Discriminative Ratio of Spectral Power and Relative Power Features Derived via Frequency-Domain Model Ratio with Application to Seizure Prediction

The ratio of spectral power in two different bands and relative band power have been shown to be sometimes more discriminative features than the spectral power in a specific band for binary classification of a time series for seizure prediction. However, why and which ratio of spectral power and relative power features are better discriminators than a band power have not been understood. While general answers to why and which are difficult, this paper partially addresses the answer to these questions. Using auto-regressive modeling, this paper, for the first time, theoretically explains that for high signal-to-noise ratio (SNR) cases, the ratio features may sometime amplify the discriminability of one of the two states in a time series, as compared with a band power. This paper, also for the first time, introduces a novel frequency-domain model ratio (FDMR) that can be used to select the two frequency bands. The FDMR computes the ratio of the frequency responses of the two auto-regressive model filters that correspond to two different states. It is shown that the ratio implicitly cancels the effect of change of variance of the white noise that is input to the auto-regressive model in a non-stationary environment for high SNR conditions. It is also shown that under certain sufficient but not necessary conditions, the ratio of the spectral power and the relative band power, i.e., the band power divided by the total power spectral density, can be better discriminators than band power. Synthesized data and scalp EEG data from the MIT Physionet for patient-specific seizure prediction are used to explain why the ratios of spectral power obtained by a ranking algorithm in the prior literature satisfy the sufficient conditions for amplification of the ratio feature derived in this paper.