# Entropy and Statistical Complexity in Bioelectrical Signals: A Literature Review
## 3 Results
### Permutation Entropy
However, despite these advantages, PE lacks stability concerning its initial parameters. Its accuracy can vary depending on these parameters, potentially leading to inconsistent results [35]. Additionally, PE focuses solely on the permutation patterns of embedded vectors, disregarding the actual amplitude of the samples [42] or the time series [24; 49]. The limitations of PE include its exclusive consideration of sequence order [13] or amplitude values [24], without accounting for the actual differences between them. Additionally, it cannot encompass all ordinal patterns when the order n is large in finite time series [36], making it challenging to capture all variations due to computational constraints. This results in the omission of important informational aspects [24], such as the dynamic trajectory [49]. Since PE does not account for the differences or similarities between the elements of a vector, its ability to capture patterns within a process is diminished [13; 38]. Additionally, it is ineffective as a standalone feature in classification algorithms. While PE can quantify information [38], it struggles to distinguish effectively between random and chaotic systems, prompting the development of more specific and discriminative measures [47]. In 2002, multiscale entropy was introduced [13], inspired by [PERSON]'s proposal [34]. Commonly referred to as MSE [10; 13; 34; 38; 40; 50; 51; 52; 53; 54], it has been extensively utilized across various fields of research [52], including disciplines such as biomedical and mechanical engineering, as well as the field of hydrology [51]. MSE is a method [10; 38; 40; 50], a measure [51; 53], a tool [51], or an approach [10; 34] that is valuable for evaluating and quantifying [10; 13; 38; 51; 52] complexity [10; 38; 40; 50; 51; 53; 54] and irregularity [51] in dynamic systems [10], physiological [10; 53], signals [40; 53], time series [10; 51; 52; 54], biomedical [52; 54], and particularly those that are short and noisy [51]. Similarly, MSE is also used to analyze [13] various types of entropy [10; 13] considering different levels of detail [10] or multiple time scales [10; 13; 34; 38; 40; 50; 51; 52], rather than relying on a single scale [38]. This approach stems from the premise that a system's complexity varies depending on the scale of observation [10]. Unlike traditional entropy methods, MSE extracts information from previously unknown scales [51]. The MSE algorithm generates multiple new series, referred to as coarse-grained versions [40; 51; 52] using different scale factors [40; 51] derived either from the original signal [52] or from a single time series obtained from a biological system [13]. Notably, using a scale factor of one is equivalent to analyzing the original signal [40]. After the granulation process, entropy is computed for each coarse-grained time series [13; 40; 51]. Despite its utility, MSE can exhibit discrepancies across different scales, complicating the comparative evaluation of complexity between time series. For short records, its estimation accuracy decreases significantly. Additionally, MSE faces computational efficiency challenges, including a substantial workload due to its calculation process, which involves nested loops. These limitations significantly impact its effective application in the analysis of physiological signals under real-world conditions [53].