# A Hybrid Autoencoder Network for Unsupervised Image Clustering
## 4 Numerical Experiment
### Experiment Result  
Taking the first dataset as an example, the training process of the loss functions for CAE, AAE, and SAE can be depicted, respectively, as shown in Figures 3-5. The training processes of all loss functions slowly decline and show the convergence of the model parameters. Note that the deep structure of CAE is represented, as shown in Table 1.  
Figure 3: The training process of CAE. Then, we can use the representation code from SAE for image clustering by \(k\)-means. Taking Model 1 in the results of the MNIST and CIFAR-10 datasets as an example, we can obtain the confusion matrices between the ground-truth and predicted labels, respectively, as shown in Figure 6a,b. The performance comparison between the proposed methods and others can be presented, as shown in Table 2. Note that the best result of each clustering criterion is highlighted in bold and the results of other methods are extracted from [26], where FCM is the fuzzy objective function algorithm [27], SC is the spectral clustering algorithm [28], LRR is the low-rank representation algorithm [29], LSR1 and LSR2 are the variants of the least squares regression (LSR) [30], SLRR is the scalable LRR [31], LSC-R and LSC-K are the variants of the large-scale spectral clustering (LSC) algorithms [32], NMF is the non-negative matrix factorization algorithm [33], ZAC is the Zeta function based agglomerative clustering algorithm [34], and DEC is the deep embedding clustering algorithm [8]. The test process is described as follows. First, we use the BAE to extract the hidden codes. Then these codes are used in \(k\)-means to run the clustering algorithm. The initial centroids are \begin{table}
\begin{tabular}{c c c} \hline \hline
**Layer** & **Output Shape** & **Number of Parameters** \\ \hline Conv2D & (28,18,16) & 160 \\ Maxpooling & (14,14,16) & 0 \\ Conv2D & (14,14,2) & 290 \\ Maxpooling & (7,7,2) & 0 \\ Conv2D & (7,7,2) & 38 \\ Upsampling & (14,14,2) & 0 \\ Conv2D & (14,14,16) & 304 \\ Upsampling & (14,14,16) & 0 \\ Conv2D & (28,28,1) & 145 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: The deep structure of CAE. Figure 4: The training process of AAE. Figure 5: The training process of SAE. determined randomly and the number of the clusters is predefined by the datasets, i.e., 10 clutters for each dataset. The distance between the centroids and the points is calculated by the Euclidean distance. Finally, we calculate the ACC, NMI, and ARI of each model in both datasets. Note that we run five times of the above test process and select the best solution. The \(k\)-means algorithm is the most popular benchmark of the clustering methods. The result of Table 1 indicates that the \(k\)-means algorithm performs better than many algorithms. In addition, the empirical results indicate that the proposed models outperform others with respect to the criteria of ACC, NMI, and ARI in both datasets. The CIFAR-10 dataset is harder to recognize than the MNIST dataset; however, the proposed models can obtain better results than others. Even though the result of DEC also performs well, the result shows that the proposed models are more competitive. In addition, the DEC algorithm seems to have difficulty dealing with the CIFAR-10 dataset, since the criteria of the ACC, NMI, and ARI of DEC are worse than the benchmark; i.e., the \(k\)-means algorithm.