Akademik Veri Yönetim Sistemi
TURKISH JOURNAL OF ELECTRICAL ENGINEERING AND COMPUTER SCIENCES, cilt.18, ss.23-30, 2010 (SCI-Expanded)
https://journals.tubitak.gov.tr/elektrik/vol18/iss1/2/
ABSTRACT: In the present study, a step-wise least square estimation algorithm (SLSA), unplemented in a Matlab package called as A Rfit, has been newly applied to clinical data for estimation of the accurate Auto-Regressive (AR) model orders of both normal and ietal EEG series where the power spectral density (PSD) estimations are provided by the Burg Method. The ARfit module is found to be useful in comparison to a large variety of traditional methods such as Forward Prediction Error (FPE), Akaike's Information Criteria (AIC), Minimum Description Lenght (MDL), and Criterion of Autoregression Transfer function (CAT) for EEG discrimination.
According
to tests, the FPE, AIC and CAT give the identical orders for both normal and
epileptic series whereas the MDL produces lower orders. Considering the
resulting PSD estimations, it can be said that the most descriptive orders are
provided by the SLSA. In conclusion, the SLSA can mark the seizure, since the
estimated AR model orders meet the EEG complexity/regularity such that the low
orders indicate an increase of EEG regularity in seizure. Then, the SLSA is
proposed to select the accurate AR orders of long EEG series in diagnose for
many possible future applications. The SLSA implemented by ARfit module is
found to be superior to traditional methods since it is not heuristic and it is
less computational complex. In addition, the more reasonable orders can be
provided by the SLSA.
Key Words: EEG, seizure, AR model, stepwise least square
algorithm
DISCUSSION
Both
cortical normal EEG measurements and intracortical epileptic EEG series, in
addition to intracortical ictal records, are analyzed in the present study.
Several traditional methods and the ARfit are implemented in Matlab to estimate
the optimum AR model orders of these diagnostic records. Among them, the ARfit
algorithm is found to be reliable and superior.
In literature, it was stated that the changes on the time series components such as oscillation periods and damping times can be characterized by MVAR models with respect to their SVD pairs [14]. Then, the ARfit module is developed to detect these changes. The current results show that the electrophysiological variations on EEG series can also be identified by using the ARfit. In other words, the meaningful sharp oscillations in EEG can be detected owing to the implementation of the ARfit module. Moreover, neither spurious peaks in the spectrum (in case of too high order), nor loss of spectral detail (in case of excessively low order) are encountered in the assessment of the ARfit. Also, regarding as the PSD estimations, it can be said that the useful AR model orders can also be estimated by using the algorithms of FPE, AIC and CAT. Nevertheless, FPE, AIC and CAT are known to be heuristic and more subjective choices in many applications [21]. However, the ARfit is not heuristic and it is considerable less computational complex such that the optimum model can be estimated about pmax −pmin +1 times faster than with those traditional algorithms that require pmax − pmin + 1 separate QR factorizations. The other criterion so called the MDL can not produce the adequate orders. In selecting of AR model order, the methods of FPE and AIC minimize the average error variance for a one-step and an information theoretical function, respectively [21]. The methods of FPE and AIC do not yield consistent estimates of the model order as the length of the time series increases whereas both are asymptotically equivalent [21]. The MDLcriterion, also called the Bayesian information criterion, uses a penalty function which provides consistent estimation of the model order [22]. In the ARfit module, the both the effect of rounding errors and data errors are minimized in the SLSA in association with determined approximate confidence interval [16]. The SLSA is stated as a numerically stable procedure in reference [23]. The using of the SLSA provides to obtain a more reliable residual noise variance. In fact, ARfit solves a regularized estimation problem with respect to an ill-conditioned moment matrix weighted with a regularization parameter. In summary, ARfit module is proposed as very useful, fast and efficient tool in brain activities to estimate a reliable AR model order. The results show that the estimated AR model orders can be used as markers to support the clinical findings in diagnose when ARfit is used.