# Double Deep Autoencoder for Heterogeneous Distributed Clustering
## 4 Experiments
From Table 3, it can be seen that the spectral algorithm outperforms the others in terms of the _CAI_, and the _CAI_ values ranging between 0.75 and 0.81 also indicate the high consistency between the centralized and the proposed clustering results. However, the performance of the DDA+SOM is the worst in this experiment, and shows that the compression features cannot provide essential information for SOM in-clustering. On the other hand, we can also use the unsupervised clustering accuracy (ACC) [44], as shown in Table 4, to evaluate the average performance of the clustering algorithms with respect to the matching results between predicted labels and ground truth labels. From the results shown in Table 4, we can see that the spectral algorithm also outperforms the others, with ACC values ranging between 0.60 to 0.74. These values are also competitive with respect to the centralized methods, without losing too much information under the distributed and heterogeneous environments. The results of the ACC values also indicate that SOM has the worst performance, no matter the centralized or distributed situation. In addition, we also compare the classification accuracy between the centralized and the proposed algorithms. The centralized algorithms use raw data to run the deep autoencoder, and add a softmax layer to predict the classes of the data points. In contrast, we use the global code derived by the DDA algorithm to predict the correct class of the data by adding the softmax layer--also known as the hyperbolic tangent function--here. The centralized and distributed network setting of classification is shown in Table 5.  
The results of the classification accuracy between centralized and distributed algorithms, as shown in Table 5, also indicate the usefulness of the code to extract and retain the important information between distributed features. In addition, the information loss is only about 5.66% to 9.18%. The best performances of the proposed methods are shown in Figure 6.  
Note that the information loss is influenced by the result of the classification based on the experiment results. Hence, more consistent data will perform better with our methods. In sum, \begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multirow{2}{*}{**ACC**} & **Centralized** & \multirow{2}{*}{**DDA+K-Means**} & **Centralized** & \multirow{2}{*}{**DDA+SOM**} & **Centralized** & \multirow{2}{*}{**DDA+Spectral**} \\  & **DA** & & & & & \\ \hline Mnist & 0.7621 & 0.7354 & 0.7315 & 0.7030 & 0.7924 & 0.7416 \\ Covertype & 0.5604 & 0.5524 & 0.4430 & 0.4347 & 0.6488 & 0.6076 \\ SDDD & 0.6630 & 0.6584 & 0.6656 & 0.6586 & 0.7506 & 0.7245 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Performance of the DDA clustering algorithm. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Clustering** & **Mnist** & **Covertype** & **SDDD** \\ \hline DDA+K-means & 0.8060 & 0.6744 & 0.6837 \\ DDA+SOM & 0.6641 & 0.5427 & 0.6832 \\ DDA+Spectral & 0.8090 & 0.7576 & 0.7691 \\ \hline \hline \end{tabular} Note: DDA is the deep double autoencoder method.  
\end{table} 
Table 3: Consistent accuracy index (_CAI_) comparisons between different algorithms. \begin{table}
\begin{tabular}{c c c c} \hline \hline  & **Mnist** & **Covertype** & **SDDD** \\ \hline Centralized DA+softmax & 0.9973 & 0.6742 & 0.7251 \\ Network structure & 784-500-300-100-10 & 54-50-40-30-10 & 48-50-30-20-10 \\ DDA+softmax & 0.9408 & 0.6123 & 0.6754 \\ \hline Information loss & 5.66% & 9.18\% & 6.85\% \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Classification accuracy of the centralized and proposed methods (Parameters Setting: 70% training set, 30% validation set, 5-fold cross validation). these indices show that the accuracy of the proposed method is competitive, even under a distributed environment.