A Nonparametric Frequency Domain EM Algorithm for Time Series Classification with Applications to Spike Sorting and Macro-Economics

TL;DR

This paper introduces a nonparametric frequency domain EM algorithm for classifying time series based on their spectral properties, applicable to non-stationary and stationary signals, demonstrated in neural spike sorting and socio-economic data.

Contribution

It presents a novel frequency domain EM algorithm that classifies time series without assuming parametric models, suitable for diverse dynamic structures.

Findings

Effective in classifying neural spike data

Applicable to socio-economic time series

Robust to non-stationary signals

Abstract

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.