A nonparametric frequency domain EM algorithm for time series classification with applications to spike sorting and macro-economics



I propose a frequency domain adaptation of the Expectation Maximization algorithm to group a family of time series in classes of similar dynamic structure. It does this by viewing the magnitude of the discrete Fourier transform of each signal (or power spectrum) as a probability density/mass function (pdf/pmf) on the unit circle: signals with similar dynamics have similar pdfs; distinct patterns have distinct pdfs. An advantage of this approach is that it does not rely on any parametric form of the dynamic structure, but can be used for nonparametric, robust and model-free classification. This new method works for non-stationary signals of similar shape as well as stationary signals with similar auto-correlation structure. Applications to neural spike sorting (non-stationary) and pattern recognition in socioeconomic time series (stationary) demonstrate the usefulness and wide applicability of the proposed method. © 2011 Wiley Periodicals, Inc. Statistical Analysis and Data Mining 4: 590–603, 2011