## 4 Experimental Result of IGSAE
### Authentication of Main Innovation  
The main innovation of this study is to solve the overfitting problem of the autoencoder model. Overfitting of the autoencoder is mainly divided into two categories: learning the distribution of the identity function and transforming unrelated data such as training data [39; 40; 41; 42]. To solve the two overfitting categories, experiments were conducted in two phases. First, we designed an experiment to prove that IGSAE is not learning the distribution of identity functions. Second, the experiment was conducted to test whether the deep features extracted from IGSAE could potentially express the main information. In this section, an ablation study was applied to prove the performance of the basic structure of IGSAE and the effects of sparse regularization and Wasserstein regularization. Table 3 shows the results of using SVM as a classifier. The symbols in Table 3 are explained as follows. RF: raw features; DF: deep features trained by IGSAE without Wasserstein regularization and sparse regularization; DF & WR: deep features with Wasserstein regularization; and DF & WR & SR: deep features with Wasserstein regularization and sparse regularization. As shown in Tables 1 and 3, our methods have low-dimensional features compared to conventional RF in most datasets. However, the results show no significant performance degradation. DF & WR (DW) and DF & WR & SR (DWS) showed excellent results as follows: DWS shows 0.17% higher on the Heart; DWS shows 0.59% lower on the Wine; DW shows 1.42% lower on the USPS; DWS shows 1.73% lower on the Fashion-MNIST; DWS shows 3.21% lower on the Yale; and DWS shows 0.86% lower on the COIL-100. In most cases, the performance slightly decreases, but the training efficiency increases a lot as follows: the efficiency increases about 31% from 13 features to 9 on the Heart; the efficiency increases about 33% from 12 to 8 on the Wine; the efficiency increases about 29% from 256 to 180 on the USPS; the efficiency increases about 29% from 784 to 549 on the Fashion-MNIST;  
\begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multicolumn{1}{c}{**Dataset**} & \multicolumn{1}{c}{**Guiding Units of IGSAE**} & \(\varepsilon\) & \(\lambda\) & \(\mu\) \\ \hline Heart & 64 – 32 – 64 & 0.040 & 0.119 & 0.004 \\ Wine & 64 – 32 – 64 & 0.035 & 0.166 & 0.003 \\ USPS & 256 – 128 – 256 & 0 & 0.025 & 0.001 \\ Fashion-MNIST & 256 – 128 – 256 & 0.030 & 0.115 & 0.003 \\ Yale & 512 – 256 – 512 & 0.030 & 0.171 & 0.002 \\ COIL-100 & 512 – 256 – 512 & 0.035 & 0.172 & 0.003 \\ \hline \hline \end{tabular}
\end{table}
Table 2: Parameters of IGSAE for six datasets.  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multicolumn{1}{c}{**Dataset**} & \multicolumn{1}{c}{**Classes**} & \multicolumn{1}{c}{**Features**} & \multicolumn{1}{c}{**Training**} & \multicolumn{1}{c}{**Testing**} & \multicolumn{1}{c}{**Dimensionality after**} \\  & Heart & 2 & 13 & 240 & 63 & 9 \\ Low-dimension & Wine & 2 & 12 & 4873 & 1624 & 8 \\ Medium-dimension & USPS & 10 & 256 & 7291 & 2007 & 180 \\ Fashion-MNIST & 10 & 784 & 60,000 & 10,000 & 549 \\ High-dimension & Yale & 15 & 1024 & 130 & 35 & 717 \\ COIL-100 & 100 & 1024 & 1080 & 360 & 717 \\ \hline \hline \end{tabular}
\end{table}
Table 1: Summary of six public datasets.  
the efficiency increases about 30% increase from 1024 to 717 on the Yale; and the efficiency increases about 30% increase from 1024 to 717 on the COIL-100. Most of the results show a high learning efficiency of about 30%. Therefore, this strategy has been proven to be effective and can improve the performance and stability of the existing autoencoder model.