Higher-order tensor decompositions for muscle synergy analysis

This doctoral thesis outlines several methodological advances in the application of higher-order tensor decomposition for muscle synergy analysis estimated from surface Electromyogram (EMG). This entails both assessing current muscle synergy extraction methods and a novel direct approach to estimate useful muscle synergies using higher-order tensor decomposition. The underlying hypothesis is that higher-order tensor decompositions provide advantages in the estimation of temporal profiles and muscle synergies thanks to the consideration of other domains such as spectral, task or repetition information. Moreover, we implement these advances to inspect potential applications of tensor synergies in biomechanical analysis and myoelectric control. Firstly, we provide an overview of the current mathematical models for the concept of muscle synergies and compare the common matrix factorisation methods for muscle synergy extraction, in addition to second-order blind identification (SOBI), a technique which has not been used for muscle synergy estimation previously. Synthetic and real EMG datasets related to wrist movements from the publicly available Ninapro dataset were used in this evaluation. Results suggest that a sparse synergy model and a higher number of channels would result in better-estimated synergies. SOBI has better performance when a limited number of electrodes is available, but its performance is still poor in that case. Overall, non-negative matrix factorisation (NMF) is the most appropriate method for synergy extraction and, therefore, it is considered as a benchmark in the rest of the thesis. We then show the benefits of higher-order tensor decompositions of EMG data for muscle synergy analysis, discussing possible 3rd and 4th-order tensors models for EMG data. We explore muscle synergy estimation from 4th-order EMG tensors by taking the spectral profile into account and utilise this model for classification between the wrist's movements in comparison with NMF. The results provide a proof-of-concept for higher-order tensor decomposition as classification accuracy is slightly improved using tensor decomposition over NMF. However, the addition of spectral mode -with time-frequency analysis- increases the computational cost for tensor synergy estimation. After the previous proof of concept, we focus on the 3rd -order tensor model for efficient and reliable extraction of meaningful muscle synergies. The most prominent tensor decomposition models (Tucker and PARAFAC) are compared under different constraints. We notice that unconstrained Tucker decomposition cannot extract unique and consistent muscle synergies as it converges into different local minima, while PARAFAC model cannot deal with a higher number of synergies or tasks as the decomposition deviates from the trilinear model. As a result, we introduce a constrained Tucker decomposition model as a framework for muscle synergy analysis. The advantages of this method over NMF are highlighted in the biomechanical application of identifying shared and task-specific muscle synergies. This benefits from the natural multi-way form of the EMG data, which makes higher-order tensor decompositions a better option than applying matrix factorisation repetitively. The constrained Tucker decomposition can successfully identify shared and task-specific synergies and is robust to disarrangement regarding task-repetition information, unlike NMF. The constrained Tucker model is then used as a framework to extract synergistic information that could be applied to proportional upper limb myoelectric control. The consistency of extracted muscle synergies with the increase of the wrist's task dimensionality into 3 degrees of freedom (DoF) is investigated in comparison with NMF. In the literature, NMF approaches for synergy-based proportional myoelectric control were viable only with a task dimension of 2 DoF. In contrast, the results show that a constrained Tucker model identifies consistent muscle synergies from 3-DoFs dataset directly. Moreover, a tensor-based approach for proportional myoelectric control is introduced and compared against NMF and sparse NMF as state of the art benchmarks. To sum up, higher-order tensor decomposition had not been utilised in EMG analysis despite the substantial attention it received in biomedical signal processing applications in recent years. This thesis explores higher-order tensor decompositions for synergy extraction to account for the natural multi-way structure of EMG data. We hope that it will pave the way for the development of muscle activity analysis methods based on higher-order techniques in broader applications.