Abstract
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.
Highlights
T HERE is large variability in the walking motion of an individual
In this study, we developed a new index for gait variability using generalized principal motion analysis (GPMA), which is an extended Principal motion analysis (PMA) method, that can mask the effect of a certain factor for computing the principal motions
Using PMA and GPMA, we computed the PM ellipsoids of the walking motions recorded at two gait-speed levels
Summary
T HERE is large variability in the walking motion of an individual. For example, the gait of a human varies depending on the gait speed [1], [2] and step length [3], [4] during walking. The MeanSD [7] and maximum Lyapunov exponent [8] are the most popular indices for evaluating gait variability. Indices to represent gait variability are invaluable in enhancing commercial applications, such as walking aids, and in the clinical scenario [12], [13] where gait variability is an important characteristic of neurological disorders [14]. As these indices are represented by single scalar quantities, they are unsuitable for discussing the variation in walking motion, they are suitable for discussing the level of gait variability
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