Time Series Alignment with Gaussian Processes

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 typically obtained by repeated measurements of a biological, chemical or physical process. In time series alignment, we are required to estimate a common shape function, which describes a common structural patter shared among a set of time series, and time transformation functions, each of which represents time shifts involved in individual time series. In this paper, we introduce a generative model for time series data in which the common shape function and the time transformation functions are modeled nonparametrically using Gaussian processes and we develop an effective Markov Chain Monte Carlo algorithm, which realizes a nonparametric Bayesian approach to time series alignment. The effectiveness of our method is demonstrated in an experiment with synthetic data and an experiment with real time series data is also presented.