Tensor decomposition and mixed-effects modeling reveal speed-dependent neuromuscular and kinematic coordination during walking

Understanding how walking speed affects neuromuscular and kinematic coordination requires methods that maintain the multidimensional structure of gait data. This study used tensor decomposition and linear mixed-effects modeling to identify speed-dependent adaptations in latent muscle activation and joint kinematic patterns. Twenty-seven healthy adults walked at different speeds while surface electromyography and 3D joint kinematics were recorded. Data were structured into three-way tensors and decomposed using CP/PARAFAC, with component number set by core consistency diagnostic. Linear mixed-effects models identified latent components linked to walking speed. Speed significantly affected one kinematic component ( η p 2 = 0.1312 ), involving hip and ankle, and two muscle activation components: the first ( η p 2 = 0.2996 ) reflected quadriceps and tibialis anterior during swing-to-stance, while the second ( η p 2 = 0.2167 ) showed plantarflexor activity in late stance and swing. Cross-correlation showed moderate to strong temporal links between muscle and joint components, with plausible temporal lags. Overall, walking speed selectively influenced a few latent coordination patterns, supporting reweighting of existing strategies rather than new ones. The proposed framework offers a rigorous approach for identifying latent coordination patterns while retaining gait data’s multidimensional structure.