Defining gait patterns using Parallel Factor 2 (PARAFAC2): A new analysis of previously published data

Abstract Three-dimensional gait analysis (3D–GA) is commonly used to answer clinical questions of the form “which joints and what variables are most affected during when”. When studying high-dimensional datasets, traditional dimension reduction methods (e.g. principal components analysis) require “data flattening”, which may make the ensuing solutions difficult to interpret. The aim of the present study is to present a case study of how a multi-dimensional dimension reduction technique, Parallel Factor 2 (PARAFAC2), provides a clinically interpretable set of solutions to typical biomechanical datasets where different variables are collected during walking and running. Three-dimensional kinematic and kinetic data used for the present analyses came from two publicly available datasets on walking (n = 33) and running (n = 28). For each dataset, a four-dimensional array was constructed as follows: Mode A was time normalized cycle points; mode B was the number of participants multiplied by the number of speed conditions tested; mode C was the number of joint degrees of freedom, and mode D was variable (angle, velocity, moment, power). Five factors for walking and four factors for running were extracted which explained 79.23% and 84.64% of their dataset’s variance. The factor which explains the greatest variance was swing-phase sagittal plane knee kinematics (walking), and kinematics and kinetics (running). Qualitatively, all extracted factors increased in magnitude with greater speed in both walking and running. This study is a proof of concept that PARAFAC2 is useful for performing dimension reduction and producing clinically interpretable solutions to guide clinical decision making.