# Hypergraph Analysis of Functional Brain Connectivity During Figurative Attention
## 4 Experimental Data Analysis
### Artifact Removal
The blink detection threshold (blink value trigger) was set at 97%, which means that any value above this threshold was recognized as a blink. The selection of the 97% activation threshold for blink detection was based on experimental analysis using data from 28 participants. During threshold optimization, lower values significantly increased the rate of false positives, compromising the integrity of the neuronal signal. The 97% threshold was identified as the optimal balance between sensitivity and specificity, allowing robust identification of ocular artifacts without affecting the underlying signal. The signal correlation was established at 70% relative to a predefined blink template. This algorithm enhances detection accuracy by ensuring that triggers are only activated for signals with a high morphological similarity to a characteristic blink pattern, thereby reducing the erroneous detection of other artifacts. Additionally, a visual analysis using back-projection (Inverse ICA) was implemented as a validation method. This technique allowed the eliminated components to be projected back into the original domain, facilitating a visual inspection of the processed data. This procedure confirmed that ocular artifact suppression was performed selectively, preserving relevant neuronal activity while minimizing EEG signal distortion. These values were experimentally determined by considering their influence on attenuating the signal of interest in the spectral regions of \(f_{1}\) and \(f_{2}\) in the occipital lobes (O1, Oz, O2 channels). Lastly, we conducted ICA to find the optimal unmixing matrix to separate independent sources using statistical methods. To assess component independence, methods such as Maximum Negentropy, Kurtosis, Maximum Likelihood, and Mutual Information were employed. The optimization process for the optimal unmixing matrix ended when the maximum time independence of the components was achieved within a maximum number of steps or iterations. For this process, the extended nondeterministic INFOMAX algorithm with a maximum of 512 steps was selected as the optimal configuration. This ICA training method was adjusted after each convergence step to enhance signal separation. Convergence was deemed achieved when the algorithm reached a stable solution, favoring Independent Components (ICs) with Kurtosis (\(K\)) values greater than 0 (indicating components with a non-Gaussian distribution) and less than 0 for noise, such as electrical network noise. Following decomposition into ICs, quality control was performed by examining the number of steps used in decomposition of the ICs and comparing them with components initially flagged as possible ocular artifacts during visual inspection of the raw time series. As a final step, an inverse ICA of ICs and topographic retroprojection were performed to determine the brain lobes to which these possible signals corresponded. The analysis involved a comprehensive evaluation of the properties of IC, including their waveforms over time, energy, and kurtosis (\(K<0\), \(K=0\), \(K>0\)). It should be noted that ICA was performed on full-rank data without any preprocessing steps that could affect its rank [64].