## 3 Materials and Methods
### Experimental Methods  
In this section, the impact of NT on the prediction rate of TL across individual TDs is investigated. In this case, the EMC-MMFT algorithm was introduced and compared with three domain selection algorithms (ROD, DTE, and LSA-MMFT) mainly to determine the effect of NT on performance. The four algorithms were evaluated based on performance after the selection of highly beneficial domains and the rejection of less-beneficial domains. Moreover, the impact of multi-class inter-session and inter-subject classification on transfer mapping performance was further investigated. Therefore, all four domain selection algorithms were first implemented based on a two-class inter-session and inter-subject classification scenario and then further extended to adapt the idea of two-class inter-session and inter-subject classification for MMFT to multi-class classification problems. Consequently, each domain selection algorithm was first extended to a three-class inter-session and inter-subject classification scenario and further extended to a four-class inter-session and inter-subject classification scenario. Notably, the domain selection algorithms were extended to multi-class classification scenarios mainly to evaluate the impact of a three-class problem on TL performance and also determine whether the complexity of a four-class problem contributed to the effect of NT. Therefore, the performance of all the domain selection algorithms was evaluated and compared under two-class, three-class,  
Figure 4: Our own MI dataset experimental paradigm timing scheme. and four-class inter-session and inter-subject classification problems. In this case, when all four domain selection algorithms were employed, the class labels (y) for each domain and the multi-class (z) samples from the various sources or domains (sessions or subjects) were received as the input parameters. Each algorithm iterated (N) through the domains, while samples from each domain took turn as the TD (\(X_{t}\)), and the remaining samples were selected to be SDs (\(X_{s}\)) in each iteration. As such, the classifier made use of the source domains labels (\(Y_{s}\)) to predict the corresponding target domain labels (\(Y_{t}\)). However, each domain selection algorithm first performed source selection using different techniques to identify closely related highly beneficial domains, followed by transfer mapping using the identified highly beneficial domains as the SDs. All four domain selection algorithms analysed in this study first perform source selection followed by transfer mapping to combat the effect of NT, which leads to poor classification performances across individual TDs. As such, when EMC-MMFT is applied, the overall number of available domains is first checked and then each domain takes turn as the TD. Each time a TD is assigned, EMC-MMFT iterates through the remaining domains mainly to discard all the less-beneficial domains at once and selects only the best combination of highly beneficial domains, which are then assigned to the roles of SDs when transfer mapping is employed [12]. However, to select the best combination of highly beneficial domains, EMC-MMFT takes advantage of a MATLAB function depicting binomial coefficients, denoted by \(B=nchoosek\left(v,k\right)\), which is utilized to generate a possible combination of closely related highly beneficial domains in each iteration. Once the highly beneficial SDs have been selected and the TD has been assigned, the distribution means are aligned and the tangent space features extracted from the SDs and the TD, respectively. After feature extraction, Grassmann manifold feature learning is applied, followed by the MMFT classifier, utilized to predict the TD. Moreover, when LSA-MMFT is applied, the number of available domains is first determined, while each domain takes turn being the TD. Whenever a domain is selected to be the TD, LSA-MMFT iterates through the remaining domains, discarding a single less-beneficial domain in each iteration until two domains remain.