A Frequency Domain EM Algorithm to Detect Similar Dynamics in Time Series with Applications to Spike Sorting and Macro-Economics

• Activity Number: 63
• Type: Topic Contributed
• Date/Time: Sunday, July 31, 2011 : 4:00 PM to 5:50 PM
• Sponsor: Section on Statistical Learning and Data Mining
• Author(s): Georg M. Goerg*+
• Companies: Carnegie Mellon University
• Keywords: statistical learning

Abstract

In this work I propose a frequency domain adaptation of the Expectation Maximization (EM) algorithm to separate a family of sequential observations in classes of similar dynamic structure, which can either mean non-stationary signals of similar shape, or stationary signals with similar auto-covariance function. It does this by viewing the magnitude of the discrete Fourier transform (DFT) of the signals (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. 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.