## 4 Discussion and Conclusions
Similarly, a high correlation was also observed between the AFCL and SE, and the AFCL and DET, thus indicating that these three indices maintain a strong relationship between each other, linking the linear and the nonlinear domain. Finally, as expected, the AFCL and DF were also highly correlated. Altogether, these high correlations indicate that the selection of such indices for a substrate assessment is the right choice because they have been able to capture the essence of the atrial electrophysiological substrate. The study of the discriminatory power of DF\({}_{\text{FIPV}}\) using statistical tests led to the wrong conclusion that the index is not discriminative, as the null hypothesis of no differences between ParAF and PerAF was accepted. Contrarily, the feature selection ranked the DF\({}_{\text{FIPV}}\), together with SE\({}_{\text{POS}}\), DF\({}_{\text{LSPV}}\), and DF\({}_{\text{RSPV}}\), as the set of most important variables to discriminate between the CFAEs of the ParAF and PerAF, reaching the highest accuracy of 88.3%. Therefore, the careful selection of limited sets of indices feeding straightforward classifiers are able to discriminate accurately between the CFAE of different AF types. Furthermore, the use of just one nonlinear index, such as DET\({}_{\text{LIPV}}\), provided a classification accuracy as high as 82.2% for any segment length. This result can serve as a starting point to prove that simple classification models, which are readily understandable, can be built to provide improved methodologies for atrial substrate characterization in AF. The proposed analysis has also some limitations that merit consideration. Firstly, the study has been carried out using a limited set of data which, lately, has been reduced more due to the discarding process. Obviously, in order to obtain more generalizable results, a wider database with many more patients would be desirable. In this regard, our group is now working toward the expansion of the database for future studies. Secondly, regarding the creation of the classification models, the generalization of the results for the classification between the ParAF and PerAF could provoke model overfitting, especially using the Random Forest algorithm. However, given that the accuracy obtained with a single index has been high enough (82.4%) with respect to the accuracy provided by the most performing model (88.2%), it is reasonable to consider that overfitting has a reduced effect in overall classification performance. As an overall conclusion, the observed high variability of the CFAE has shown that averaging data in one recording place or among different recording places may lead to an unfair oversimplification of the CFAE-based atrial electrophysiological substrate characterization. Furthermore, a thoughtful selection of the limited combinations of features feeding straightforward classification models are able to discriminate accurately between the CFAEs of the ParAF and PerAF, thus providing improved therapeutic decision making for AF management, as well as clearer insight concerning the evaluation of the atrial substrate. Conceptualization, E.F., R.A. and J.J.R. ; data gathering and annotation of the datasets, E.F., A.Q. and F.H. ; methodology E.F., E.J.C., H.G., R.A. and J.J.R. ; software and validation E.F., R.A. and J.J.R. ; resources, A.Q., F.H. and J.J.R. ; data curation, E.F., A.Q., E.J.C. and J.J.R. ; original draft preparation, E.F.; review and editing, E.F., A.Q., E.J.C., H.G., F.H., R.A. and J.J.R. All authors have read and agreed to the published version of the manuscript. This research has received partial financial support from public national grants DPI2017-83952-C3, PID2021-00X128525-IV0, and PID2021-123804 OB-I00 of the Spanish Government with DOI 10.13039/501100011033 jointly with the European Regional Development Fund (EU), and regional grants SBPLY/17/180501/000411 from Junta de Comunidades de Castilla-La Mancha and AICO/2021/286 from Generalitat Valenciana.