## 5 Discussion  
In this section, we delve into this study's findings, offering a thorough interpretation of their implications and identifying potential directions for future research. During our previous research [36], the selection of the six distinct feature sets--statistical, wavelet analysis, Hjorth parameters, Higher-Order Spectra, fractal dimensions, and a combined multi-dimensional feature set--was motivated by their proven effectiveness in capturing different aspects of EEG signal complexity in prior emotion recognition research. Specifically, statistical features and wavelet analysis capture general signal trends and time-frequency characteristics, respectively; Hjorth parameters offer insights into activity, mobility, and complexity; Higher-Order Spectra provide information on signal non-linearity and interactions across frequencies; and fractal dimensions quantify complexity and self-similarly within EEG signals. Combining these diverse feature extraction techniques aimed to leverage complementary strengths, enhancing the overall disseminative power of the classification pipeline. This work expands on the existing research by integrating different fractal dimension (FD) combinations, including Katz, Petrosian, Higuchi, box-counting, DFA, MFDFA, and correlation dimension, into a single framework for motor imagery (MI) classification. As noted in the Introduction, FDs capture nonlinear characteristics in EEG data, potentially uncovering complex signal details that simpler features may miss. Our expanded set of FD methods reinforces the idea that combining distinct fractal measures enhances the representation of brain dynamics, thereby improving classification performance. Our results also show that LinearSVM repeatedly achieves the highest accuracy, followed by Gaussian SVM (GSVM) and SVM with a polynomial kernel (SVM Poly). In contrast, decision trees (CART) were found to underperform, likely due to overfitting on fractal dimension-based EEG signals. Adding stochastic gradient descent (SGD) provided a useful comparison against LinearSVM, demonstrating lower performance despite its effectiveness in dealing with high-dimensional data. These findings underscore the central role of the careful choice of machine learning models; even strong feature sets can yield weaker results without an appropriate classifier. The refinement of the Higuchi fractal dimension (HFD) function serves as an essential improvement to this study's methodology; it is addressed in the present study, ensuring \begin{table}
\begin{tabular}{c c c c c c c c c c c} \hline \hline
**Method** & **Year** & **A01** & **A02** & **A03** & **A04** & **A05** & **A06** & **A07** & **A08** & **A09** & **Mean** \\ \hline TSLDA & 2012 & 80.5 & 51.3 & 87.5 & 59.3 & 45.0 & 55.3 & 82.1 & 84.8 & 86.1 & 70.2 \\ Multi-Scale CSP & 2018 & 86.8 & 57.2 & 86.5 & 61.4 & 61.2 & 50.7 & 92.4 & 87.8 & 79.1 & 73.7 \\ Multi-Scale Riemannian & 2018 & 90.0 & 55.4 & 81.3 & 71.9 & 69.6 & 56.7 & 85.6 & 83.8 & 84.9 & 75.5 \\ HSS-ELM & 2019 & 81.1 & 49.9 & 78.0 & 63.3 & 44.0 & 49.4 & 81.1 & 81.5 & 81.4 & 67.8 \\ SineNet & 2021 & 75.2 & 39.5 & 79.4 & 49.1 & 62.7 & 39.3 & 64.4 & 74.9 & 64.1 & 63.1 \\ FBRTS & 2022 & 86.1 & 65.2 & 90.0 & 63.8 & 75.6 & 52.4 & 91.1 & 89.0 & 86.5 & 77.7 \\ TSFSCPS-GA & 2023 & 86.5 & 59.0 & 89.2 & 69.4 & 63.2 & 54.5 & 87.2 & 80.2 & 81.6 & 74.5 \\ IFNet & 2023 & 88.5 & 56.4 & 91.8 & 73.8 & 69.7 & 60.4 & 89.2 & 85.4 & 88.7 & 78.2 \\ TWBS & 2024 & 89.3 & 66.9 & 89.3 & 69.3 & 74.1 & 60.1 & 89.4 & 88.0 & 85.6 & 79.1 \\ KFD vs. PFD vs. HFD (Updated) & 2024 & 85.0 & 69.3 & 90.4 & 64.9 & 82.1 & 47.9 & 93.0 & 90.9 & 87.3 & 79.0 \\ KFD vs. BCFD vs. CDFD & 85.0 & 70.0 & 90.4 & 65.7 & 82.1 & 47.9 & 93.0 & 91.3 & 87.3 & **79.2** \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Comparative classification accuracy on Dataset 2a: our method vs. other approaches. that extracted fractal dimensions align with their expected mathematical properties.