  I propose a frequency domain adaptation of the Expectation Maximization (EM)
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 (DFT) 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 non-parametric, 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 socio-economic time series (stationary) demonstrate the usefulness and wide
applicability of the proposed method.
