Estimating Effective Degrees of Freedom in Motor Systems Export

@article{clewley2008, abstract = {Studies of the degrees of freedom and "synergies" in musculoskeletal systems rely critically on algorithms to estimate the "dimension" of kinematic or neural data. Linear algorithms such as principal component analysis (PCA) are the most popular. However, many biological data (or realistic experimental data) may be better represented by nonlinear sets than linear subspaces. We evaluate the performance of PCA and compare it to two nonlinear algorithms [Isomap and our novel pointwise dimension estimation (PD-E)] using synthetic and motion capture data from a robotic arm with known kinematic dimensions, as well as motion capture data from human hands. We find that PCA can lead to more accurate dimension estimates when considering additional properties of the PCA residuals, instead of the dominant method of using a threshold of variance captured. In contrast to the single integer dimension estimates of PCA and Isomap, PD-E provides a distribution and range of estimates of fractal dimension that identify the heterogeneous geometric structure in the experimental data. A strength of the PD-E method is that it associates a distribution of dimensions to the data. Since there is no a priori reason to assume that the sets of interest have a single dimension, these distributions incorporate more information than a single summary statistic. Our preliminary findings suggest that fewer than ten DOFs are involved in some hand motion tasks. Contrary to common opinion regarding fractal dimension methods, PD-E yielded reasonable results with reasonable amounts of data. Given the complex nature of experimental and biological data, we conclude that it is necessary and feasible to complement PCA with methods that take into consideration the nonlinear properties of biological systems for a more robust estimation of their DOFs.}, author = {Clewley, R. H. and Guckenheimer, J. M. and Valero-Cuevas, F. J.}, booktitle = {Biomedical Engineering, IEEE Transactions on}, citeulike-article-id = {4131918}, citeulike-linkout-0 = {http://dx.doi.org/10.1109/TBME.2007.903712}, citeulike-linkout-1 = {http://ieeexplore.ieee.org/xpls/abs_all.jsp?arnumber=4360110}, doi = {10.1109/TBME.2007.903712}, journal = {Biomedical Engineering, IEEE Transactions on}, keywords = {grundlagen, pca}, number = {2}, pages = {430--442}, posted-at = {2009-03-04 14:21:35}, priority = {4}, title = {Estimating Effective Degrees of Freedom in Motor Systems}, url = {http://dx.doi.org/10.1109/TBME.2007.903712}, volume = {55}, year = {2008} }

TY - JOUR ID - clewley2008 L3 - citeulike-article-id:4131918 N2 - Studies of the degrees of freedom and "synergies" in musculoskeletal systems rely critically on algorithms to estimate the "dimension" of kinematic or neural data. Linear algorithms such as principal component analysis (PCA) are the most popular. However, many biological data (or realistic experimental data) may be better represented by nonlinear sets than linear subspaces. We evaluate the performance of PCA and compare it to two nonlinear algorithms [Isomap and our novel pointwise dimension estimation (PD-E)] using synthetic and motion capture data from a robotic arm with known kinematic dimensions, as well as motion capture data from human hands. We find that PCA can lead to more accurate dimension estimates when considering additional properties of the PCA residuals, instead of the dominant method of using a threshold of variance captured. In contrast to the single integer dimension estimates of PCA and Isomap, PD-E provides a distribution and range of estimates of fractal dimension that identify the heterogeneous geometric structure in the experimental data. A strength of the PD-E method is that it associates a distribution of dimensions to the data. Since there is no a priori reason to assume that the sets of interest have a single dimension, these distributions incorporate more information than a single summary statistic. Our preliminary findings suggest that fewer than ten DOFs are involved in some hand motion tasks. Contrary to common opinion regarding fractal dimension methods, PD-E yielded reasonable results with reasonable amounts of data. Given the complex nature of experimental and biological data, we conclude that it is necessary and feasible to complement PCA with methods that take into consideration the nonlinear properties of biological systems for a more robust estimation of their DOFs. IS - 2 JF - Biomedical Engineering, IEEE Transactions on EP - 442 TI - Estimating Effective Degrees of Freedom in Motor Systems VL - 55 T2 - Biomedical Engineering, IEEE Transactions on SP - 430 KW - grundlagen KW - pca AU - Clewley, RH AU - Guckenheimer, JM AU - Valero-Cuevas, FJ PY - 2008/// UR - http://dx.doi.org/10.1109/TBME.2007.903712 ER -