# An Ensemble Feature Selection Approach to Identify Relevant Features from EEG Signals
## 2 Materials and Methods
### Dataset
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\(\circ\) Mobility Mobility measures the standard deviation of the slope concerning the standard deviation of the amplitude. \[\odot\]1  
\(\circ\) Complexity This parameter is associated with the wave shape. \[\odot\]2
* Discrete Wavelet Transform The discrete wavelet transform allows the analysis of a signal in a specific segment. The procedure consists of expressing a continuous signal to expand coefficients of the internal product between the particular segment and a mother wavelet function. As a result, the wavelet transform's discretization changes from a continuous mapping to a finite set of values. This process is done by changing the integral in the definition by an approximation with summations. Hence, the discretization represents the signal in terms of elementary functions accompanied by coefficients. \[\odot\]3  
The mother wavelet functions include a set of scale functions. The parent functions represent the fine details of the signal, while the scale functions calculate an approximation. Thus, considering the above, a function or signal can be described as a summation of wavelet functions and scale functions. \[\odot\]4A signal can be decomposed into various levels from the time domain to the frequency domain in wavelet analysis. The decomposition is done from the detail coefficients as well as the approximation coefficients. Figure 1 describes the different encoding paths for n levels of decomposition. The upper level of the tree represents the temporal representation. As the decomposition levels increase, an increase in the compensation in the time-frequency resolution is obtained. Finally, the last level of the tree describes the representation of the signal frequency. * Fast Fourier Transform  
The fast Fourier transform computes a short version of the discrete Fourier transform of a signal by decomposing the original signal into different frequencies (smaller transforms). The decomposed signals are used to calculate the resulting transform signal. FFT is used to convert a signal from the time domain to a representation in the frequency domain or vice versa. Features extracted from the fast Fourier transform calculation are as follows:  
* Spectral Centroid  
The spectral centroid is a statistical measure used to describe the spectrum's shape in digital signal processing. This centroid defines the spectrum as a probability distribution and represents where the center of mass of the spectrum is located. \[\odot\]5  
* Spectral Flatness  
The Spectral Flatness defines the ratio of the geometric mean to the arithmetic mean of a power spectrum. \[\odot\]6  
* Crest Factor  
The crest factor defines how extreme the peaks are in a signal. \[\odot\]7  
* Matched Filter  
Matched filters are basic signal analysis tools used to extract known waveforms from a signal that has been contaminated with noise. For example, in the context of the detection of epileptic spikes, given a signal \(x(t)\) that describes the brain activity (EEG), the  
\[\odot\]8 Wavelet decomposition. matched filter \(h(t)\) seeks a well-known pattern of epilepsy \(s(t)\); then, if the signal contains an epileptiform pattern, the signal is described by the brain activity \(n(t)\) with the abnormality \(s(t)\) generating \(x(t)=s(t)+n(t)\). Otherwise, the signal only contains the normal brain activity \(x(t)=n(t)\). Considering the above, 21 descriptors were applied on the normal and abnormal EEG segments, and their wavelet coefficients (5) were generated from the original segments generating 126 features. The 21 descriptors are min, max, mean, median, high median, low median, variance, standard deviation, Shannon entropy, approximate entropy, Renyi entropy, kurtosis, skewness, energy, Higuchi fractal dimension, Petrosian fractal dimension, Hurst exponent, zero-crossing rate, Hjort activity, Hjort mobility, and Hjort complexity.