A nonparametric Bayesian approach to time series alignment

We propose a nonparametric Bayesian approach to time series alignment. Time series alignment is a technique often required when we analyze a set of time series in which there exists a typical structural pattern common to all the time series. Such a set of time series is usually obtained by repeated measurements of a biological, chemical or physical process. In time series alignment, we required to estimate a common shape function, which describes a common structural patter shared among a set of time series, and time transformation (time warping) functions, each of which represents time shifts involved in individual time series. In our approach, the common shape function and the time transformation functions are modeled nonparametrically by using Gaussian process priors. We introduce an effective Markov Chain Monte Carlo algorithm and it enables a fully Bayesian analysis of time series alignment.