Generalized feature extraction for time-varying autoregressive models

In this paper, a feature extraction scheme for a general type of nonstationary time series is described. A non-stationary time series is one in which the statistics of the process are a function of time; this time dependency makes it impossible to utilize standard globally derived statistical attributes such as autocorrelations, partial correlations, and higher order moments as features. In order to overcome this difficulty, the time series vectors are considered within a finite-time interval and are modeled as time-varying autoregressive (AR) processes. The AR coefficients that characterize the process are functions of time that may be represented by a family of basis vectors. A novel Bayesian formulation is developed that allows the model order of a time-varying AR process as well as the form of the family of basis vectors used in the representation of each of the AR coefficients to be determined. The corresponding basis coefficients are then invariant over the time window and, since they directly relate to the time-varying AR coefficients, are suitable features for discrimination. Results illustrate the effectiveness of the method