Muscle Activity Analysis using Higher-Order Tensor Decomposition: Application to Muscle Synergy Extraction

Ahmed Ebied, Eli Kinney-lang, Loukianos Spyrou, Javier Escudero

Research output: Contribution to journalArticlepeer-review


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 3rd-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 the 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 taskspecific 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.
Original languageEnglish
Pages (from-to)27257-27271
Number of pages15
JournalIEEE Access
Issue number1
Early online date28 Feb 2019
Publication statusPublished - 1 Dec 2019


  • Muscles
  • Task analysis
  • Electromyography
  • Matrix decomposition
  • Wrist
  • muscle synergy
  • NMF
  • Shared synergies
  • Task-specific synergies
  • Tensor decomposition
  • Tucker decomposition


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