## 3 Results
### Validation Results
#### 3.2.2 Evaluating the Practicability of Data Augmentation
Moreover, when it is difficult to apply the current approach, it may be necessary to modify the algorithms in this study with reference to useful approaches to improving deep learning algorithms [58]. Some points must also be considered when applying our validation approach. Our validation approach can be directly applied when the nature of the original data is obvious. However, if the nature is unknown, confirming the generated data quality becomes challenging compared with the original data. Therefore, setting an appropriate number of epochs is hard with the overall quality score, column shapes, and column pair trends. In this situation, machine learning algorithms must be used for all generated data to select the appropriate generated data. Further research is required to confirm the usefulness of data augmentation with the synthesized data generated by the DGNNs in various marketing analysis fields. In conclusion, applying a data augmentation method using DGNNs for consumer survey data with a small sample size could enhance the predictive performance. Moreover, the predictive performances of the data synthesized by DGNNs were superior to those of the actual data. However, our results also showed that the methods in the current study might enable slight improvement but pose challenges in drastically improving the degree of discrepancy with the feature importance score between large- and small-sample-size data despite augmenting or synthesizing small data. Given that the results using the data generated by CopulaGAN yielded better performance than the other DGNN-basedsynthesizers, our result might provide a starting point for reducing the discrepancies by considering the correlations between variables in an algorithm. The following supporting information can be downloaded at: [[https://www.mdpi.com/article/10.3390/app14199030/s1](https://www.mdpi.com/article/10.3390/app14199030/s1)]([https://www.mdpi.com/article/10.3390/app14199030/s1](https://www.mdpi.com/article/10.3390/app14199030/s1)), Figure S1(A). Correlation analysis results: (A) boosting classification correlation plot. Figure S1(B). Correlation analysis results: (B) random forest classification correlation plot. Table S1. Questionnaire. Table S2. Descriptive statistics: (A) original and (B) seed data. Table S3. Hyperparameters. Table S4. Descriptive statistics: (A) synthesized data from the CTGAN; (B) synthesized data from the TVAE); and (C) synthesized data from the CopulaGAN. Table S5. Parameter setting in each machine learning algorithm: (A) boosting classification; (B) random forest classification; (C) support vector machine classification <radial-based function>; and (D) support vector machine classification <linear function>. Table S6. Results of the machine learning algorithms in each datum. Table S7. Confusion matrix. Table S8. Feature importance: (A) boosting classification; (B) random forest classification. Table S9. (A) Correlation analysis results: (A) boosting classification, correlation table. Table S9. (B) Correlation analysis results: (B) random forest classification correlation table. Table S10. Original dataset. Table S11. Seed dataset. Conceptualization, S.W., K.E. and T.M. ; methodology, S.W. ; software, S.W. ; validation, S.W., K.E. and T.M. ; formal analysis, S.W. ; investigation, S.W. ; resources, S.W., K.E. and T.M. ; data curation, S.W. and K.E. ; writing--original draft preparation, S.W. ; writing--review and editing, S.W. ; visualization, S.W. ; supervision, S.W., K.E. and T.M. ; project administration, S.W. and K.E. ; funding acquisition, K.E. and T.M. All authors have read and agreed to the published version of the manuscript. This research received no external funding. Not applicable. The original contributions presented in the study are included in the article/Supplementary Material; further inquiries can be directed to the corresponding author. We thank [PERSON] for his assistance with data collection and screening. The authors declare no competing interests.