## 5 Simulation Experiments and Result Analysis
### Simulation Experiments on UCI Standard Datasets  
The simulation experiment introduced three UCI standard datasets, i.e., '_Abalone_', '_Heart Disease_', and '_Bank Marketing_', for performance comparison of data restoration in the Matlab 2012a environment. In this simulation experiment, the incomplete sample proportion in the total samples was set as 20%, and the information loss rate was 25%. Incomplete data sample and missing indexes were randomly selected. The detailed information of the three UCI standard datasets is as shown in Table 3. Taking '_Abalone_' dataset as an example, 60 samples were randomly selected from a total of 4177 data samples as the incomplete samples. In these 60 samples, two indexes were randomly picked out to delete their corresponding information, and formed a data sample set that to be repaired. In order to verify the data restoration performance of the proposed GANs-HDI algorithm on UCI standard datasets, k-nearest neighbors (k-NN), error-back propagation (BP), matrix completion [14], \begin{table}
\begin{tabular}{c l l l} \hline \hline \multirow{2}{*}{**Inputs**} & Establish the original dataset \(D=\{d_{i}\in\mathbb{R}^{K}\}_{i=1}^{N}\); initialize discrimination rate threshold \(c\), reducing pace \(\alpha\), \\  & sample number \(\overline{N}\), activation function \(\mathbf{g}\) and \(\boldsymbol{t}\), hidden neural node number \(L\), thresholds \(R_{1}\), \(R_{2}\), clustering threshold \(k\). \\ \hline
**Step 1** & Initialize central point set \(\boldsymbol{C}\boldsymbol{C}\boldsymbol{U}=D\), and initialize peak point set \(\boldsymbol{Temp\_Peaks}=\{\}\). \\ \hline \multirow{4}{*}{**Step 2**} & Select all data samples with all measurement indexes complete from heterogeneous database \(D=\{d_{i}\}_{i=1}^{N}\), and denote them as a dataset \(\overline{D}=\{d_{i}\}_{i=1}^{N}\). Train generative adversarial networks, and obtain the generator and discriminator. \\  & Determine whether the discrimination rate of newly generated samples falls within the interval \(|0.5-c,0.5+c|\) by using discriminator \(\mathbf{D}\). If this condition is satisfied, combine the new generated samples and original dataset, \\  & and denote the combination as \(D_{GANs}=\{d_{i}\}_{i=1}^{N+M}\), and return to Step 3. Otherwise, the discriminative error of \(\mathbf{D}\) is \\  & back propagated to retraining of generator \(\mathbf{G}\). \\ \hline \multirow{2}{*}{**Step 3**} & Employ peak clustering algorithm to repair the samples with incomplete information, and assume the restoration of \\  & original dataset \(\hat{D}=\{d_{i}\}_{i=1}^{N}\). \\ \hline \multirow{2}{*}{**Step 4**} & Determine whether the repaired samples can be verified by discriminator. If it fails, the threshold \(c\) would be reduced \\  & to \(c-\alpha\) based on the reducing pace \(\alpha\), and return to Step 2.3; otherwise, return integrated dataset \(\hat{D}=\{\hat{d}_{i}\}_{i=1}^{N}\). \\ \hline
**Outputs** & Integrated dataset \(\hat{D}=\{d_{i}\}_{i=1}^{N}\). \\ \hline \hline \end{tabular}
\end{table} 
Table 2: GANs Based Heterogeneous Data Integration. \begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{**Datasets**} & **Incomplete** & **Total Sample** & **Missing Dimensional** & **Total Dimensional** \\  & **Sample Number** & **Number** & **Number** & **Number** \\ \hline Abalone & 835 & 4177 & 2 & 8 \\ Heart Disease & 60 & 303 & 19 & 75 \\ Bank Marketing & 9042 & 45,211 & 4 & 17 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Detail information of UCI standard datasets. Deep Learning [18], and proposed Peak Clustering in Section 2 were chosen as control groups with parts of the model parameters selected by experience. Specifically speaking, the cluster number was equal to the sample class number in k-NN algorithm. The numbers of hidden neural nodes were set to be 10/25/12 and the layer number set to be 8 for three UCI standard datasets in BP algorithm with Sigmodal function as the activation function.