Discriminant Analysis of Time Series in the Presence of Within-Group Spectral Variability

TL;DR

This paper introduces a novel discriminant analysis method for time series that accounts for within-group spectral variability by modeling transfer functions as stochastic variables, improving group separation.

Contribution

It develops a new model and discriminant analysis approach for time series that incorporates within-group spectral variability, which was lacking in prior methods.

Findings

Effective in classifying new observations with within-group variability

Consistent estimation through simple discriminant analysis of cepstral coefficients

Empirical validation via simulation and gait variability analysis

Abstract

Many studies record replicated time series epochs from different groups with the goal of using frequency domain properties to discriminate between the groups. In many applications, there exists variation in cyclical patterns from time series in the same group. Although a number of frequency domain methods for the discriminant analysis of time series have been explored, there is a dearth of models and methods that account for within-group spectral variability. This article proposes a model for groups of time series in which transfer functions are modeled as stochastic variables that can account for both between-group and within-group differences in spectra that are identified from individual replicates. An ensuing discriminant analysis of stochastic cepstra under this model is developed to obtain parsimonious measures of relative power that optimally separate groups in the presence of within-group spectral variability. The approach possess favorable properties in classifying new observations and can be consistently estimated through a simple discriminant analysis of a finite number of estimated cepstral coefficients. Benefits in accounting for within-group spectral variability are empirically illustrated in a simulation study and through an analysis of gait variability.