Wavelet first-order

A wavelet defined as above is called a first-order wavelet. From Eq. (21) we conclude that the extrema points of the first-order wavelet transform provide the position of the inflexion points of the scaled signal at any level of scale. Similarly, if i/ (f) = d it)/dt, then the zero crossings of the wavelet transform correspond to the inflexion points of the original signal smoothed (i.e., scaled) by the scaling function, tj/it) (Mallat, 1991). 

The combination of PCA and LDA is often applied, in particular for ill-posed data (data where the number of variables exceeds the number of objects), e.g. Ref. [46], One first extracts a certain number of principal components, deleting the higher-order ones and thereby reducing to some degree the noise and then carries out the LDA. One should however be careful not to eliminate too many PCs, since in this way information important for the discrimination might be lost. A method in which both are merged in one step and which sometimes yields better results than the two-step procedure is reflected discriminant analysis. The Fourier transform is also sometimes used [14], and this is also the case for the wavelet transform (see Chapter 40) [13,16]. In that case, the information is included in the first few Fourier coefficients or in a restricted number of wavelet coefficients. 

In the case of the Coifman function of order 30, as the analyzing wavelets W and 256 X 256 pixel image, the difference image D is decomposed to five wavelets levels. In Eq. (4), the first term W SoW is called Level 0 which shows the lowest space frequency, and the last term W S4W is called Level 4 which shows the highest space frequency. The low level indicates the whole information of D, and the high level indicates the peculiar information of D. The Fourier spectrum of the analyzing wavelets W is shown in Fig. 3. Each level operates as a kind of band pass filter. 

Trial to trial provides informative features that describe habituate response or non-habituate response. In order to extract the moment of the habituation presence, we further analyze the wavelet coherence results with novelty detection. We have observed in [5] that reduction of wavelet coherence (habituation) occurs after several trials after the experiment began. Therefore, we take these first q trials (training set) to train a classifier. This classifier is generated by all information of q trials and forms a hypothetical sphere with center c and radius K. To minimize this sphere so that the learning machine free from false negative errors, the problem is solved by... 

The EOG and EMG artifacts were removed before the EEG data was further processed. An automatic EEG artifact removal method that combines the Blind Source Separation method with the Wavelet method is used here. The EEG signals are first decomposed into independent components using the Second Order Blind Identification (SOBI)... 

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