Dynamics and Synchrony from Oscillatory Data via Dimension Reduction
  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. 
J. Zhang, K. Zhang, J. Feng, J. Sun, X. Xu, M. Small