# An Ensemble Feature Selection Approach to Identify Relevant Features from EEG Signals
## 2 Materials and Methods  
### Dataset  
The EEG repository built in [21] contains 200 records from 200 patients that, given their structure, cannot be processed by machine learning algorithms. Each EEG record was acquired under the electrode positioning system 10-20, considering a sampling rate of 200 samples per second for 21 channels and an approximate duration of 30 min. The 200 EEG records were diagnosed by a pediatric neurologist with 20 years of experience reading this kind of exam. Besides, each EEG was decomposed channel by channel, and 672 segments diagnosed as abnormal were extracted and described using a set of feature extractors. Each segment had 200 samples. This same process was carried out for a set of 672 segments considered normal. Thus, the dataset was built with 142 features extracted from 1344 EEG segments. Since all the descriptors were applied to all the segments, the dataset did not contain columns with null data. The descriptors used to extract the features from the EEG signals are described below. * Basic Descriptors  
Statistical features allow summarizing the values that describe a segment of EEG signal in a single value. The measures of this type that will be applied in the construction of the dataset are min, max, mean, median, low median, high median, variance, and standard deviation. * Entropy  
Entropy is considered a family of statistical measures that quantify the variant complexity in a system. In this study, we evaluated three different ways of measuring Entropy:  
\[H_{\alpha}(\varphi)=\frac{1}{1-\alpha}\text{log}_{2}\bigg{\{}\frac{\sum_{k=1 }^{m}P_{k}^{\alpha}}{\sum_{k=1}^{n}Pk} \tag{1}\]  
\[\odot\]  
Approximate Entropy  
\[\text{ApEn}(m,r,N)=\varnothing^{m}(r)-\varnothing^{m+1}(r) \tag{2}\]  
\[\odot\]  
Renyi Entropy \[(x,m)=\text{SamEn}(x,m,r)+log(2r)\] (3)  
* Kurtosis and Skewness The skewness and kurtosis are higher-order statistical attributes of a time series. \[\odot\]  
Skewness represents the degree of distortion from the symmetrical bell curve or the normal distribution. In other words, the lack of symmetry in data distribution is measured by skewness. \[\odot\]  
Kurtosis measures the peakedness of the probability density function (PDF) of a time series. It is used to measure the outliers present in the distribution. * Energy  
The signal is viewed as a function of time, and energy represents its size. The energy can be measured in different ways, but the area under the curve is the most common measure to describe the size of a signal. It measures the signal strength, and this concept can be applied to any signal or vector. \[E_{x}=\int\limits_{-\infty}^{\infty}|\text{x}(t)|^{2}dt \tag{4}\]  
* Fractal Dimension--Higuchi  
The fractal dimension corresponds to a noninteger dimension of a geometric object. Based on this principle, fractal dimension analysis is used to analyze biomedical signals. In this approach, the waveform is considered a geometric figure [22]. \[D=\frac{d\text{log}(L(k))}{d\text{log}(k)} \tag{5}\]* Fractal Dimension--Petrosian This type of analysis provides a quick mechanism to calculate the fractal dimension bypassing the series in a binary sequence. For example, the following describes the equation that calculates the Petrosian fractal dimension [22]: \[F_{Petrosian}=\frac{log_{10}(n)}{log_{10}(n)+\log_{10}(\frac{n}{n+0.4N_{\Delta}})}\] (6)
* Hurst Exponent This exponent is a measure of the predictability of the signal. It is a scalar between 0 and 1 which measures long-range correlations of a time series [23]. * Zero-Crossing Rate The zero-crossing rate is a statistical feature that describes the number of times that a signal crosses the horizontal axis. * Hjort Parameters The Hjort parameters describe statistical properties in the time domain [12]. Usually, these are used to analyze electroencephalography signals. \(\circ\) Activity  
Activity, also known as the variance or mean power, measures the squared standard deviation of the amplitude.