## 3 Materials and Methods
### Parameter Optimization and Fine-Tuning Process
As a third step, a common average reference montage was used, with its filtered axis set to 1 and the dimension parameter enabled. This configuration guarantees that all channels share a uniform reference, and that the data's original structure remains maintained. Fourth, a total of 24 CSP filters spanned each class and temporal segment of interest. We selected a Butterworth filter (order 2) to target a maximum frequency of 40 Hz. The filter bandwidths (_bw_) were defined by the list [2; 4; 8; 16; 32] Hz--a set chosen to isolate different EEG bands, such as alpha and beta. In addition, we adapted the start and end times for processing by multiplying them with the sampling rate (250 Hz), thus enabling CSP to extract features within multiple overlapping time frames. Following these steps, we optimized additional fractal dimension feature extraction parameters, such as Higuchi, box-counting, correlation dimension, multifractal detrended fluctuation analysis (MFDFA), and detrended fluctuation analysis (DFA). For the Higuchi feature set, the maximum number of intervals (kmax) was 10, indicating the scaling factor used in creating subsequences. For the box-counting approach, we used 10 different scaling levels, with minimum and maximum box sizes set to 1 and 874, respectively. In the correlation dimension method, we selected an embedding dimension of 5, a delay of 5, and a set of radii defined by \(\text{logspace}(-3,0,30)\). Additionally, a small epsilon value of \(1\times 10^{-12}\) was included to safeguard the numerical stability. As for MFDFA, the chosen \(q\)-values ranged from \(-5\) to 5, while the minimum and maximum scales were set to 4 and 437, respectively, with a scaling ration of 2.0. Finally, for DFA, we used the same minimum and maximum scales (4 and 437) and scale ration (2.0), ensuring a uniform multi-scale analysis across these fractal dimension estimators. Finally, we fine-tuned the parameters of five classifiers: LinearSVM, CART, GSVM, SVM with a polynomial kernel, and SGD and validated their performance with 5-fold cross-validation. LinearSVM was configured with C = 0.1, intercept_scaling = 1, hinge loss, a limit of 1000 iterations, a one-vs-rest (ovr) multi-class strategy, an L2 penalty, random_state = 1, and tol = 0.00001. GSVM employed C = 20, an RBF kernel, a kernel degree of 10, \(\gamma\) = auto, coeff = 0.0, tol = 0.001, a cache size of 10,000, max_iter = \(-1\), and an ovr decision function. \begin{table}
\begin{tabular}{c c c} \hline
**Parameter** & **Related to** & **Value** \\ \hline gsvm\_coef0 & GSVM & 0.0 \\ gwvm\_tol & GSVM & 0.001 \\ gsvm\_cache\_size & GSVM & 10,000 \\ gsvm\_max\_iter & GSVM & \(-1\) \\ gsvm\_decision\_fx & GSVM & ovr \\ sgd\_loss & SGD & hinge \\ sgd\_penalty & SGD & 12 \\ sgd\_max\_iter & SGD & 1000 \\ sgd\_tol & SGD & 0.001 \\ sgd\_alpha & SGD & 0.1 \\ sgd\_random\_state & SGD & 1 \\ fs & BCI IV 2a Set Sampling Frequency & 250.0 \\ no\_channels & No. of EEG Channels & 22 \\ no\_subjects & No. of Subjects & 9 \\ no\_classes & No. of Classes & 4 \\ no\_splits & No. of Folds in Cross-Validation & 5 \\ \hline \end{tabular}
\end{table} 
Table 2: _Cont._For CART, we set a max_depth = 10, random_state = 1, the Gini criterion, a best splitter, min_samples_split = 2, and min_samples_leaf = 1. The SGD classifier used a hinge loss, an L2 penalty, max_iter = 1000, tol = 0.001, \(\alpha\) = 0.1, and random_state = 1. We ended with the polynomial kernel SVM that adopted a poly kernel (degree of 10), \(\gamma\) = auto, coef0 = 0.0, tol = 0.001, a cache size of 10,000, max_iter = \(-\)1, and an ovr decision scheme.