Evaluating anatomy-constrained GWO-assisted non-negative matrix factorization for muscle synergy extraction in cowboy-dance kicking across synergy numbers

Abstract

Abstract Cowboy-dance kicking is a rapid, multi-joint lower-limb task that requires coordinated activation of multiple muscles, resulting in complex electromyographic patterns for which low-dimensional muscle-synergy analysis can provide a compact description of the recorded coordination structure. Conventional non-negative matrix factorization (NMF) is widely used for such decomposition, but its solutions can be sensitive to initialization and local convergence, and solutions with similar reconstruction quality may still differ in their internal muscle-loading structure. This study therefore evaluated an anatomy-informed Grey Wolf Optimization-assisted NMF framework (GWO-NMF) designed to refine low-dimensional synergy structure while balancing anatomical guidance against reconstruction fidelity. Surface EMG was recorded from eight muscles of the dominant left kicking limb in 12 sports-dance students during metronome-paced cowboy-dance kicking, with 83 valid trials retained for analysis. Following EMG preprocessing and time normalization to a common 0–100% movement cycle, conventional NMF and anatomy-constrained GWO-NMF were compared across synergy numbers k = 3–6. Outcomes included synergy-weight sparsity ( Δsparsity w ), anatomy adherence, global VAF, RMSE, R 2 , cross-trial stability, and computational runtime. Trial-level outcomes were analyzed using linear mixed-effects models with algorithm, synergy number, and their interaction as fixed effects, while accounting for repeated trials within participants; planned contrasts were adjusted using the Holm procedure. GWO-NMF largely preserved the dominant muscle-weight composition and temporal activation patterns while increasingly modifying secondary loadings as k increased. Synergy-weight sparsity was significantly higher under GWO-NMF at k = 4 (Δ = 0.01295, p = 0.003), k = 5 (Δ = 0.03161, p < 0.001), and k = 6 (Δ = 0.06356, p < 0.001), but not at k = 3. Anatomy adherence improved significantly only at k = 6 (Δ = 0.02636, p < 0.001). No significant reconstruction differences were detected at k = 3–4, whereas GWO-NMF showed lower VAF and R 2 and higher RMSE at k = 5–6 (all Holm-adjusted p < 0.001).Cross-trial stability showed a lower directional estimate at k = 5 but did not reach statistical significance (Δ = − 0.03267, Holm-adjusted p = 0.077); a significant reduction was observed at k = 6 (Δ = − 0.06165, p < 0.001). Computation time was approximately 133–138 times longer for GWO-NMF across the tested synergy numbers. GWO-NMF should be regarded as a k -dependent, anatomy-guided refinement framework rather than a universal replacement for conventional NMF. At lower decomposition orders, particularly k = 4, it increased structural compactness without a detectable reconstruction penalty, whereas stronger structural modification at higher k was accompanied by reduced reconstruction fidelity, lower cross-trial stability, and substantially greater computational cost. Improvements in sparsity and anatomy adherence therefore describe structural properties of the extracted decomposition and should not be interpreted as direct evidence of specific biomechanical functions or greater neurophysiological validity without independent kinematic, kinetic, or neural validation.

The authors' abstract, as published at the source. Scientific Reports, 2026 · DOI ↗