# Entropy and Statistical Complexity in Bioelectrical Signals: A Literature Review
## 3 Results
### Diffuse Entropy
Despite its usefulness, ApEn is usually a biased measure [13; 14; 33] of regularity [33], as it incorporates self-matching [13; 14] to avoid calculating the logarithm of zero. This incorporation tends to yield a result with a higher probability [13]; this approach overestimates the actual similarity in the data [14]. Sample entropy was introduced by [PERSON] and [PERSON] in 2000 [10; 34]. It is commonly referred to as SampEn [10; 14; 22; 24; 29; 34; 35; 36; 39; 40], SampEnt [19], or SaEn [32]. SampEn is based on [PERSON]'s complexity model [19]. It serves as an algorithmic alternative [10; 34] and an optimized extension of approximate entropy [14; 19; 22; 29; 32]. It is considered a method [39], metric [41], or measure [10; 35; 36] of the magnitude of newly formed patterns [10]. It depends, to a lesser extent, on the size of [18; 36] time series [18; 35; 39] or signals [10; 36; 41]. It is capable of evaluating [36; 41] the complexity [10; 36] and regularity of the latter, either by comparing it with a previous version [41] or by quantifying the prediction of future values based on prior values [18]. It is also employed to address issues related to computational efficiency and to enhance effectiveness in time series analysis [35]. It is resistant to mild noise and suitable for both stochastic and deterministic processes [19]. It exhibits consistency [29; 32] relative [29] to known randomness [32]. Unlike other methods, this approach focuses on a precise description of the distribution sequence [10]. SampEn excludes patterns derived from counts of self-coincidences [13; 14; 29; 34; 35; 39; 40], avoiding not only bias [29] but also overestimation of similarity [14], and reducing processing time [34; 35] by half compared to ApEn [34]. However, the absence of matching templates when using short data lengths can result in undefined outcomes [14]. To calculate it, it is necessary to consider three variables [29]: the length of a time series [32], a signal [10], or a segment [41] with N data points [10; 29; 32], along with the prior determination of two parameters, m and r [10; 29; 32; 34; 41]. The parameter m [32; 41], also known as the embedding dimension, indicates the number of data samples that constitute a pattern [41]. It defines the length of the sequences to be compared and can be calculated through the estimation of the false nearest neighbor [32]. Meanwhile, the parameter r defines the tolerance threshold [29; 32; 41] that allows for the recognition or establishment of identical patterns among different segments [32; 41]. The latter is determined as a proportional fraction of the standard deviation [29; 32] of the N amplitude values [29]. It is also suggested that r be maintained between 0.1 and 0.2 times the aforementioned standard deviation [32]. SampEn segments the embedded vectors [10; 42], sequences [13], or amplitude subsequences [39] into similar [10; 13; 39; 42] and distinct groups based on distances [10]. Its computation is grounded in the relative [39] frequency [39; 41] and the individual conditional probability [10; 13; 36; 40] of these occurrences [13; 36]. SampEn applies the negative natural logarithm [13; 32] to the probability that a sequence or series of length n or m [13; 36; 40], selected randomly [36], remains unchanged [13; 40] or matches [36], when extended by one term [13; 40], given a specific tolerance threshold [40; 42]. As SampEn decreases, the self-similarity [10; 41], regularity [41], or repeatability [13] of the sequence [10], signal [41], or time series increases, approaching values near zero [13]. Conversely, entropy values trending toward infinity [13] reflect higher complexity [31] or randomness [13; 41] within the sequence, signal, or time series. Finally, it proves to be inefficient in handling time series [35; 42], extensive [42], erratic, or those with peaks [35], as well as situations that demand real-time analysis [42]. Additionally, SampEn does not quantify all information related to distances [10].