### Original Research ARTICLE

However, the choice Unlike the Fourier transform, in which basis functions are of good mother wavelet is essential to achieve good results. Bandarabadi, C. Teixeira and A. Dourado are with the Centre for for a given signal. A mother wavelet is simply a wavy function Coimbra, Portugal, Wavelet transform is in fact a measure of C. Genetic Algorithm similarity between a signal and basis functions mother Genetic Algorithm GA is one of the commonly used wavelets.

Here similarity means the analogy between approaches in optimization problems, introduced by John frequency contents. In other words, wavelet coefficients Holland [12].

Crossover and fitness factor are the two indicate the closeness of signal to the wavelet in the desired characteristics of the GA algorithm having major impact the scale. Thus, if the desired signal has a major component in resulting outcome. In contrast, mutation plays a less the frequency corresponding to the scale under analysis, the important role.

Crossover determines the way through which scaled wavelet will be similar to that signal. Therefore the pairs of parents are mixed to generate new off-springs. In coefficient of the wavelet transform calculated for this scale this work the scattered crossover [13] is employed. On the would have a rather large value. Adaptive Feasible Compactly supported orthogonal wavelets have found mutation function embedded in the Matlab toolbox is used in common applications in various signal processing problems.

The population size is which have been widely used by research community.

## Optimization algorithms, an effective tool for the design of digital filters; a review

The dependent on the number of variables to be optimized as following parametric equations introduced in [10], are used well as the range of the changes of these variables. In our for building length-8 compactly supported scaling functions study, population size of chromosomes is selected to of orthogonal mother wavelets: allow a sufficiently large coverage of the search space. The fitness function drives the population toward better solutions [14]. So, the definition of a good fitness function that rewards the right population of individuals is the most important stage in optimizing a wavelet using genetic 1 algorithms.

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As soon as a wavelet is designed, the performance of the wavelet should be evaluated. One has to increase the classification performance to achieve better predictions. On the Thus one has three degrees of freedom to select a wavelet. Although the choice of the three parameters can be done freely, yet only some optimized sets of these parameters exist for specific applications and should be found. To carry 3 out this, an optimization problem has to be formulated and solved. Considering the very large search space of this The criterion PER can achieve better results compared to optimization problem, not every search method can be pure error rate, as it provides more details about the effectively employed.

In such cases, particular search separability of features in the feature space.

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In classifiers because they are considered to have the best the next GA is presented to obtain the optimized parameters. SVM classifiers in their simplest form use linear boundaries to classify two sets of data. To classify datasets with nonlinear boundaries, SVM Apply the Calculate the Train the SVM designed wavelet employ a kernel function to transform the nonlinear energy of signal using trining on the EEG in each sub-band samples boundary into a linear one.

Block Diagram of Fitness Function. Seizures Sampling Rate Rec. Time hours of the margin width and the minimization of the number of misclassified samples in the training set [16]. Also, the 1 6 Hz These two parameters are coded in the 3 5 Hz 35 h chromosomes of the GA population, and are optimized 4 9 Hz The F.

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Proposed Algorithm selected patients had a total of 24 epileptic seizures. For each Initially, Alpha, Beta and Gamma parameters are patient half of the seizures were chosen for wavelet design. The fourth parameter Theta is also Preictal periods are the time interval from 10 minutes to 1 calculated by solving the equation 2 , and employing minute before every seizure. These four parameters are then fed into the the interval starting at 90 minutes before every seizure and parameterized wavelet equations to obtain the scaling ending at 30 minutes after that same seizure was selected.

Sampling rates of The designed wavelets are applied to the raw EEG these EEG recording were Hz for two first patients, segments of both inter-ictal and preictal classes to Hz for the third one and Hz for the last one. Before decompose every segment into its corresponding sub-bands. During every 6-level SVMs are trained in a part of the data and tested in a decomposition iteration, signals are decomposed to obtain different one.

Finally, the PER of the classification, i. We also optimized the parameters of the SVM classifier The optimal wavelets were then computed for each patient inside the fitness function to find the best results that could Table II and applied to the respective one channel EEG be achieved with the designed wavelet. The classification results achieved are presented in algorithm converges to an optimized solution. This criterion is considered by some authors to database [19] with long-term continuous multichannel EEG be superior to the error rate criterion, to measure the quality recordings were used to evaluate the proposed method of a classification algorithm [20].

## Matlab Toolboxes

All patients had focal seizures. Dourado, R. Martins, J. Schelter, M. Winterhalder, T. Maiwald, A. Brandt, A. Schad, A. Le Van Quyen, J. Martinerie, M. Baulac, and F. Direito, A. Dourado, M. Vieira, and F. Mirowski, Y. Lecun, D. Madhavan, and R. Kuzniecky, Chisci, A. Mavino, G.

## Genetic algorithm wavelet design for signal classification - IEEE Journals & Magazine

Perferi, M. Sciandrone, C. Anile, G. The experiments showed that the nearest feature line NFL was most appropriate, considering its accuracy, the amount of information variance needed and the number of distance calculations. Fuentes proposed a face recognition method divided into two stages: feature extraction by discrete wavelet transform DWT reducing image dimensionality and classification of feature vectors through a multilayer perceptron NN.

The latter type of network was able to solve highly nonlinear problems and enabled non-parametric classification of facial features.

The feature vectors extracted by DWT were suitable for face recognition. Daubechies wavelet filters of order 3 and order 12 Symlet had the highest recognition rates.

Recent research has applied hybrid algorithms combining several intelligent techniques to improve pattern recognition. Umamaheswari proposed using GA and NN to detect human faces and locate eyes in real time. The hybrid algorithm focusing on face recognition was more efficient than current digital image processing techniques, such as wavelets. Jeong et al. The method was for classifying defects in steel from images to improve quality inspection system performance.

The above results have shown that using intelligent algorithms for pattern recognition has led to better classification performance.