Alternating Minimization for Time-Shifted Synergy Extraction in Human Hand Coordination

Identifying motor synergies -- coordinated hand joint patterns activated at task-dependent time shifts -- from kinematic data is central to motor control and robotics. Existing two-stage methods first extract candidate waveforms (via SVD) and then select shifted templates using sparse optimization, requiring at least two datasets and complicating data collection. We introduce an optimization-based framework that jointly learns a small set of synergies and their sparse activation coefficients. The formulation enforces group sparsity for synergy selection and element-wise sparsity for activation timing. We develop an alternating minimization method in which coefficient updates decouple across tasks and synergy updates reduce to regularized least-squares problems. Our approach requires only a single data set, and simulations show accurate velocity reconstruction with compact, interpretable synergies.