# Automatic Identification of Children with ADHD from EEG Brain Waves
## 5 Feature Extraction and Feature Selection
\begin{table}
\begin{tabular}{c c c} \hline \hline
**Feature Name** & **Definition** & **Mathematical Description** \\ \hline Standard Deviation & It is a statistical feature that is a measure of how spread out the data is to the mean. & \(\sigma=\sqrt{\frac{\sum_{n=1}^{N}\left(x_{n}-\mu\right)^{2}}{N-1}}\) \\  & It is a statistical feature that is a measure of how spread out the data is to the mean. & \(x_{n}=n\)-th data sample, \(N=\) Total No. of samples, \(\mu=\) mean [33, 34] \\ RMS & RMS is the square root-mean-square value of a signal & \(RMS=\sqrt{\frac{\sum_{n=1}^{N}\left(x_{n}\right)^{2}}{N}}\) \\  & & \(x_{n}=n\)-th data sample, \(N=\) Total No. of samples [35] \\ Skewness & Skewness is the measure of the lack of symmetry from the mean of the dataset. & \(g=\frac{\sum_{n=1}^{N}\left(x_{n}-\mu\right)^{2}/N}{\sigma^{3}}\) \\  & Kurtosis is a measure of whether the data are heavy-tailed or light-tailed relative to a normal distribution. & \(k=\frac{\sum_{n=1}^{N}\left(x_{n}-\mu\right)^{4}/N}{\sigma^{4}}-3\) \\  & It is the variance of the amplitude of the & \(\text{Hjorth Activity}\) & \(\text{signal in a time function. Represent the signal power.}\) \\  & The mobility is the square root of the & \(H\text{jorth Mobility}\) & \(H\text{jorth Mobility}\) \\  & & \(x^{\prime}(t)=1\text{st}\) derivation of the amplitude of the signal & \(k=\frac{\sum_{n=1}^{N}\left(x_{n}-\mu\right)^{4}/N}{\sigma^{4}}-3\) \\  & It represents the change in frequency. It is & \(x_{n}=n\)-th data sample, \(N=\) Total No. of samples, \(\mu=\) mean [36] \\ Hjorth Complexity & H = var(x(t)) \\ Shannon’s Entropy & Shannon’s entropy measures the uncertainty/randomness in a dataset & \(H=\sum_{n=1}^{N}-(P_{n}\times logP_{n})\) \\ Spectral Entropy (SEN) & SEN is the normalized Shannon’s entropy & \(SEN=-\frac{\sum_{n=1}^{N-1}P_{1}logP_{2}P_{3}}{logN}\) \\ Power Spectral Density (PSD) & PSD of the signal describes the power present in the signal as a function of frequency [40] \\ Band Power & It measures both power and power spectral density in a specified channel bandwidth [41] \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Summary of EEG features employed in this study. Feature reduction is necessary to remove highly correlated features to avoid overfitting. We used PCA, an unsupervised method for dimension reduction, with 80%, 85%, 90%, and 95% explained variance. Explained variance is a statistical measure of how much variation in a dataset can be attributed to each of the principal components generated by the PCA method [45]. For the classification, we used a Gaussian support vector machine (SVM) classifier, a supervised machine learning algorithm. SVM algorithms use a set of mathematical functions that are defined as the kernel [46]. The function of the kernel is to take data input and transform it into the required form [47] so that a nonlinear decision surface can be transformed into a linear equation in a more dimensional space. It returns the dot product between two points in standard feature dimensions [48]. Gaussian is one of the kernel functions that is often used when there is no prior knowledge of a given dataset [49]. The Gaussian kernel can be expressed as \(k(x,y)=\exp\left(-\frac{||x-y||^{2}}{2\sigma^{2}}\right)\)[50]. Here, \(K\) is the kernel function, \(x\) and \(y\) are n-dimensional inputs. Before applying the classifier, the dataset was split for holdout and k-fold cross-validation. Cross-validation is a statistical method used to estimate the true generalization performance of machine learning models [51]. The holdout method is the simplest cross-validation and randomly splits the dataset. For this, the dataset was separated into three sets, \"training set,\" \"validation set,\" and \"test set.\" This method is good to use when the dataset is very large [52, 53]. From the present dataset, we took 70% for the training set, 15% for the test set, and 15% for the validation set.