Filtering noise from time series by means of elastic wave propagation and flux-corrected transport in a discrete medium

We propose an efficient nonparametric method, named FEFCT, to eliminate noise from time-series data. We analyze noised time series data as a discrete wave packet that travels in one-dimensional finite-element grids discretized from a one-dimensional elastic medium. Then the techniques of flux-corrected transport are applied to filter the signal. The FEFCT is fast, accurate and performs well without Gaussian distribution assumption of noise. More importantly, when FEFCT is applied to infer regulatory network from human cell cycle data, it dramatically improves the association between genes, indicating FEFCT has captured the real signal in the complex biological system. Including but not limited to gene expression data, FEFCT can be easily extended to any other types of time-series data, which will be extremely important in the era of big data.