}_{i},\ \hat{B}_{i}\big{)}\ =\ (R_{i},\ G_{i},\ B_{i})/255,\]  
\[Cmax_{i}\ =\ \max\big{(}\hat{R}_{i},\ \hat{G}_{i},\ \hat{B}_{i}\big{)},\]  
\[Cmin_{i}\ =\ \min\big{(}\hat{R}_{i},\ \hat{G}_{i},\ \hat{B}_{i}\big{)},\]  
\[\Delta\ =\ Cmax_{i}-Cmin_{i}\,\]  
\[S_{i}\ =\ \begin{cases}0,\ if\ Cmax_{i}\ =\ 0\\ \frac{\Delta}{Cmax_{i}},\ otherwise\end{cases}\]  
\[DAS(\%)\ =\ Normalization\big{(}\frac{1}{n}\sum_{i\ =\ 0}^{n}\big{(}S_{i}\times w \big{)}\big{)}\times 100\%. \tag{3}\]  
Specifically, the DA-S technique, which relies on saturation adjustment, was employed. An experiment on saturation was conducted using a function provided on TensorFlow. This function, defined by Equation (3), applies values multiplied by the saturation of each pixel in an image, enabling representation from 0% to 100%.  
In Equation (3), \(i\ =\ (0,\ 1,\ \ldots,\ n-1,\ n)\) represents the pixel index. \(R_{i}G_{i}B_{i}\) denotes the RGB value of each pixel, ranging from 0 to 255. \(\hat{R}_{i}\hat{G}_{i}\hat{B}_{i}\) are normalizing RGB values of each pixel, ranging from 0 to 1. Among the \(\hat{R}_{i}\hat{G}_{i}\hat{B}_{i}\) values, the highest value is indicated as \(Cmax_{i}\), the lowest value as \(Cmin_{i}\), and the difference between the highest and lowest values is \(\Delta\). \(S_{i}\) refers to the saturation for each pixel. When \(Cmax_{i}\) is 0, the value of saturation is 0. When \(Cmax_{i}\) is not 0, the value of saturation is calculated by dividing \(\Delta\) by \(Cmax_{i}\)[20]. In our proposed model, \(S_{i}\) is multiplied by a saturation weight \(w\) to adjust the saturation of each pixel. \(n\) denotes the number of pixels in an image. Each pixel undergoes multiplication by saturation weights, and the resulting values are summed. The mean of this sum is then calculated. Furthermore, to readjust the range after multiplication, by the weights, normalization was performed to express values between 0 and 1. Multiplying by 100% yields DAS (%), representing the saturation of a single image.  
Hence, in our proposed model, Original DB-T was tripled in size through saturation weights (\(w\)) multiplication, using values of 0 and 2. The proposed model used Original DB-T including 11,192 data samples (the mean saturation of images: 69.75%), the DA-S DB including 11,192 data samples and multiplied by a saturation weight 0 (the mean saturation of images: 0%), and the DA-S DB including 11,192 data samples and multiplied by a saturation weight 2 (the mean saturation of images: 99.49%). This resulted in a total of 33,576 images for training by the proposed model. Figure 4 illustrates an original image from Original DB-T alongside representative images generated through multiplication by saturation weights 0, 2, and 3, respectively. Figure 4a displays the original image, Figure 4b depicts an image with 0% saturation generated by multiplying each pixel by 0, Figure 4c shows an image with 99.33% saturation generated by multiplying each pixel by 2, and Figure 4d shows an image with 99.64% saturation generated by multiplying each pixel by 3. An image with a weight of 1 was not generated, as multiplying by this weight produces an image identical to the original. Similarly, images with weights of 4 or higherwere not generated, as their saturation levels are equivalent to those produced with a weight of 3.