Analyzing individual and group differences in multijoint multiwaveform gait data using the Parafac2 model

Locomotion research often involves analyzing multiwaveform data (e.g., velocities, accelerations, etc.) from various body locations (e.g., knees, ankles, etc.) of several subjects. Therefore, some multivariate technique such as principal component analysis is often used to examine interrelationships between the many correlated waveforms. Despite its extensive use in locomotion research, principal component analysis is for two-mode data, whereas locomotion data are typically collected in higher mode form. In this paper, we present the benefits of analyzing four-mode locomotion data (subjects × time × joints × waveforms) using the Parafac2 model, which is a component model designed for analyzing variation in multimode data. Using bilateral hip, knee, and ankle angular displacement, velocity, and acceleration waveforms, we demonstrate Parafac2's ability to produce interpretable components describing (i) the fundamental patterns of variation in lower limb angular kinematics during healthy walking and (ii) the fundamental differences between normal and atypical subjects' multijoint multiwaveform locomotive patterns. Also, we illustrate how Parafac2 makes it possible to determine which waveforms best characterize the individual and/or group differences captured by each component. Our results indicate that different waveforms should be used for different purposes, confirming the need for the holistic analysis of multijoint multiwaveform locomotion data, particularly when investigating atypical motion patterns.