## 3 Results and Discussion
### Matrix Expandability Analysis and the Selection of the Best Matrix Architecture  
Once it has been decided that the variance of the norm will be used as the metric of choice, further investigation indicates a challenge in selecting the optimum matrix architecture among PMLD, MA1 and MA2. This concern emerges from the closeness in variance values produced by all the architectures for both healthy and unhealthy candidates. For example, when examining the healthy candidate \(H_{1}\), it is observed that the variances of the norm for each architecture are rather close to each other: MA1 = 0.0016, MA2 = 0.0010, and PMLD = 0.0012, respectively. This trend persists consistently across all candidates for both healthy and unhealthy participants. Thus, a selection criterion is needed to discover the best matrix architecture. The first criterion for the selection of matrix architecture revolves around the expandability of a matrix by focusing on the six requirements [18]. These requirements facilitate the integration of additional data or cardiac parameters into the matrix structure. As mentioned previously, both the MA1 and PMLD architectures can be naturally expanded due to their inherent properties. However, the MA2 architecture fails to fulfil the requirements due to the loss of balance among its elements, rendering it unsuitable for further analysis and leading to its exclusion from the selection criteria. Moreover, upon a closer examination of the MA1 architecture, it can also be observed that the principle diagonal elements are multiplied by a scalar. As previously discussed, the multiplication of the zero-order elements by a scalar factor greater than one does decrease its ability to detect the subtle variations in the investigated signals [18]. Consequently, the MA1 architecture is also excluded from the selection criteria. Thus, based upon the selection criteria, the PMLD architecture emerges as the most reliable choice for the subsequent computations, expandability analysis, and the development of the classification techniques. Its balanced structure, coupled with its ability to accommodate new data, positions the PMLD architecture as the optimal matrix architecture for the analysis of complex signals like ECG. Table 3 provides results for the norm of the PMLD matrix for the healthy candidates from the second to the fifth orders. A general trend is observed in both the sensitivity and the variability of the produced data. As defined already, sensitivity in the context of this paper is defined as the ability of the matrix to produce larger variance values as the size of the matrix is expanded. For instance, candidates such as \(H_{2}\), \(H_{4}\), \(H_{6}\), and \(H_{8}\) show higher sensitivity as the order of the matrix is increased. Other candidates like \(H_{1}\)\(H_{3}\), \(H_{5}\) and \(H_{7}\) also show an increase in variance values except for the fourth-order PMLD. For example, the individual \(H_{7}\) has shown an increase in variance values in the second-, third-, and fifth-order matrices, but it displays a lower variance value in the fourth-order as compared to the third-order PMLD. Also, variability is defined as the qualitative measure that reflects the extent of data spread under the Gaussian distribution curves, which is important for the classification of individuals. The variability of the data obtained for a healthy cohort for the third-order PMLD and the fifth-order PMLD is seen in Figure 3a. From the data tabulated in Table 4, it can be observed that the candidates \(U_{1}\), \(U_{3}\), \(U_{6}\), and \(U_{8}\) show an increase in sensitivity as the matrix order is increased. Candidate \(U_{2}\) shows a very consistent sensitivity as the order of the matrix is increased. In terms of variability, while there is some degree of variation present within the unhealthy cohort, if a comparison is made between the variability of the healthy and the unhealthy cohort, a higher degree of variability will be observed in the healthy group.