# Prediction of Cell-Penetrating Peptides Using a Novel HSIC-Based Multiview TSK Fuzzy System
## 4 Discussion and Conclusions  
In this study, a novel multiview TSK fuzzy system is proposed. First, SSA and Pse-AAC descriptors were employed to convert the original sequence into multiview data. Second, we utilized the correlation-based feature selection algorithm to obtain the optimal feature subset. Finally, the resulting feature subset was input into the multiview TSK fuzzy system based on the HSIC, and a multiview decision result was then obtained. We compared the performance of the proposed model with several classical machine learning algorithms by a five-fold cross-validation. The empirical results demonstrate that the proposed method outperforms the classical methods in terms of ACC, SN, SP, and MCC metrics. We validated the performance of the model using the CPP dataset, the AUC reached 0.975 and 0.990 and the ACC achieved 92.2% and 96.2% on the training and test sets, respectively. The results prove that our method is superior to the existing CPP predictors.  
Through feature analysis, we found that Pse-AAC features played a more important role than SSA features in identifying CPPs. We believe that this is because Pse-AAC features contain physicochemical information that can distinguish CPPs from non-CPPs. Also feature selection is necessary to alleviate the overfitting problem, remove redundant features, reduce data dimension and lower computational cost. When the data matrix **X** is converted to the input matrix **X\({}_{g}\)** of the TSK fuzzy system, the dimension increases dramatically, which can seriously deteriorate the computational efficiency of the model if no feature selection is performed.  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Method** & **ACC (\%)** & **SN (\%)** & **SP (\%)** & **MCC** & **AUC** \\ \hline PPTTPP & 74.9 & 71.6 & 78.1 & 0.498 & 0.824 \\ ITP-PRED & 89.0 & 86.3 & 93.2 & 0.787 & 0.962 \\ PEPred & 91.2 & 90.3 & 92.2 & 0.824 & 0.972 \\ MV-TSK-PS-HSIC & 92.2 & 90.8 & 93.5 & 0.844 & 0.975 \\ \hline \hline \end{tabular}
\end{table}
Table 4: Comparison of existing methods using the CPP740 dataset and five-fold cross validation.  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Method** & **ACC (\%)** & **SN (\%)** & **SP (\%)** & **MCC** & **AUC** \\ \hline PEPred & - & - & - & - & 0.952 \\ PPTTPP & - & - & - & - & 0.967 \\ ITP-PRED & 95.1 & 92.8 & 97.8 & 0.904 & 0.989 \\ MV-TSK-FS-HSIC & 96.2 & 96.7 & 95.7 & 0.924 & 0.990 \\ \hline \hline \end{tabular}
\end{table}
Table 5: Comparison of existing methods with an independent test set and five-fold cross validation.  
Although the proposed model has been proven to be effective in experiments, there is still room for improvement. In future research, we expect to introduce a novel multi-view mechanism to investigate the relationships between different views and enhance the interpretability of TSK fuzzy systems.  
Conceptualization, Y.D.; methodology, Y.D.; software, P.L.; validation, S.Z.; formal analysis, S.Z. and P.L.; investigation, S.Z.; resources, Q.Z.; data curation, P.L.; writing--original draft preparation, P.L.; writing--review and editing, Y.D.; visualization, P.L.; supervision, Q.Z.; project administration, Q.Z. All authors have read and agreed to the published version of the manuscript.  
The work was supported by the National Natural Science Foundation of China (No. 62172076, 61902271), and the Municipal Government of Quzhou under Grant Number 2020D003 and 2021D004.  
Not applicable.  
The data used in this paper can be downloaded at [[http://lab.malab.cn/~acy/BioseqData/Protein/ITP-Pred.rar](http://lab.malab.cn/~acy/BioseqData/Protein/ITP-Pred.rar)]([http://lab.malab.cn/~acy/BioseqData/Protein/ITP-Pred.rar](http://lab.malab.cn/~acy/BioseqData/Protein/ITP-Pred.rar)) (accessed on 16 January 2022). We thank [PERSON] for his contribution to this paper.  
The authors declare no conflict of interest.