Objective: Higher-order tensor decompositions have hardly been used in muscle activity analysis despite the fact that multichannel electromyography (EMG) datasets used in muscle synergy studies naturally present multi-way structure . Here, we seek to discuss and demonstrate the potential of tensor decomposition as a framework to estimate muscle synergies from 3^{rd}-order EMG tensors constructed by stacking repetitions of multi-channel EMG for several tasks. Methods: We compare the two most common decomposition models -Parallel Factor Analysis (PARAFAC) and Tucker- in muscle synergy extraction from the three main degrees of freedom (DoF) of the wrist using the first Ninapro database. We then utilise the power tensor factorisation to create a novel direct method for shared and task-specific synergy estimation from two biomechanically related tasks by developing a constrained Tucker decomposition method . Our approach is compared with the current standard approach of repetitively applying non-negative matrix factorisation (NMF) to a series of the movements. Results: The results show that the constrained Tucker method successfully identified the shared and task-specific synergies for all 3 DoF tensorsdirectly and it was robust to misassignments with regard to task-repetition information unlike NMF, thanks to exploring the multi-way structure of muscle activity. Conclusions: We showed the potential of tensor factorisations to study and characterise muscle activity and developed a new direct method for shared and task-specific synergy identificationwith a constrained Tucker decomposition. Significance: We expect that this study will pave the way for the development of  muscle activity analysis methods based on higher-order techniques.
 Higher-order tensor decompositions have hardly been used in muscle activity analysis despite multichannel electromyography (EMG) datasets naturally occurring as multi-way structures . Here, we seek to demonstrate and discuss the potential of tensor decompositions as a framework to estimate muscle synergies from 3^{rd}-order EMG tensors built by stacking repetitions of multi-channel EMG for several tasks. We compare the two most widespread tensor decomposition models -- Parallel Factor Analysis (PARAFAC) and Tucker -- in muscle synergy analysis of the wrist's three main Degree of Freedoms (DoFs) using the public first Ninapro database. Furthermore, we proposed a constrained Tucker decomposition (consTD) method for efficient synergy extraction building on the power of tensor decompositions. This method is proposed as a direct novel approach for shared and task-specific synergy estimation from two biomechanically related tasks . Our approach is compared with the current standard approach of repetitively applying non-negative matrix factorisation (NMF) to a series of movements. The results show that the consTD method is suitable for synergy extraction compared to PARAFAC and Tucker. Moreover, exploiting the multi-way structure of muscle activity, the proposed methods successfully identified shared and task-specific synergies for all three DoFs tensors. These were found to be robust to disarrangement with regard to task-repetition information , unlike the commonly used NMF. In summary, we demonstrate how to use tensors to characterise muscle activity and develop a new consTD method for muscle synergy extraction that could be used for shared and task-specific synergies identification. We expect that this study will pave the way for the development of novel muscle activity analysis methods based on higher-order techniques.
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Objective:
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the fact that
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used in muscle synergy studies naturally present
naturally occurring as
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structure
structures
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discuss and demonstrate
demonstrate and discuss
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decomposition
decompositions
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constructed
built
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Methods:
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common decomposition models -Parallel
widespread tensor decomposition models -- Parallel
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Tucker-
Tucker --
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extraction from the three main degrees of freedom (DoF) of the wrist using the
analysis of the wrist's three main Degree of Freedoms (DoFs) using the public
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We then utilise the power tensor factorisation to create a novel direct method
Furthermore, we proposed a constrained Tucker decomposition (consTD) method for efficient synergy extraction building on the power of tensor decompositions. This method is proposed as a direct novel approach
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by developing a constrained Tucker decomposition method
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the movements. Results:
movements.
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constrained Tucker method successfully identified the
consTD method is suitable for synergy extraction compared to PARAFAC and Tucker. Moreover, exploiting the multi-way structure of muscle activity, the proposed methods successfully identified
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3 DoF tensorsdirectly and it was robust to misassignments
three DoFs tensors. These were found to be robust to disarrangement
R
unlike NMF, thanks to exploring the multi-way structure of muscle activity. Conclusions: We showed the potential of tensor factorisations to study and
, unlike the commonly used NMF. In summary, we demonstrate how to use tensors to
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developed a new direct method for
develop a new consTD method for muscle synergy extraction that could be used for
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synergy identificationwith a constrained Tucker decomposition. Significance:
synergies identification.
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novel