# Multiple Kernel Stein Spatial Patterns for the Multiclass Discrimination of Motor Imagery Tasks
## 4 Results
### Model Interpretability  
We evaluate the model interpretability from three points of view: the data, spectral, and spatial representations. For analyzing the data representation, Figures 5 and 6 illustrate the three-dimensional mapping of \(K_{\mu}\) using Kernel Principal Component Analysis (KPCA) for the best-(S07) and worst-performing (S02) subjects, respectively. At the first two KPCA components of S07, MKSSP discriminated Left and Right from Foot and Tongue classes. Those two components also allow classifying between Left and Right, whereas the third one separated Foot and Tongue. Despite being less evident, MKSSP identified three trial groups from Subject S02, namely Foot, Tongue, and hands. The first two KPCA components better separated Foot from the remaining classes, while the first and third ones enhanced Tongue discrimination. As Table 1 presented, subject S05 benefited the most from the proposed MKSSP, in comparison with the challenge winner. For such a subject, Figure 7 compares the trial data distribution resulting from four approaches: CSP, with a single 8-to-30 Hz band-pass filter, and Filter-Banked CSP (FBCSP), with filters as in Section 3.2, representing the baseline spatial-filtering and spectro-spatial-filtering techniques. MKSSP without spatial filtering (i.e., \(\mathbf{W}\) is the \(C\times C\) identity matrix \(\mathbf{I}_{C}\)) and with the optimal number of components \(Q^{*}=4\) contrast the former approaches as spectral and spectro-spatial representations. For the sake of visualization, PCA and KPCA map trial features to two dimensions for CSP-bases and MKSSP-based representations, respectively. It is worth noting that CSP features without spectral filtering (top-left) and MKSSP without spatial filtering (bottom left) lacked any class separability. In turn, FBCSP separated Left and Right but mixed Foot and Tongue within the four classes. Lastly, optimal MKSSP not only increased Left and Right distance but also unraveled Foot and Tongue. Regarding the spectral representation, Figure 8 illustrates the MKL weights of each band per subject, descending-ordered on the Y-axis (from best to worst based on the kappa score). A visual inspection of spectral weights segment subjects into two groups: Subjects S07, S01, S03, S08, and S09; and subjects S05, S04, S06, and S02. The first group, holding the best performing subjects, concentrates weights at frequencies lower than 26 Hz. Besides, the reduced number of highlighted spectral bands translates into a computational burden reduction. The second group, with kappa lower than 0.83, widely spreads all over the signal bandwidth, without accentuating any spectral filter. Accordingly, the weight distribution marks the MKSSP performance on the subject. Figure 4: Noise sensitivity test per class for additive Gaussian noise using the optimal parameter set. (**a**) Left class. (**b**) Right class. (**c**) Foot class. (**d**) Tongue class. Figure 5: Resulting MKSSP kernel projected into three Kernel Principal Component Analysis (KPCA) components for the best performing subject (S07). Figure 6: Resulting MKSSP kernel projected into three KPCA components for the worst-performing subject (S02). Figure 7: Cont. For the spatial representation, Figure 9 depicts the spatial patterns of the best and worst performing subjects for MKSSP (S07 and S02, respectively) and the most favored one (S05), since such topographic maps represent the projection of estimated brain activity sources to electrodes [7]. For each subject, the top and bottom row hold the least and most weighted frequency band, respectively, while columns sort the first four components. For subject S07, the first two columns highlight a contralateral activity localized over the motor cortex region at the most relevant frequency band, which may be associated with the Right and Left classes [37]. On the contrary, the subject S02 lacks any activity over such cortex, yielding patterns without MI interpretation.