# Nonlinear Random Forest Classification, a Copula-Based Approach
## 5 Conclusions  
A copula-based algorithm has been employed in a random forest classification. In this regard, the most important features were extracted based on their associated copulas. The simulation study as well as real data analysis have shown that the proposed couple-based algorithm may be helpful when the explanatory variables are connected nonlinearly and when we are going to extract the most important features instead of all features.  
The idea of this paper may be extended in some manners. One may use this idea in a multi-class random forest classification. Additionally, a random forest regression considering the connecting copula of features will be useful. Moreover, the associated copula of features in order classification tasks such as the support vector machine, discriminant analysis and naive Bayes classification will be of interest. Many extensions of random forest have been investigated by several authors, for example, boosted random forest, deep dynamic random forest, ensemble learning methods random forest, etc. Each extension of the random forest classification may be combined with our approach to obtain better results. We are going to extend these results in a longitudinal dataset in which the outcome variables are connected using some copulas.  
Conceptualization, R.M. and A.S. All authors have read and agreed to the published version of the manuscript.  
APV-18-0052 and VEGA 1/0006/19.  
Not applicable.  
Data Availability Statement[[https://archive.ics.uci.edu/ml/datasets/diabetes+130-us+hospitals+for+years+1999-2008](https://archive.ics.uci.edu/ml/datasets/diabetes+130-us+hospitals+for+years+1999-2008)]([https://archive.ics.uci.edu/ml/datasets/diabetes+130-us+hospitals+for+years+1999-2008](https://archive.ics.uci.edu/ml/datasets/diabetes+130-us+hospitals+for+years+1999-2008)) (accessed on 2 June 2021).  
\begin{table}
\begin{tabular}{c c c c c} \hline \(n\) & **Names of Attributes** & **Sensitivity** & **Specificity** & **Accuracy** \\ \hline
2 & num\_medications, num\_procedures & 0.742 & 0.756 & 0.708 \\ \hline
3 & num\_medications, num\_procedures, A1 Cresult & 0.766 & 0.771 & 0.780 \\ \hline
5 & num\_medications, num\_procedures, A1 Cresult, epiglinide, & 0.837 & 0.806 & 0.801 \\ \hline
10 & num\_medications, number\_diagnoses, age, A1 Cresult, & & & \\ repaglinide, max\_glu\_serum, weight, glimepiride, rosiglitazone, & 0.921 & 0.948 & 0.871 \\ \hline
20 & num\_medications, number\_diagnoses, age, A1 Cresult, & & & \\ repaglinide, max\_glu\_serum, weight, glimepiride, rosiglitazone, & & & & \\  & & & & \\  & & & & \\  & & & & \\  & & & & \\ \hline
50 & All attributes & 0.986 & 0.981 & 0.978 \\ \hline \end{tabular}
\end{table}
Table 3: Selected features with their measures of assessment in Diabetes 130-Us hospital dataset.  
**Acknowledgments:** The work of the first author was supported by the project APVV-18-0052 and VEGA 1/0006/19. Additionally, the authors wish to thank the anonymous reviewers for the comments and suggestions that have led to a significant improvement of the original manuscript.  
**Conflicts of Interest:** The authors declare no conflict of interest.