## 5 Discussion and Conclusions  
The main objective of the work has been to characterize the fragmentation within the ECG, and more specifically inside the QRS complex. To this end, preprocessing has been carried out to eliminate noise and non-intrinsic components. Signal adjustment was performed applying the described statistical signal filtering, which consolidates a suitable shaping of the signal for further processing using the described beat templates. For convenience and to analyze fragmentation behavior with multivariate analysis, a subrogated model including fragmented components, has been developed based on said beats templates from healthy patients. The results of the different experiments, using PCA and ICA, have originated to the conclusions detailed below. First, the exclusive use of the independent components of the ECG, both in PCA and in ICA, substantially improves the behavior in the comparative analysis of the subrogated signals versus the signals not including fragmentation. In particular, in the case of PCA using only the 8 independent components, it was shown a dispersion reduction to the half (0.14 to 0.07), compared to case when all ECG components were incorporated in the processing. Second, although it would be desirable the fragmentation consolidation in the _principal and cleaner_ lower order components after PCA or ICA transformations, our results did not show it. Alternatively, results showed that the injected fragmentation materializes with a greater proportion in the _detail-leads_ (larger order). In particular, its average quadratic contribution, estimated as the RMSE of the difference of both signals before and after the transformation, for the case of PCA, showed quantitative improvement in more than 99% of the cases using only the three last components of the transformed signals, versus the best results in the original signals. Figure 22: Distribution of the normalized ICA transformation matrix for the last principal component of the twelve-lead model. (**a**) Distribution of the transformation matrix components for each control patient. (**b**) Distribution of the transformation matrix components for each subrogated fragmented patient. (**c**) Aligned distribution of transformation matrix components for each control patient. (**d**) Aligned distribution of transformation matrix components for each subrogated fragmented patient. The red line shows the value of transformation vector used in the alignment. Third, since this type of affections visually debut in certain regions, and being consistent with the clinical criteria, we assumed that the analysis using only the corresponding leads where the fragmentation is found, would eventually facilitate the automated detection. However, the results obtained contradict this assumption. From this perspective, it could be argued that, although conceptually it makes sense, the existence of a greater number of components, together with the redundancy of the information included the mathematically dependent leads, contributes positively to the fragmentation isolation in the detail components. Finally, note that the obtained results showed better performance of the multivariate analysis using PCA versus ICA. In this setting, it could be argued that the requirement of independence of the components challenges the model, forcing not necessary and additional restrictions to the multivariate transformation, and limiting the consolidation capacity of the fragmented elements to be isolated in the detail components. Additionally, it should be mentioned that a very extensive analysis has been developed in this work as far as the fragmentation is concerned. We evaluated most of the mathematically possible alternatives for representing the fragmentation wave. In particular, a wide range of amplitudes, duration's, frequencies, and affected leads were evaluated. This extremely complex variety of possibilities really challenged the model beyond clinically real expected fragmentation events.