**5.3 Design of the neural classifier**

244 Recurrent Neural Networks and Soft Computing

the ECG has been investigated by a number of dedicated research workers (Gomis et al., 1997). The high frequency components are associated with late potentials (LPs) emanating from areas of delayed conduction and outlast the normal QRS period (80-100 msec). LPs are linked with malignant ventricular tachycardia (VT) after a myocardial infarction (dead zone or scar tissue in the ventricular muscle). The later is highly correlated with sudden cardiac death. Common methodology for detecting LPs in the time domain involves temporal scanning of the S-T region of the cardiac cycle and relies upon accurate identification of the QRS boundaries (Li et al., 1995). The detection problem is exacerbated by the fact that LP's are relatively weak (mv) and often below the noise floor. In the frequency domain, secondorder statistics can offer a limited success. The shapes of power spectra of normal and abnormal (malignant VT) ECGs are invariably broadly similar and without significant features above the noise floor, at approximately -70 dB (Rizk et al., 1998). LPs are essentially non-linear transient events (Gomis et al., 1997) and consequently interact with the inherent non-linearity of the cardiac waves as well as certain class of recursive non-linearly attributed

Previous work (Zgallai et al., 1997) showed that results obtained using HOS offer some empirical evidence that: (i) ECG signals contain intrinsic as well as quadratic and higherorder non- linearities, (ii) the QRS wave is predominantly linear non-Gaussian, the P and T waves are characterized by having quadratic and cubic non-linearities, (iii) the QRS wave can be totally resolved from the motion artifact in the bispectrum domains and (iv) disproportionately high-frequency non-linearity in the bicoherence squared is indicative of abnormality in an otherwise innocent looking ECG. However, non-linear filtering and a high resolution technique such as the spectral MUSIC incorporates an optimised window must be applied to a short duration data sample (without compromising the variance), prior to the application of HOS (Zgallai et al., 1997). Third-order Volterra filtering applied to raw data can be beneficial in isolating quadratic and cubic non-linearity in the higher-domains

The higher-order statistical features are selected and enhanced using sampled weights of a non-linear function based on a priori information about distinguished abnormality signatures in the higher domains. The function is modified adaptively during the training of the neural network which employs ten 1-d cumulants every 1000 or less cycles per patient. After this the updated version of the function parameters are fixed over the next 1000 cardiac cycles. Subsequently, a simple neural network classifier based on a modified version (Jacobs, 1988, and Hush and Salas, 1988) of the back-propagation algorithms performs accurate LPs and even ischemic ECG classification (Zgallai, 2011 a, Zgallai, 2011 b, and

The experimental setup consists of an ECG monitor, interface card and a workstation. Raw ECG data are measured using three orthogonal surface electrodes, sampled at 500 Hz and fed to the computer which performs the following operations. Accurate on-line QRS detection. This involves Volterra whitening filters in the time domain or / and the highresolution spectral MUSIC in the frequency domain. Positions of ECG peaks are pinpointed in the time domain. The MUSIC algorithm incorporates two sliding sets of three overlapping Kaiser windows and adaptive thresholding operations which not only

to external factors such as motion artefact (Zgallai et al., 1997).

**5.2 Higher-order statistics feature selection and enhancement** 

(Zgallai et al., 2007).

Zgallai, 2011 c).

Fig. 5.2 shows the network preceded by a preprocessing unit which performs the task of determining a set of meaningful and representative features in the HOS domains. A sigmoid logistic function is used to describe the input-output relation of the non-linear device. The neural network is designed to classify two classes; normal and abnormal third-order cumulants. The combined use of skewness and kurtosis can provide more accuracy in difficult cases.The utility of the diagonal slice of the fourth-order cumulant can be of more help when used in the desired response for the third output. The use of higher than the third-order statistics adds more complexity to the network.
