## 2 Related Work
### Enhanced Multi-Class MMFT (EMC-MMFT)  
A novel enhanced multi-class MMFT [12] is presented in this section to evaluate the effect of less-beneficial and highly beneficial multi-class sources on transfer learning performance and, at the same time, address the challenge of NT, which has a severe implications for the prediction rate across individual target domains [12]. The EMC-MMFT framework adapts the idea of the two-class inter-subject classification for MMFT in multi-class classification problems, using three-class and four-class classifications as examples. The novel EMC-MMFT framework, in this instance, first performs source selection to minimize individual differences across the domains and then utilizes the selected sources to perform transfer mapping. Hence, the EMC-MMFT approach iterates through the domains to select only beneficial sources with a high transferability from a pool of domains and then utilizes the selected combination of beneficial sources to enhance learning performance in the target domain [12].  
The EMC-MMFT is, at first, implemented based on a two-class inter-subject scenario and then is further extended to adapt the idea of two-class inter-subject classification for MMFT to a multi-class classification problem [12]. In this case, the EMC-MMFT framework is extended to three-class and four-class inter-subject scenarios, mainly to investigate the effect of less-beneficial and highly beneficial source domains on transfer mapping performance. To facilitate our investigation, EMC-MMFT is compared with three domain selection algorithms (ROD, DTE, and LSA-MMFT) based on two-class, three-class, and four-class problems mainly to identify highly beneficial SDs for transfer learning and, at the same time, discard the less-beneficial SDs constituting the NT phenomenon that significantly deteriorate the classification performance. As such, EMC-MMFT consists of two components, namely, source selection to search, identify, and then discard low-beneficial sources and the optimal selection of high beneficial sources for TL [12]. As such,EMC-MMFT utilizes binomial coefficients to evaluate the relationship between domains using the MATLAB function depicted as nchoosek [16].  
\[C(n,k)=\frac{n(n-1)...(n-k+1)}{k!}=\frac{n}{k}\frac{n-1}{k-1}\frac{n-2}{k-2}... \frac{n-k+1}{1} \tag{13}\]  
Moreover, the MATLAB function utilized to compute the binomial coefficients is depicted as \(B=nchoosek(v,k)\), whereby the number of all possible combinations of closely related sources is acquired using Equation (13) [16]. Therefore, \(C(n,k)\) represents the binomial coefficients to be computed, with the number of possible combination being denoted by \(k\), with \(n\) representing all the sources from which high beneficial domains are being selected [16; 17]. Once source selection has been completed, the second component of EMC-MMFT utilizes the selected sources to execute transfer mapping as depicted in Figure 1. To achieve this goal, the second component utilizes four phases to perform transfer mapping. The second component first performs domain distribution mean alignment (DMA), whereby the distribution means of each domain on a symmetric positive-defined (SPD) manifold are aligned utilizing _KL_ divergence to evaluate similarities between the domains [12; 18]. Then, tangent space features are generated from both the source and target domains, respectively, once the distribution means have been aligned [19]. After tangent space feature extraction, Grassmann manifold feature learning is implemented to learn feature mapping using a geodesic flow kernel [20; 21]. Finally, the MMFT classifier is utilized to predict the target domain labels utilizing knowledge from the source domains.