Temporal dynamics of inter-limb coordination in ice climbing revealed through change-point analysis of the geodesic mean of circular data

This study examined the temporal dynamics of the inter-limb angles of skilled and less skilled ice climbers to determine how they explored ice fall properties to adapt their coordination patterns during performance. We observed two circular time series corresponding to the upper- and lower-limbs of seven expert and eight inexperienced ice climbers. We analyzed these data through a multiple change-point analysis of the geodesic (or Fréchet) mean on the circle. Guided by the nature of the geodesic mean obtained by an optimization procedure, we extended the filtered derivative method, known to be computationally very cheap and fast, to circular data. Local estimation of the variability was assessed through the number of change-points computed via the filtered derivatives with p-value method for the time series and integrated squared error (ISE). Results of this change-point analysis did not reveal significant differences of the number of change-points between groups but indicated higher ISE that supported the existence of plateaux for beginners. These results emphasized higher local variability of limb angles for experts than for beginners suggesting greater dependence on the properties of the performance environment and adaptive behaviors in the former. Conversely, the lower local variance of limb angles assessed in beginners may reflect their independence of the environmental constraints, as they focused mainly on controlling body equilibrium.