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1 Department of Biomedical Engineering and Physical Medicine and Rehabilitation, Northwestern University, Chicago, IL, USA
2 Division of Health Sciences, Harvard Medical School and Massachusetts Institute of Technology, Cambridge, MA, USA
3 Department of Neuromotor Physiology, IRCCS Fondazione Santa Lucia, Rome, Italy
* To whom correspondence should be addressed. E-mail: m-tresch{at}northwestern.edu.
Several recent studies have used matrix factorization algorithms to assess the hypothesis that behaviors might be produced through the combination of a small number of muscle synergies. Although generally agreeing in their basic conclusions, these studies have used a range of different algorithms, making their interpretation and integration difficult. We therefore compared the performance of these different algorithms on both simulated and experimental data sets. We focused on the ability of these algorithms to identify the set of synergies underlying a data set. All data sets consisted of non-negative values, reflecting the non-negative data of muscle activation patterns. We found that the performance of principal component analysis (PCA) was generally lower than that of the other algorithms in identifying muscle synergies. Factor analysis with varimax rotation (FA) was better than PCA, and was generally at the same levels as ICA and NMF. Independent component analysis (ICA) performed very well on data sets corrupted by constant variance Gaussian noise, but was impaired on data sets with signal dependent noise and when synergy activation coefficients were correlated. Non-negative matrix factorization (NMF) performed similarly to ICA and FA on data sets with signal dependent noise and was generally robust across data sets. The best algorithms were ICA applied to the subspace defined by PCA (ICAPCA) and a version of probabilistic ICA with non-negativity constraints (pICA). We also evaluated some commonly used criteria to identify the number of synergies underlying a data set, finding that only likelihood ratios based on factor analysis identified the correct number of synergies for data sets with signal dependent noise in some cases. We then proposed an ad hoc procedure, finding that it was able to identify the correct number in a larger number of cases. Finally, we applied these methods to an experimentally obtained data set. The best performing algorithms (FA, ICA, NMF, ICAPCA, pICA) identified synergies very similar to one another. Based on these results, we discuss guidelines for using factorization algorithms to analyze muscle activation patterns. More generally, the ability of several algorithms to identify the correct muscle synergies and activation coefficients in simulated data, combined with their consistency when applied to physiological data sets, suggest that the muscle synergies found by a particular algorithm are not an artifact of that algorithm, but reflect basic aspects of the organization of muscle activation patterns underlying behaviors.
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