# Double Deep Autoencoder for Heterogeneous Distributed Clustering
## 5 Discussion and Conclusions  
Although traditional data mining mainly considers handling data in centralized datasets, with the increasing amount of data, centralized storage devices are inadequate for storage of this data. In light of the above issue, distributed databases have been proposed. However, distributed databases complicate the procedures of data mining. In addition, the issue of preserving privacy has also facilitated the emergence of DDM algorithms.  
In this paper, we consider a deep learning structure with a double autoencoder setting in local sites and the server, simultaneously. The first deep autoencoder is used to derive the codes for local sites, and the second deep autoencoder is used to derive the global encoder by combining these local encoders. The global encoder should be a good representative for all local features, and achieves this by learning the nonlinear relationships between features. Finally, we can use various kinds of clustering algorithms to obtain global clusters.  
The experiment results indicate that DDA and spectral clustering have the highest _CAI_, between 0.7 and 0.8, compared with k-means and SOM--that is, over 70% of the data points of the central and distributed datasets are assigned to the same clusters. Therefore, we can conclude that DDA can learn the important patterns from the local codes of the intra-datasets. In addition, from the comparisons between accuracy and _CAI_, it can be inferred that the performance of the _CAI_ is affected by the consistency of the data structure. Therefore, if the data consistency is higher, the value of the _CAI_ becomes higher. Note that the data consistency is reflected in the accuracy of the classification. The higher the accuracy, the higher the data consistency. Furthermore, the results of the ACC and information loss also indicate that the proposed algorithms can account for the clustering analysis under the distributed and heterogeneous environments.  
In addition, the empirical results show that the DDA+Spectral algorithm outperforms others in all datasets. Since the input data of the proposed three algorithms are the same, the performance of the algorithms are determined by the ability of the clustering algorithm. In the past research, the performance of the spectral clustering was found to be better than k-means and is consistent with the conclusion here.  
The characteristics of the proposed algorithm have the following advantages. First, the local code layers, derived by the deep autoencoder in the replica, can usefully retain the important information of  
Figure 6: The performance evaluation of the proposed methods.  
the data and can consider the privacy-preserving issue with fewer features. Second, the mini-batch Nesterov algorithm enables training of the appropriate weights, even with big data. Third, the global code contains all the information of the local codes, and represents them with fewer features. Finally, all centralized algorithms can be embedded in our algorithm to obtain the global clustering results without further modification.  
Writing--original draft, J.-J.H.; Writing--review & editing, C.-Y.C.  
This research received no external funding.  
The authors declare no conflict of interest.