Bispectral-Based Methods for Clustering Nonlinear Time Series

• Activity Number: 578
• Type: Topic Contributed
• Date/Time: Wednesday, August 4, 2010 : 2:00 PM to 3:50 PM
• Sponsor: Section on Nonparametric Statistics
• Author(s): Jane L. Harvill*+ and Nalini Ravishanker and Bonnie Kathryn Ray
• Companies: Baylor University and University of Connecticut and IBM T.J. Watson Research Center
• Keywords: Nonlinear time series ; Bispectral density function ; Distance measures ; Clustering ; EEG data

Abstract

It is well-known that in general, second-order properties are insufficient for describing nonlinear time series. In particular, it is easily shown that the normalized bispectral density function is constant for a linear, Gaussian series, but typically not for nonlinear series. Furthermore different nonlinear time series models have different bispectral signatures. Based on these properties, we propose the use of various distance measures computed on the square modulus of the estimated normalized bispectrum as a means for clustering nonlinear series. In this presentation, we empirically investigate misclassification rates of the various distance measures. We then apply the methods to a set of EEG data for a single patient collected at six different locations in the brain during an epileptic seizure.