## 4 Experimental Results  
### The Effect of the Number of Submodule Inputs on the DNFS  
This section mainly focuses on the effect of the number of submodule inputs on the DNFS for the first three datasets. The corresponding DNFSs with 3, 4, and 5 submodule inputs are DNFS3-0, DNFS4-0, and DNFS5-0, respectively. The performance comparison of DNFSs with different submodule inputs on the first three test datasets are shown in Tables 2-4. The prediction charts performed by the three \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Index** & **Dataset** & **No. of Features** & **No. of Samples** & **Application Field** \\ \hline
1 & Parkinson’s 1  & 21 & 5875 & Parkinson’s telemonitoring \\
2 & Wdbc 2  & 30 & 569 & Breast cancer diagnosis \\
3 & Superconductor 3  & 81 & 10,000 & Superconductor temperature prediction \\
4 & Music 4  & 69 & 1059 & Geographic origin of music \\
5 & Residential Building 5  & 108 & 372 & Residential building cost \\ \hline \hline \end{tabular}  
* \({}^{1}\) [[http://archive.ics.uci.edu/ml/datasets/Parkinsons+Telemonitoring](http://archive.ics.uci.edu/ml/datasets/Parkinsons+Telemonitoring)]([http://archive.ics.uci.edu/ml/datasets/Parkinsons+Telemonitoring](http://archive.ics.uci.edu/ml/datasets/Parkinsons+Telemonitoring)) (accessed on 20 March 2021); 2 [[http://archive.ics.uci.edu/ml/datasets/Breast+Cancer+Wisconsin+%28](http://archive.ics.uci.edu/ml/datasets/Breast+Cancer+Wisconsin+%28) Progenstic%29]([http://archive.ics.uci.edu/ml/datasets/Breast+Cancer+Wisconsin+%28](http://archive.ics.uci.edu/ml/datasets/Breast+Cancer+Wisconsin+%28) Progenstic%29) (accessed on 20 March 2021); 3 [[http://archive.ics.uci.edu/ml/datasets/Superconductiv+Data](http://archive.ics.uci.edu/ml/datasets/Superconductiv+Data)]([http://archive.ics.uci.edu/ml/datasets/Superconductiv+Data](http://archive.ics.uci.edu/ml/datasets/Superconductiv+Data)) (accessed on 20 March 2021); 4 [[http://archive.ics.uci.edu/ml/datasets/Geographical+Original+of+Music](http://archive.ics.uci.edu/ml/datasets/Geographical+Original+of+Music)]([http://archive.ics.uci.edu/ml/datasets/Geographical+Original+of+Music](http://archive.ics.uci.edu/ml/datasets/Geographical+Original+of+Music)) (accessed on 20 March 2021); 5 [[http://archive.ics.uci.edu/ml/datasets/Residential+Building+Data+Set](http://archive.ics.uci.edu/ml/datasets/Residential+Building+Data+Set)]([http://archive.ics.uci.edu/ml/datasets/Residential+Building+Data+Set](http://archive.ics.uci.edu/ml/datasets/Residential+Building+Data+Set)) (accessed on 20 March 2021).[ENDFOOTNOTE]  
\end{table} 
Table 1: Summary of the five regression datasets. DNFSs on the first three test datasets are shown in Figure 3. The analysis of the results obtained was as follows:  
DNFS5-0 outperformed DNFS3-0 and DNFS4-0 in the prediction accuracy, which determined that its comprehensive score was always the highest among the three cases. The MAE, RMSE, and SMAPE of DNFS5-0 were smaller than the other two algorithms on the three datasets. As shown in Figure 3, it also can be seen that DNFS5-0 achieved the best fitting effect, while the other two algorithms performed relatively poor. In terms of model complexity, DNFS5-0 had the minimum layers and submodules, followed by DNFS4-0 and DNFS3-0. It can be concluded that more submodules and layers needed to be built to decompose the high-dimensional data with fewer submodule inputs. Meanwhile, DNFS5-0 had the most parameters and DNFS3-0 the least on average. The AIC of DNFS3-0 was the minimum for the first two datasets, while DNFS5-0 obtained the best AIC on Dataset No. 3. The average computational time that DNFS3-0, DNFS4-0, and DNFS5-0 spent on the three datasets was 31.21 s, 36.44 s, and 58.32 s respectively. It can be concluded that DNFS3-0 is the most efficient method for the three cases. Based on the analysis above, DNFS5-0 can ensure the optimal performance with less complexity. The advantage of DNFS5-0 was further revealed with the increase of dimensionality, by which the high-dimensional data could be divided into submodules more rapidly.