  Complex, oscillatory data arises from a large variety of biological,
physical, and social systems. However, the inherent oscillation and ubiquitous
noise pose great challenges to current methodology such as linear and nonlinear
time series analysis. We exploit the state of the art technology in pattern
recognition and specifically, dimensionality reduction techniques, and propose
to rebuild the dynamics accurately on the cycle scale. This is achieved by
deriving a compact representation of the cycles through global optimization,
which effectively preserves the topology of the cycles that are embedded in a
high dimensional Euclidian space. Our approach demonstrates a clear success in
capturing the intrinsic dynamics and the subtle synchrony pattern from
uni/bivariate oscillatory data over traditional methods. Application to the
human locomotion data reveals important dynamical information which allows for
a clinically promising discrimination between healthy subjects and those with
neural pathology. Our results also provide fundamental implications for
understanding the neuromuscular control of human walking.
