## 3 Methodology
### Feature Selection  
Feature selection plays a crucial role in enhancing classification performance. Often characterized as an NP-hard combinatorial problem due to the exponential growth of potential feature subsets, it requires careful selection of a significant subset for optimal model building. Relying on independent features is crucial for successful performance in statistical techniques. Therefore, selecting informative and non-redundant features becomes the primary goal of feature selection algorithms [24]. Feature selection is a commonly used technique to reduce the dimensionality of a dataset. It involves four main steps: generating a feature subset, evaluating it, checking termination conditions, and validating results. Feature selection methods can be supervised, unsupervised, or semi-supervised. Categorized by selection strategy, feature selection methods fall into three main types: filter, wrapper, and embedded. Figure 1: Standard 10–20 EEG setup that consists of 19 channels. Figure 2: Topographical comparison of mean power spectral density (PSD) across frequency bands in healthy and depressed groups. Filter methods rely on intrinsic data properties, independent of any learning algorithm. They employ ranking and scoring techniques to select features based on criteria like discriminative power or correlation with the target variable. Filter methods are fast and flexible but may not be optimal for specific algorithms. Wrapper methods use prediction models to thoroughly search for the best subsets of predictors. They iteratively refine the selection based on the model's performance, ensuring that chosen features optimize prediction. While effective, wrapper methods are computationally intensive due to the large search space. Embedded methods strike a balance between filter and wrapper methods by integrating feature selection into the algorithm's training process. It balances the speed of filter methods with the accuracy of wrappers [25; 26]. This section presents a comparative analysis of established feature selection techniques frequently utilized in the domains of emotion recognition and depression detection using EEG signals. Selecting features is a crucial aspect of designing expert systems, particularly in supervised learning. The processed dataset comprises 1140 candidate features, 114 PSD and 1026 FC, as follows. Features were extracted from each frequency band individually, including delta, theta, alpha, beta, high beta, and gamma. Additionally, features were extracted from all six bands combined. Demographic and cognitive factors such as age, sex, education, and IQ were considered as additional features. The number of features used in the models ranged from 19-channel PSD in the delta band to 1140 [(19-channel PSD + 171 pair FC) \(\times\) all six bands]. This wide range reflects the flexibility in feature selection for EEG-based classification. Various research methodologies have explored training and testing models using combinations of PSD bands and functional connectivity (FC) features in EEG-based machine learning applications, such as Delta PSD + FC. Notably, performance outcomes are often superior when features are selected from both PSD and FC [29]. Combining PSD and FC provides a more comprehensive representation of brain activity. While PSD measures the intensity of brain oscillations, FC reveals connectivity between brain regions. This dual approach enhances the model's ability to differentiate between depressed and non-depressed states. In this study, six feature selection approaches were examined: (1) Elastic Net, (2) Mutual Information (MI), (3) Chi-Square, (4) Forward Feature Selection with Stochastic Gradient Descent (FFS-SGD), (5) Support Vector Machine-based Recursive Feature Elimination (SVM-RFE), and (6) Minimal-Redundancy-Maximal-Relevance (mRMR). Table 1 summarizes the feature selection methods used in this study, categorizing them into filter, wrapper, and embedded approaches based on their underlying techniques.