## 2 Introduction
Subsequently, a highest prediction rate of 91.34% was achieved for multi-class within-subject classification. [PERSON] et al. [14] further illustrated the impact of TL on the prediction rate for a two-class cross-subject classification problem by evaluating the performance of five pre-trained CNN architectures (VGG16, Xception, DenseNet121, MobileNetV2, and InceptionResNetV2). The CNN models were employed to predict two classes for responder and non-responder, to Selective Serotonin Reuptake Inhibitors (SSRI) antidepressants in patients with Major Depressive Disorder (MDD). A highest CA of 95.74% was achieved when DenseNet121 was employed for a two-class cross-subject classification problem. [PERSON] et al. [15] proposed a deep CNN model based on a two-class problem, mainly to address the challenge of sessional and inter-subject variations. The network was first trained and evaluated on the same subject's data, then after the model was trained on a set of subjects and evaluated on a new target subject [13, 16]. Subsequently, samples from the same session were used for training and validation for subject-specific classification, while for subject-independent classification, data from all subjects except the target subject were used to train, and the target subject was used to test the classifier. Subsequently, deep CNN obtained a highest classification accuracy of 84.19% for a two-class cross-subject classification or subject-independent. Transfer learning is by far the best solution for cross-subject classification problems emerging as a result of significant variations in EEG dynamics. However, current existing studies have demonstrated that TL has been limited to or implemented based on a two-class problem. Furthermore, multi-class problems are only implemented with a focus on within-subject classification due to the complexity of multi-class cross-subject classification problems. Moreover, transfer learning suffers from the effect of NT. Therefore, domain selection has been introduced to address the challenge of NT originating from non-related domains. However, for more complex multi-class classification problems, removing a single non-related domain at a time when domain selection is employed by iterating through source domains to identify the most beneficial source domains can create a severe implication on classification performance, mainly because a single source domain can respond differently to different combinations of sources. In this study, we first propose a multi-class MMFT framework to investigate the impact of three-class and four-class cross-subject classification problems on transfer learning performance. Secondly, we propose an enhanced multi-class MMFT framework to address the challenge of negative transfer originating from non-related sources, whereby enhanced multi-class MMFT firstly searches and selects only the optimal combination of source domains, then utilizes the best selected closely related sources to perform transfer learning. The main contributions of this study are as follows:  
1. A multi-class MMFT approach is developed to investigate the impact of multi-class cross-session and cross-subject classification problems on transfer learning performance. The proposed multi-class MMFT enhanced performance of individual target domains for both three-class and four-class cross-session and cross-subject classification problems. 2. A comparative performance analysis between multi-class MMFT, manifold embedded knowledge transfer (MEKT), and a traditional BCI pipeline based on two classical machine learning algorithms (Linear discrimination analysis (LDA) and Regression tree (RegTree)) is carried out. The proposed approach outperforms all classification algorithms for three-class and four-class cross-session and cross-subject classification problems. 3. An enhanced multi-class MMFT framework is proposed for domain selection, mainly to minimize the impact of negative transfer in multi-source transfer mapping.