Singular value analysis through divided time-series data and its application to walking difficulty evaluation

Motion time-series data observed with various sensing systems are usually analyzed to extract embodied knowledge which is remembered by the human body and reflected by the dexterity in the motion of the body. A method based on singular value analysis through divided time-series data (SVA-DTS) is proposed for extracting features from time-series data. Matrices are composed from the subsets of time-series data and the left singular vectors of the matrices are extracted as the patterns of the motion and the singular values as a scalar, by which the corresponding left singular vectors affects the matrices. The SVA-DTS was applied to a walking difficulty evaluation experiment in which three levels of walking difficulty were simulated by restricting the right knee joint. The accelerations of the middles of the shanks and the back of the waist were measured. Singular values were calculated from the normalized acceleration time-series data with the SVA-DTS. The results showed that the first singular values inferred from the acceleration data of the right shank significantly related to the increase of the restriction to the right knee. The first singular values of the acceleration data of the right shank were suggested to be reliable criteria to evaluate walking difficulty. We visualize the first singular values in a 3D space to provide intuitive information about walking difficulty which can be used as a tool for evaluating walking difficulty.