Principal Motion Ellipsoids: Gait Variability Index Invariant With Gait Speed

The walking motion of an individual involves considerable variability. We develop a gait variability index that determines how and to what degree repeated human gait motions vary, based on generalized principal motion analysis (GPMA). Principal motion analysis (PMA) is an extension of principal component analysis and decomposes multivariate time-series data, such as human joint angles during walking, into a linear combination of several principal motion bases. The developed gait variability index is defined by the size of an ellipsoid referred to as a PM ellipsoid and approximates the distribution of repeated gait motions on the motion base space. We expand the method to compute PM ellipsoids using GPMA, which enables us to mask the effects of a certain factor affecting gait motion observed under multiple factors. We compute the principal motion bases invariant with the gait speed from the gait motions of nine participants at two speed levels, 3.5 and 4.0 km/h. The sizes of the PM ellipsoids computed using GPMA do not depend on the gait speed and exhibit good agreement with the MeanSD, i.e., a typical gait variability index with correlation coefficients greater than 0.87.