## 2 Materials and Methods
### Signal Pre-Processing and Data Extraction  
The sEMG signals were high-pass filtered by a 2 nd order, zero-phase Butterworth digital filter with a cut-off frequency of 10 Hz, in order to remove low frequency artifacts due to sensor displacements. Considering the limited bandwidth of the Myo signals, due to the low sampling rate, and in order to avoid further information loss about muscular activity, the usual band-pass filtering, ranging from 10 to 500 Hz, was not applied in the present case. For each gesture sequence, the muscular activations' intervals were then identified through the software tool described in [42]. The FEn and PEn were then computed on each muscular activation window for all the 8 armband channels and for different entropy computation parameters. The FEn was computed by using a fixed embedding dimension of 2 and for all the 9 combinations of \(r=(0.1,0.3,0.5)\) and \(n=(1,2,5)\). The PEn embedding dimension \(d\) was chosen within the set \((3,5,7)\). The FEn and PEn were computed on sEMG signals of two out of the eight Myo armband channels and visualized on the plane defined by the two entropy values, following [16]. This procedure allowed us to obtain a clustering of hand gestures, based on entropy values. The channel selection criterion was the lowest signal-to-noise ratio. The optimal number of clusters was assessed by the k-means algorithm, using the gap statistic (GS) for each gesture set and for each subject [43]. Then, for those parameters' settings which ensure proper gesture recognition, the goodness of clustering was evaluated in terms of mean distance of each point from the centroid of the corresponding cluster and the mean distance of each point from every cluster centroid. The choice of this kind of evaluation, i.e., clustering goodness rather than classification accuracy, is based on [16; 27]. In order to assess the validity of the proposed complexity measures with respect to different sEMG features, a set of 18 time and frequency domain features was also computed. In particular, the classical [PERSON]'s feature set [21] was considered, together with the feature set proposed in [22]. In addition, another ten features proposed in [9] were also extracted from sEMG signals. The final feature set thus encompassed the following measures: mean absolute value (MAV), modified mean absolute value type 1 (MAV1), integrated EMG (IEMG), waveform length (WL), zero crossing (ZC), Willison amplitude (WA), slope sign change (SSC), variance (VAR), root mean square value (RMS), square integral (SI), absolute value of the third temporal moment (TRD), absolute value of the fourth temporal moment (FRTH), absolute value of the fifth temporal moment (FFTH), mean frequency (MNF), median frequency (MDNF), total spectral power (TSP), mean spectral power (MSP) and sample entropy (SEn). For detailed explanations of the computations of features, the reader can refer to [3; 9]. Then, in order to compare the FEn and PEn with the above listed more classical features, the minimum redundancy maximum relevance (mRMR) algorithm was used [44]. In brief, mRMR is a feature selection algorithm which quantifies the redundancy and relevance of each feature within a predefined set and provides on ordered rank of the features according to their predictive importance scores, indicating which is a compact subset of features with the best predictive impact for the considered dataset. Therefore, for each set of gestures all the 20 features have been pooled together and analyzed through the mRMR algorithm, which presents the significant advantage of being independent from a specific classification algorithm, relying purely on the maximization of the dependency of the feature set with the target class [44]. For this analysis, the computational parameters of FEn and PEn have been chosen as those which provided the best clustering results within each gesture set. Eventually, in order to provide a direct comparison between FEn and PEn, they have been also evaluated in terms of gestures classification accuracy.