Tresch Matthew C, Cheung Vincent C K, d'Avella Andrea
Department of Biomedical Engineering and Physical Medicine and Rehabilitation, Northwestern University Chicago, Illinois, USA.
J Neurophysiol. 2006 Apr;95(4):2199-212. doi: 10.1152/jn.00222.2005. Epub 2006 Jan 4.
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 nonnegative values, reflecting the nonnegative 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 (FA) with varimax rotation was better than PCA, and was generally at the same levels as independent component analysis (ICA) and nonnegative matrix factorization (NMF). 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. Nonnegative 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 nonnegativity 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, suggests 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.
最近的几项研究使用矩阵分解算法来评估一种假说，即行为可能是通过少数肌肉协同作用的组合产生的。尽管这些研究在基本结论上总体一致，但它们使用了一系列不同的算法，这使得对其进行解释和整合变得困难。因此，我们在模拟数据集和实验数据集上比较了这些不同算法的性能。我们关注这些算法识别数据集背后协同作用集的能力。所有数据集都由非负数值组成，反映了肌肉激活模式的非负数据。我们发现，主成分分析（PCA）在识别肌肉协同作用方面的性能通常低于其他算法。采用方差最大化旋转的因子分析（FA）优于PCA，并且总体上与独立成分分析（ICA）和非负矩阵分解（NMF）处于同一水平。ICA在受恒定方差高斯噪声干扰的数据集上表现非常好，但在具有信号相关噪声的数据集上以及协同作用激活系数相关时会受到影响。非负矩阵分解（NMF）在具有信号相关噪声的数据集上的表现与ICA和FA相似，并且在整个数据集上总体稳健。最佳算法是应用于由PCA定义的子空间的ICA（ICAPCA）和具有非负约束的概率ICA版本（pICA）。我们还评估了一些常用的标准来确定数据集背后协同作用的数量，发现只有基于因子分析的似然比在某些情况下能为具有信号相关噪声的数据集识别出正确数量的协同作用。然后我们提出了一种临时程序，发现它能够在更多情况下识别出正确的数量。最后，我们将这些方法应用于一个实验获得的数据集。表现最佳的算法（FA、ICA、NMF、ICAPCA、pICA）识别出的协同作用彼此非常相似。基于这些结果，我们讨论了使用分解算法分析肌肉激活模式的指导原则。更一般地说，几种算法在模拟数据中识别正确的肌肉协同作用和激活系数的能力，以及它们应用于生理数据集时的一致性，表明特定算法发现的肌肉协同作用不是该算法的人为产物，而是反映了行为背后肌肉激活模式组织的基本方面。
