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

By Georg M. Goerg

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.Comment: Winner of the JSM 2011 student paper competition in "Statistical Learning and Data Mining (SAM)"; 34 pages. Accepted for publication in SA

Topics: Statistics - Machine Learning, Physics - Data Analysis, Statistics and Probability, Statistics - Applications, Statistics - Methodology
Year: 2011
OAI identifier: oai:arXiv.org:1103.3300
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