## 1 Introduction  
The electrocardiogram (ECG) is a clinical test used to record the myocardial electrical activity. In healthy subjects, this activation is homogeneous, and it does not present abrupt changes generating clear deflections in the ECG. In some diseases the ECG homogeneity is broken, and this is reflected as abrupt changes in the myocardial electric activation, generating the apparition of additional peaks and notches in the ECG, a condition that is known as fragmentation. One of the causes of this phenomena is fibrosis, which is characterized by apparition of non-conductive tissue zones dispersed in healthy myocardial the tissue, so that these non-conductive zones break the homogeneous conduction. The fibrosis is an unspecific tissue response, which is shared by several illness, such as: Ischemic cardiopathy; Dilated, hypertrophic, or restrictive cardiomyopathy; Or heart failure [1; 2; 3; 4]. The effects of fibrosis can be divided in two groups: Mechanical, in which fibrosis increases the myocardial rigidity difficulties the diastole; and electrical, because the dispersion of non-conductive tissue aids the appearance of reentry arrhythmias, which are potentially serious and are related with the sudden death. The fibrosis diagnoses is performed by pathological anatomy, which requires the extraction of tissue fragment to analyze. In clinical practice, this detection is carried by the use of magnetic resonance image with late gadolinium enhanced (MRI-LGE), but this technique is expensive and cannot be performed in all cases. The potential relation between the fibrosis and the fragmentation presented in the ECG suggest searching for fragmentation markers in it, as it would represent a cheaper and faster technique than MRI-LGE. Nevertheless, the fragmentation detection by clinicians presents some drawbacks, as the different definitions presented by the fragmentation literature, and the high inter-observer variability, due to the fragmentation magnitude is low and it can be masked by noise. Therefore, the main goal of this paper is to elaborate, and if possible to propose, a multilead transformation of the ECG that effectively consolidates the existing fragmentation components into one, or into a minimum number of leads, where this information is enhanced for clinical inspection or for further processing, and eventually to suggest a specific pathology index detection. To do so, we propose the use of multivariate techniques, such as principal components analysis (PCA) and independent component analysis (ICA), which can allow us to decompose the ECG in different sub-signals as a new approach to the fragmentation detection. Although a few works have been recently published in this field [5; 6], the strategy proposed in those papers mainly focus on standard morphological analysis, after a previous denoising process, but this kind of approach presents a critical drawback. As fragmentation is revealed in the ECG as a high frequency noise, a significant part of its expression is filtered out by standard and conventional high-frequency filtering. In other words, it is especially thoughtful in these analysis the fact that high-frequency noise filtering could have undesired effects on the fragmentation components as they may (or at least partially) share the same spectrum. However, of course, if no denoising is performed, high-frequency noise might hinder the extraction of the fragmentation itself. So, traditional approaches will always require a choice between soft-filtering to prevent cancelling of fragmentation effect but keeping the noise, or a much harder filtering that might remove part of the fragmentation. In our work, and with the aim of not damaging the target-components, we propose a statistical filtering by properly averaging specific consecutive beats. This technique allows us to statistically eliminate random noise, without damaging the relevant part of the fragmentation present in high frequencies.