## 2 Materials and Methods
### Clustering of Common GradCam Maps across Subjects Using Centered Kernel Alignment  
We used group-level analysis to address MI skills enhancement by clustering the neural responses derived from the relevant spatial activations that could be considered characteristic and distinctive of a particular subject subset. As a result, to find common discriminatorybrain activations between subjects, we use the centered kernel alignment (CKA) approach (see [50]) that quantifies the similarity between kernelized spaces based on the projection of the GradCam++ set onto a reproducing kernel Hilbert space. Optimization of spatial map relevance implies adjusting the GradCam++ inputs, \(\xi_{m}\)=\([\) vec(\(\mathbb{E}\{\xi_{m,n}^{\lambda}\):\(\forall n\in N\}\)):\(\forall\lambda\in\)\(\Delta\)\(]\), and output accuracy values \(y_{m}\)\(\in\)\(\mathbb{R}[0,1]\) for each \(m\)-th subject with (\(m\in M\)). Notation \(\mathbb{E}\{\cdot\}\) stands for the expectation operator. Therefore, for the subject set, we determine the matrix \(\Xi\)\(\in\)\(\mathbb{R}^{M\times I}\), holding each row vector \(\xi_{m}\)\(\in\)\(\mathbb{R}^{J}\) with \(J\)=\(WHZ\), and the score vector \(y\)\(\in\)\(\mathbb{R}^{M}\). As part of the CKA-based approach, we choose two kernels (\(\kappa_{\Xi}\):\(\mathbb{R}^{J}\)\(\times\)\(\mathbb{R}^{J}\)\(\rightarrow\)\(\mathbb{R}\) and \(\kappa_{y}\):\(\mathbb{N}\)\(\times\)\(\mathbb{N}\)\(\rightarrow\)\([0,1]\)) to assess both similarity matrices: one between GradCAM++ inputs, \(\mathbf{V}_{\Xi}\)\(\in\)\(\mathbb{R}^{M\times M}\), and another between the accuracy outputs \(\mathbf{V}_{y}\)\(\in\)\([0,1]^{M\times M}\), which are, respectively, described as:  
\[\kappa_{\Xi}(\xi_{m},\xi_{m^{\prime}}|\mathbf{\Sigma}) =\exp\Bigl{(}-\|\xi_{m}\mathbf{\Sigma}-\xi_{m^{\prime}}\mathbf{\Sigma}\| _{2}^{2}/2\Bigr{)}, \tag{8}\] \[\kappa_{y}(y_{m},y_{m^{\prime}}) =\delta(y_{m}-y_{m^{\prime}}), \tag{9}\]  
where \(\delta(\cdot)\) is the delta function, and \(\mathbf{\Sigma}\)\(\in\)\(\mathbb{R}^{J\times I^{\prime}}\) (\(J^{\prime}\leq J\)) is a projection matrix. As a next step, we calculate \(\mathbf{\Sigma}\), intending to highlight relevant spatial feature combinations from \(\Xi\) through the cost function within the optimizing CKA framework, as follows [51]:  
\[\mathbf{\hat{\Sigma}}=\arg\max_{\mathbf{\Sigma}}\log\frac{\langle\bar{\mathbf{V}}_{\Xi}( \mathbf{\Sigma}),\bar{\mathbf{V}}_{y}\rangle_{\mathbb{F}}}{\|\bar{\mathbf{V}}_{\Xi}\|_{ \mathbb{F}}\|\bar{\mathbf{V}}_{y}\|_{\mathbb{F}}}, \tag{10}\]  
where \(\mathbf{V}_{\Xi}(\mathbf{\Sigma})\) highlights the dependency of \(\kappa_{\Xi}\) with respect to the projection matrix in Equation (8), \(\mathbf{\hat{\Sigma}}\) is the centered kernel matrix computed as \(\mathbf{\hat{\Sigma}}=\mathbf{I}\mathbf{\Sigma}\mathbf{I}\), being \(\mathbf{I}=\mathbf{I}-\mathbf{1}_{M}^{\top}\mathbf{1}_{M}/M\) the centering matrix, \(\mathbf{I}\)\(\in\)\(\mathbb{R}^{M\times M}\) is the identity matrix, \(\mathbf{1}_{M}\)\(\in\)\(\mathbb{R}^{M}\) is the all-ones vector, and \(\langle\cdot,\cdot\rangle_{\mathbb{F}}\) and \(\|\cdot\|_{\mathbb{F}}\) stand for the Frobenius inner product and norm, respectively. The mapping matrix \(\mathbf{\Sigma}\) is computed by the gradient-based approach estimated for Equation (10), yielding:  
\[\
abla_{\mathbf{\Sigma}}\rho\bigl{(}\mathbf{V}_{\Xi}(\mathbf{\Sigma}),\mathbf{V }_{y}\bigr{)} =-4\Xi^{\top}\bigl{(}\
abla_{\mathbf{V}_{\Xi}}\rho\bigl{(}\mathbf{V}_{\Xi}( \mathbf{\Sigma}),\mathbf{V}_{y}\bigr{)}\odot\mathbf{V}_{\Xi}(\mathbf{\Sigma})\bigr{)}-\ldots \tag{11}\] \[\cdots-\text{diag}\bigl{(}\mathbf{1}^{\top}\bigl{(}\
abla_{\mathbf{V}_{ \Xi}}\rho\bigl{(}\mathbf{V}_{\Xi}(\mathbf{\Sigma}),\mathbf{V}_{y}\bigr{)}\odot\mathbf{V}_{\Xi} (\mathbf{\Sigma})\bigr{)}\bigr{)}\mathbf{\Xi}\mathbf{\Sigma}\]  
where \(\text{diag}(\cdot)\) is the diagonal operator and \(\odot\) is the Hadamard product.