# Multiple Kernel Stein Spatial Patterns for the Multiclass Discrimination of Motor Imagery Tasks
## 4 Results  
### Performance Results  
Figure 3 presents the subject-wise grid search results for tuning the number of spatial filters. Tuning curves evidence that performance decreases for either a very low or very high number of components. In the first case, the resulting model misses class separability patterns, due to the low flexibility in the lowest dimensional manifolds. In the second case, the methodology overfits the training data, since the component space becomes sparse, then drops the validation performance. Since four to eight components improve the classification performance in comparison to the input channel space, the proposed methodology reduces Riemmannian manifold dimension while enhancing MI discrimination. Table 1 presents the mean kappa value using different methods tested in the BCICIV2a dataset, with the highest kappa value in bold for each subject. The last column holds the \(p\)-value for a paired \(t\)-test between the proposed and each compared approaches. Subjects are sorted according the score attained by the challenge winner. Note that MKSSP outperforms other approaches at the worst performing subjects (namely S06, S05, S02, and S01). Specifically, the proposal favors the most the subject S05, as the kappa score raises between 5% and 57%. Despite MKSSP performs at subjects S09, S03, S08, and S07, the best approach on such subjects are considerably biased towards them. Furthermore, MKSSP reaches the highest average kappa score of 0.82, with significant differences in most of the comparisons. Hence, the proposed methodology collects and combines discriminative features from different spaces in a single representation, enhancing the separability of different mental tasks. \begin{table}
\begin{tabular}{c c c c c c c c c c c c} \hline \hline
**Approach** & **S06** & **S05** & **S02** & **S04** & **S01** & **S09** & **S03** & **S08** & **S07** & \(\kappa\) & \(p\)**-Value** \\ \hline Challenge winner [26] & 0.27 & 0.40 & 0.42 & 0.48 & 0.68 & 0.61 & 0.75 & 0.75 & 0.77 & 0.57 \(\pm\) 0.17 & _0.0002_ \\ SUSS-SRKDA [27] & 0.35 & 0.56 & 0.51 & 0.68 & 0.83 & 0.75 & 0.88 & 0.84 & 0.90 & 0.70 \(\pm\) 0.18 & _0.0179_ \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Mean kappa scores attained by compared approaches at each subject from the BCICIV2a dataset. The last two columns present the average kappa and the \(t\)-test \(p\)-value between Multi-Kernel Stein Spatial Patterns (MKSSP) and the corresponding approach. In bold highest kappa values, in italic \(p\)-values \(<\) 5%. Figure 3: Cross-validated classification performance along the number of components. To evaluate the proposal sensitivity to noise, we performed a nested cross-validation test by adding several noise levels to the EEG signals. For each subject, 70% of the trials were considered to learn the model parameters at the optimal number of components using a five fold inner cross-validation. The remaining 30% was firstly contaminated with additive Gaussian noise from 0 dB to 40 dB Signal-to-Noise Ratios (SNR). Then, the class-wise performance was computed from the contaminated trials while varying the SNR. Figure 4 illustrates the resulting class-wise true positive ratio (TPR) with the subjects ordered from best to worst performance, as in Figure 3.  
Overall, the proposed MKSSP reaches a stable performance from 30 dB. Within 20 to 30 dB, most of the subjects and classes increase their TPR to reach the optimal behavior. However, the overall performance drops for SNR worse than 20 dB. At the subject level, the best performing ones yield the same behavior for all classes, that is, a low TPR for SNR \(<\) 20 dB and the optimal TPR for SNR \(>\) 30 dB. On the contrary, the worse performing subjects exhibit a TPR biased towards Foot and Tongue when the SNR \(<\) 20 dB. For SNR \(>\) 30 dB, the hand-related classes evidenced higher TPR values for the best performing subjects than for the worse ones. Such findings suggest that the additive noise mostly hinders the discriminative patterns related to Left and Right.