From Learning Gait Signatures of Many Individuals to Reconstructing Gait Dynamics of One Single Individual - Hsieh, Fushing; Wang, Xiaodong (Frontiers in Applied Mathematics and Statistics, 2020)
Based on the same databases, we computationally address two seemingly highly related, in fact drastically distinct, questions via computational data-driven algorithms: 1) how to precisely achieve the big task of differentiating gait signatures of many individuals. 2) how to reconstruct an individual’s complex gait dynamics in full. Our brains can ``effortlessly’’ resolve the first question, but will definitely fail in the second one. Since many fine temporal scale gait patterns surely escape our eyes. Based on accelerometers' 3D gait time series databases, we link the answers toward both questions via multiscale structural dependency within gait dynamics of our musculoskeletal system. Two types of dependency manifestations are explored. We first develop simple algorithmic computing called Principle System-State Analysis (PSSA) for the coarse dependency in implicit forms. PSSA is shown to be able to efficiently classifying among many subjects. We then develop a multiscale Local-1st-Global-2nd (L1G2) Coding Algorithm and a landmark computing algorithm. With both algorithms, we can precisely dissect rhythmic gait cycles, and then decompose each cycle into a series of cyclic gait phases. With proper color-coding and stacking, we reconstruct and represent an individual’s gait dynamics via a 3D cylinder to collectively reveal universal deterministic and stochastic structural patterns on centisecond (10 milliseconds) scale across all rhythmic cycles. This 3D cylinder can serve as ``passtensor'' for authentication purposes related to clinical diagnoses and cybersecurity.