## 4 Experimental Result of IGSAE
### Comparison of the Benchmark Datasets  
The efficiency of the proposed IGSAE is proven in Section 4.2, and in this section, we experiment to prove that IGSAE shows better performance than existing dimensionality reduction algorithms and does not learn the distribution of identity function. When the autoencoder model learns the distribution of the identity function to minimize the reconstruction error, it is difficult to expect improvement in classification because there are few transformations of the feature. Therefore, if the classification accuracy is improved compared to the result of using only the raw features by the hybrid feature of the deep features extracted from IGSAE and the raw features, it shows that our IGSAE is not overfitted without learning the distribution of the identity function. In Table 4, Hybrid IGSAE showed improvement in accuracy of 0.75%, 1.09%, 0.45%, 0.48%, 2.02%, and 0.57% for 6 datasets, respectively. This means that IGSAE does not learn the distribution of identity functions. In addition, Table 4 illustrates how much performance improvement of IGSAE was achieved compared to the existing feature extraction methods. The proposed IGSAE is compared with representative autoencoder models and dimensionality reduction methods such as Kernel PCA, LDA, stacked autoencoder (SAE), stacked sparse autoencoder (SSAE), uniform manifold approximation and projection (UMAP), and t-Stochastic neighbor embedding (t-SNE) [43; 44; 45]. As shown in the table, the proposed method shows superior achievement in most cases compared to other methods on the six datasets. The IGSAE on the datasets Heart, USPS, Fashion-MNIST, and COIL-100 shows the best outcome. Moreover, IGSAE shows slightly lower performance by 0.62% and 0.13% on the Wine and Yale compared to the SSAE and Kernal PCA, respectively. In addition, the accuracy of Hybrid IGSAE on the dataset Heart is higher by 0.75% and 0.58% than RF. Similarly, the performance increases by 1.09% and 1.06% on the Wine, 0.45% and 1.87% on the USPS, 0.48% and 2.21% on the Fashion-MNIST, 2.02% and 5.23% on the Yale, and 0.57% and 1.43% on the COIL-100, respectively, to RF and the best algorithm. This means that the proposed method can avoid overfitting the autoencoder and display superior results.  
\begin{table}
\begin{tabular}{c c c c c c c c c c} \hline \hline \multirow{2}{*}{**Dataset**} & **RF** & **Kernel** & \multirow{2}{*}{**LDA**} & **SAE** & **SSAE** & **UMAP** & **t-SNE** & **IGSAE** & **Hybrid** \\  & **(\%)** & & **(\%)** & **(\%)** & **(\%)** & **(\%)** & **(\%)** & **(\%)** & **(\%)** \\ \hline Heart & 82.47 \(\pm\) 2.1 & 81.82 \(\pm\) 1.1 & 76.86 \(\pm\) 4.5 & 82.23 \(\pm\) 2.8 & 81.82 \(\pm\) 2.7 & 74.38 \(\pm\) 5.2 & 60.33 \(\pm\) 9.2 & 82.64 \(\pm\) 2.0 & 83.22 \(\pm\) 1.7 \\ Wine & 96.84 \(\pm\) 0.5 & 96.00 \(\pm\) 1.2 & 93.15 \(\pm\) 1.4 & 95.98 \(\pm\) 1.5 & 96.87 \(\pm\) 1.1 & 95.54 \(\pm\) 2.2 & 95.52 \(\pm\) 2.9 & 96.25 \(\pm\) 1.1 & 97.93 \(\pm\) 0.8 \\ USPS & 94.92 \(\pm\) 3.4 & 91.46 \(\pm\) 5.6 & 92.78 \(\pm\) 5.7 & 93.47 \(\pm\) 3.9 & 93.23 \(\pm\) 4.5 & 89.23 \(\pm\) 9.9 & 86.36 \(\pm\) 8.4 & 93.50 \(\pm\) 2.4 & 95.37 \(\pm\) 3.1 \\ Fashion-MNIST & 90.60 \(\pm\) 0.4 & 87.07 \(\pm\) 3.5 & 87.27 \(\pm\) 3.2 & 87.98 \(\pm\) 2.7 & 88.65 \(\pm\) 1.8 & 81.28 \(\pm\) 6.4 & 81.38 \(\pm\) 4.7 & 88.87 \(\pm\) 1.8 & 91.08 \(\pm\) 1.0 \\ Yale & 74.56 \(\pm\) 2.1 & 71.48 \(\pm\) 6.8 & 68.26 \(\pm\) 3.6 & 67.44 \(\pm\) 7.4 & 70.78 \(\pm\) 4.1 & 69.33 \(\pm\) 5.5 & 61.45 \(\pm\) 8.5 & 71.35 \(\pm\) 5.5 & 76.58 \(\pm\) 4.