2.3 Signal preprocessing and synergy extraction

Acceleration data of the wrist were first smoothed for segmenting the trials. The onset and offset of each trial were defined as the points at which the net acceleration was below a threshold. EMG data were then extracted and preprocessed offline. Raw EMG signals were band-pass filtered at 20–450 Hz (fourth-order Butterworth filter), detrended, rectified, low-pass filtered at 5 Hz (fourth-order Butterworth filter), integrated over 20 ms, and resampled. To decrease the influence of amplitude differences and ensure that the extraction of muscle synergies was not biased against low-amplitude muscles, the envelope of each muscle and trial was normalized by unit variance (Roh et al., 2015).

Muscle synergies were extracted from a pooled EMG matrix ( M∈R+600×10 , 10 muscles, 2 tasks, 3 trials of each task, and 100 samples of each trial), including all trials and tasks of each individual. The non-negative matrix factorization (NMF) algorithm (Lee and Seung, 1999; Lee and Seung, 2001) was used to extract muscle synergies. An initial input indicating the number of synergies (one to ten in this study) is required to perform the algorithm. NMF factorizes the muscle activation matrix into a time-invariant weight matrix (muscle synergy) and a time-variant activation profile matrix. The extraction was iterated 50 times to avoid a local optimal solution.

The variance accounted for (VAF) (Roh et al., 2013; Zhao et al., 2019) was computed for each initial input to determine the optimal number of synergies required to reconstruct the variation of the original muscle activation. The optimal number of synergies was defined as the point at which the VAF value was above 95% (Tang et al., 2017; Pan et al., 2018).